tag:blogger.com,1999:blog-53438331982427442952017-01-01T07:03:39.808-07:00Meaningful MathematicsHave you ever found yourself wondering how you can help your child / children with their maths work? Whether it is to boost their skills, to increase their confidence or to challenge them further?
As a Primary / Elementary School Maths Specialist my aim with this blog is to give parents guidance and ideas on how to do this. Alongside the ideas you will find explanations and examples of my experiences within the classroom to support my thinking and ideas and help develop your understanding.
Charlotte Haywardnoreply@blogger.comBlogger26125tag:blogger.com,1999:blog-5343833198242744295.post-23269665789663792812015-09-07T22:17:00.000-06:002015-11-09T20:05:05.576-07:00Review and Assess!!Dear Lovely Readers,<br /><br />I've been writing this blog for 6 months now and am so excited at how useful it has been for so many of you. Thank you all for the feedback you have been giving me, it is truly appreciated.<br /><br />As I have written the Blog, so my ideas have changed and developed and it is time for me to spend some time planning, and reviewing what I am doing and stop publishing articles for a while. Hopefully, when I relaunch it will be with a fully loaded website with ideas, resources and my weekly activities.<br /><br />In order to do this, and still manage life with two small children, I am going to take a break from publishing anything on the blog until the end of the year.<br /><br />In the meantime, your children have chance to get back into the routines of school and get their brains back into the habits of work everyday. If you have any thought / ideas / feedback for me, that I can then hopefully incorporate into my changes, I would love to hear from you. I am particularly interested to hear if there are any maths phrases and expressions that your children are coming home with that you need help interpreting :)<br /><br />For those that would still like to be doing something at home with their children then keep counting, keep looking at mathematical things around you and talking about them. Most importantly, whatever you do, make it fun :)<br /><br />Please email me your thoughts at cal@lotty.orgCharlotte Haywardhttps://plus.google.com/101613062113924736341noreply@blogger.com0tag:blogger.com,1999:blog-5343833198242744295.post-16006847595557567082015-08-28T13:30:00.000-06:002015-08-28T13:30:23.986-06:00Times TablesFor many here in the US, this week has been the first back at school and I know next week will be the start back for most of the UK. Therefore, I am expecting that most of you are going to have some pretty tired children as they readjust their body clocks back to school hours. What you will also find is that your children will all be searching hard through their brains to recall even the simplest of maths facts as a lots of these have been 'forgotten' over the long break.<br /><div><br /></div><div><a href="https://www.blogger.com/blogger.g?blogID=5343833198242744295&pli=1" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"></a>Consequently, I thought we would start the academic year with some revision of basic maths facts: those facts that we all want to know but dread the learning process of, as most of us assume learning maths facts is one of the most boring things we can do!</div><div><br /></div><div>So, time to dig through those memories and see how many times tables you can remember. Then you and your child can work together to revise what they 'should' know and then add a few more to the memory.</div><div><br /></div><div>If you have been following my blog you will have already read an article I wrote, back in June, on learning times tables and this week I am just going to link you straight back to this article. For those that read and did some of the activities it is the perfect time to revisit this and revise what you did so please don't worry about repeating old stuff. Maths is often all about repeating, revising and improving knowledge each time.</div><div><br /></div><div>'<a href="http://meaningfulmathematics.blogspot.com/2015/06/number-sequences.html" target="_blank">Number Sequences</a>'. This details exactly how I teach times tables or number sequences, as some people call them. It is as fun as I can make it. I feel the worst thing about learning times tables is the way they are often taught - it's boring and uninspiring. What we actually need to do is inspire these children with this basic knowledge and make them want to learn more.</div><div><br /></div><div>For those that want a little more fun, I read a blog post this week, written by a Mum that also finds learning times tables boring and has discovered a great way to learn them and have fun with them. Time to tune up those voices :)</div><div><br /></div><div>https://www.scarymommy.com/the-math-trick-every-kid-should-know/</div><div><br /></div><div style="text-align: center;"><b>Have fun!</b></div>Charlotte Haywardhttps://plus.google.com/101613062113924736341noreply@blogger.com0tag:blogger.com,1999:blog-5343833198242744295.post-61409872994076018302015-08-20T22:09:00.002-06:002015-08-20T22:09:59.011-06:00SymmetryAs we're getting to the end of the holidays for some and the beginning of the term for others I thought we would do another fun activity this week, without the pressure of trying to deal with numbers. I would imagine that those that are back at school are feeling a little fuzzy headed by the time they come home this week and therefore in need of something that can be fun as well as educational.<br /><br /><div style="text-align: center;"><img alt="Image result for symmetry" 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" /></div><br />So, symmetry! This is a topic that I love to teach as you can get very creative with it and have huge amounts of fun. However, there is not always time to do the fun stuff. Unfortunately the fun bit is generally the consolidation bit so this topic does not always get fully understood at school. Often the children don't realise this as they can do the obvious symmetrical activities but it's the tricky bits that always catch them out.<br /><br />Below I have described some activities that you can do with your children to really consolidate their knowledge of symmetry and to have some fun. These can all be adapted to suit the level your child is working at.<br /><br /><b>Symmetry Walk</b><br />Go for a walk around your neighbourhood or local shopping centre and find as many symmetrical things as you can. Each time one of you finds something, stop and discuss whether it is symmetrical or not. As parent you could find a couple of things that initially look symmetrical but upon discussion and closer inspection are not.<br /><br /><b>Photo Collage</b><br />Go for a walk or send your child to wonder the house and garden with a camera and ask him / her to take photographs of anything they find that is symmetrical. Once they have a specified number of photos (you will need to limit this or you will be discussing 50+ photos!) print them out (on paper, nothing special) and discuss why the item in the photo is symmetrical or not. By printing these out you are also then able to use a mirror to help work out if something is symmetrical or not.<br /><br /><b>Painting</b><br />We must have all done a symmetrical butterfly painting at some point in our lives. Here's the chance to do it again. There is the basic level butterfly of splosh some paint on half a piece of paper, fold the paper in half and press down. Unfold and 'hey presto' a butterfly has appeared. This can be extended by your child painting a specific pattern on one side and then letting it 'copy' onto the other. Another way of extending this is to get your child to paint a detailed symmetric butterfly by painting both sides and then folding it in half to check how symmetrical it really is.<br /><br /><div style="text-align: center;"><img alt="Image result for symmetry" src="https://encrypted-tbn3.gstatic.com/images?q=tbn:ANd9GcSW5WE2FPAuEH5vJ4-hZ3jZVJslA3D8ureV7r_lU3b3C94F04uB" /></div><br /><b>Cutting and Pasting</b><br />Instead of paint you and your child could create a symmetrical picture. Fold a piece of paper in half (or quarters) and then stick onto the paper coloured bits of paper, sequins, pompoms etc. Make sure both sides (or all four sides) are symmetrical. You can make this a little more interesting by creating something specific eg a butterfly by folding the paper in half and cutting a butterfly shape out of it. Or a mask, a body, a specific shape like a square or a hexagon.<br /><b><br /></b><b>Mosaics</b><br />Depending on how messy you want to be you could do a mosaic with your child. This could be done with coloured pens on squared paper or by sticking on coloured squares. This activity is great for extending the older children as you can do diagonal lines of symmetry or 4 way symmetry.<br /><br /><b>Symmetry Table</b><br />Create a table on a large sheet of paper with two columns (possibly more depending on level). One column marked symmetrical and the other marked non-symmetrical. Or this could be marked with 1 line of symmetry, 2 lines of symmetry etc. Over a period of a few days get your child to complete the table by drawing a picture of anything she finds that would fit onto either column so eventually she / he should have up to 10 items in each column.<br /><br /><div style="text-align: center;"><img alt="Image result for symmetry" src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAXQAAACHCAMAAAAxzFJiAAABp1BMVEX////wA3///wAAAADwAHzwAHr0A4HvAHjwAIDvAHb6A4T2A4L7+/vd3d3SA29vb2/IAml/f3++A2WfAlTrA3xVAS0TAArMzMzV1dWpqan29vbvAITs7Oz/+/780uULAAbbA3RbW1vU1AD71OLv7+/xLYnj4wD+9Pm+vr7+6PTKygD4osr4+AAUFBQUFADOzs77xN7+5fJOTk6VlZWuAlxra2v6ydzzYqBDACOgoKCxsbH6utn3hrvy8gD2d7SBgQDBwQBubgCQAUylpQD4mMXzSZz5mchdXQB3dwD0WaJyATyIAUgMDAD5q9D3jL1QUAD0cGkzMwA5OTn4sUpmATb95RL80yUrABf+8ACysgD1aqsgABGZmQAmJgAoKChZWQAgICDEeUbyO3P7nVn1c1b+b2H6tjPyJm7/xi7zQWfEfaPInjMsLADyIJT3k0WFJ1WuLk33YmX4nULGRVD2gFH83CDEiJ8+QwD6ujIvAAvTtcCuJWf/rzemgBzMKFvCqrayQnbFU0qJUGnPb5v6u2D0WWt5OlrzRaaZjDnMpyPUvBOnlACjcCPkf/cXAAAc+UlEQVR4nO1d/0MaSZan6eqmWwQRcFAbCFEBETOColFBYoxMgo5mxjMmIZkkl00myc6Zu5mdb7ebu729vex9/aOvqruru6r6K0jDzN69HzLNCP36ffrVq1ev3nsVCvVDsY2+vv7/NAzK8ON+gjFSdnc8fDM3xsM3uzQevhSNS+PGBfr6znj4UjQu4cfF9/rcePhSNDbQxzTC/k+DHoqNh+0vA/RxeRGz42G7/ksAfXJ5TIzHBHpmbTx8aRqT8OPiOzkms0bTuEAfk8bN/ypAz04Gw3Y9kNt60q8C9OyNTCBsxzWB/yLMS2zT/e9TZ/OB8B2Xq7ocjA6xXNzDeR4aN8kH9JBr4woDjMRl3OVdB5SHxsWCmWfrzR/5ZiWQW3vQiBZH665TlrvGzQei5+WeBBIzUaldDuLu7jQi0GMucbXy4h9v1F1En80O/3lC9aLAcdG4yEU6o1f2UYUBlhxNRLUjJj+Z6Jw4/jIIRS8XAcdxYkLkOKE4Ul3PnXSE7dTl4UiYOqz0y10ZII0DkZ79Y8T4IBS9izDXQOeEXgAMnKhSFIBUiANBWRwFO1vUc10BCx+5mbP7xuZ6AAujJuKKQedAbfgcHKiioLedhmYNSKNAfc3OrLcipvCRls0XMnwArkuuoyo6l05qoHeHz8KeyhpjBDoHlBFMJss23nY+Qmlc3vKFyWdTATzKoqyxTT6ZUC/kegBM7OhUG2Eq6KMxa1PPLP+rp2kcp2uc9Sl2A7HouuxoAlcvIp8FwMSGKhJHgM5FRmBgsjy76V8BuqJva8IDy1wazIK5C2jQwc0guFipqr3s6HFDBV2ws6fDpo0bjNp+pluXJK9rXJX5hbOjeRWqF1nQiyPx1fFUMjGTio6O7ToTDLiJhb+mC8/al2B2lPL6KDdeNjca/62sG1MMOgdGwXaSNhaVIgt6h7Yv2WBCoFuCDnrhWBOeE0YCelNmQLeM7EAoRqGYV9w1LhNQquGWZtUMrwm6LyMBvaW/7OhMSuM7Il+Vshd5fbiJ8XNd46jxNs//lYGOfbXoOTYvnVGwDS0tE+vLLX24qYEnq/AbfEApf80xga5PYZCwvMVRsA2FeGJd6q5xWT6oWNy4NN0APT1i0HeI1U7NVfjrZ0E9gwF6QR/mf+2gz5+Z63p3jZsKLD8C8zUn8NGA3h0X6GQEywA93bCCPuvLoA/kVJqgfzJS0LGmi4WBQR/Uh56axlduGjfpZ/2/ND2QgzNu0KNH2Kz1CXp22n6veddz4T6fwfkUpvDXLMJnfCRdTO682B0kN8MK+sChp772b2+yK9J+QX/GL9tuLlznp73sghFQcQE942MczWaytpDnam1FEASlc7hlvxllDQM4bijUt7Zqta28497aLL/uPzx0RdBnMzGn/ZzMGb/hoX5rugNjBR1r3KxnpksstuwQ9K13gKBKByJc8dAupIRBN+cSe9Arp90iF4EkdapOsMfW+Sm/ywkL6MA/6PPZjFuQe34Hh3ArJ72bkFo1RvLJjPbG8pyTxl2/zty0XK5AKuMNvfkNS5gYU10xliAId+XUChcOP5hek2Kzi5FvcxFg3KfouM+xfOOGrmS5k0NI1ZrttmOIWJEaYQDfK9KNZ15DP5tdRl9pSRGASJCVHr0LuaPNpcYwLxxEKdAzzHzRPO0osixH8H2Wn/FzDiOtXCQwRyRwlo33epEBHVghzaMNc4LcNtdm1XzzShuOCWjWhEikU7MdGG0cezlouIKe26pCeSOy1G2q729ylz/zU38Yy8Q6Aqlxl03i/evWw0bjVNCXzqaJW1UOlYgA8H26UJwzfjrkRE2CK4a9yGw84+imCTqb+1JuKex9hLaLuEvL2UXiFwAU7VIs2sY34i6gVw47nC4vAJ0tiCU02P4sWPlf+VQ6SsAudAjRp86Qojpp3Nozk0f5sEiJL3RimV2XodZlFF17djqNS98eNmM+oEtD1CxGrHdxj7mvPTymxI0UrYk8n2FJ8OLI5kXmoIqR9hHUsrvTfr3zWjrFbycnSNEjPUOftLhK3aJx2lYKMWWcFMlH4KITXOPPrnwvbUCH0gknpKHFmyfxI31CozZPFjuy3U0iW258e8kn/AEnEuLKCvuDqrEYdAI9V5Wo1x2NFpK/d5WXoi6Ipo/4I5F4DDhojEG3w08SGmcOc/R3c5WZp8UXudR2I2o36ZlkDzpSZkJRe3jzRJ/AASE8VDX7WwhuOw71YjR9cO1hnBQXcG3aatVY0NlNjMUOxVpMpw4StokpzsKLYryRLJCPAVHVsywm59CMj30oPJFqG8Q45l4+lSjIxcQMfwyFd9U4J9A5IJnjvc1kAwinJnodG8uiIdR0YVuDX4gWjhtxWssU6jd65gccYbqS0bfMtQEl70Rim09NcIon1gap6gKfIJFMT5CDjmvp4xxBe9NO47Ci12jDKsKBsx2HLyfimPWIqGWdSDHJxnRZxRviOAUD3zJ3KDi9NPeXXVPvF43Gk4UoYdohT2KAlfF23TberiOniSagHl2Mz/DnBfg94OSBOoCuYtV4mCRff0Q3dWjnztA4fXGEchLmtLTpSk9mhlpjJqm+PnfQa46YI7dPn8trONlIB13Wx1+96/zKbNxKG7ZiOpGiHQipaoBW1r01Y3FErMnqjAcAdWw7qc4RwH/KAF4IwF+f8zNx6jE0Zc8QKRjXjBSM+RuqO1ijfBYRypJMp/Ux6WpeQh1HVUW+gGYgKxh0fYTJ2lTTtPiJBLnnYxneLxdtIAeC1DLDfyhf0ikYxJqMZi2K0WSioL874Btz0l+OJrf5gzTxGII6zpem8L6ZAbpcg0sv5C62yFEOjRs5N3ikS9ScbLKGgKqvWOWwy6ggLci1bZ0WTB7pEua7jhaOoJaRJhWb7lyXyXvByQ8VaiUmRhOJRhpbh372UcuExolRaBpI1AGA0/YSv2HVuBgPbX2esuYTUIhj0/f0zMZquaIO0EoJZ/1weg4lkmvRxbRAEg7duZ6YXOFEtn2UpvwYfZ2gp/NFt7UwABalRq2ixcI5nzR/7W5N2aegxks6nYynCdMOeuXQLj+ra5yePctJoal1+EvSZxORJ5YkbhXxzGvuuKIHuBNzMkkY6W15N9OCVrUe0xkVfhDThUSSI8QVOqohqeI5LEmm1Z2STovIHfNPCHn7ywLLMZoD3fxGIWo8B6o6ebbZwcmMusZN7mZzlKaK4hE0TcSM4CPVNddz1XVObiGNkBAlJBT+EU6gorqZFgiaZ+FETaZ+IaaTiYQJO+CQiWnqTHACKcpbrXQpedP8tRQ5I8hujqqN7PT6Hb7Dc/64YOAHpNos/wft9obGzS5VSNMCPf1koUC6YEDxUTZSbrujHmk3OQW8/Pjq1Z8+vgESJ+VPXSH3g7lhO8yHT/DnpgMBwGkuVKdBh1NYaItCKc2ubPpOp65bxnnq4bVG2nyM5sa/qAyQxqkcqrNbhGmJFgrJOEetNkDRmsJuCwBwRRFcRr6/eBQOl+6GH7x9JSltV9PCRbq+CoRatK5DK/KQdCAi7VxIC6tKGPRcqEms/6CPhhZXFOb910PVGV1Hazb+wDQxoPpHAMc49+bNP6OxzkV/JJ4hyqWeNKjpCOm5P8wtAQSaJO77sEorn6N/H7yWJMfvQsElvxmHpyzq0H3kTcWNFOEELikKkOW4okgSuMwdmr+Ipo9nklFa3oifEWahHrPAEycK8aQ55oRu8tsPD6DG3QtffPdOOvgzoeaNJ1BNaCFcdhIslKuyb9zE/M3bsA76p9p/vwOOqAPQ9c/0hA3bRNMNNFjxvYo9+eN3F48e3Xl88f4j4Nrm8lnkGg8/SdGQQ3gGK8E7YUWHo8ew05L07X+VVOF59O9/8nj3TF1RHVHG3Bqg9aLKKbCFXZIfhBnQw187oA4ssXh3ylvFRZEB3WZAeS9Uds/vwH8uPppxIrEwYyNvy38AgBG9ZzGv0At82IADSeK+C4f3S8Ywv//8e32cQ+N2nGCGGhM88kP1lg3sErgIG6B/jq8+KJYvOgTFPejQ4nqKYmJbjbVLkZ91bnfv0K9aLKTO4xMiw9t95e1Oiz3WHRPTx/x2IgrQKL97Hwv/mC+F36O/RtPQj2Uhlw4Hee31nsRiIH1nYB5eeG5cvraqeqTouB3tQpWWxGrZROoh30hLL38I06CHL95ImrwJjmOsedFjMeZJtS6r7WjVdfQ14lvi9zXQV/mn8ON7hUseJdOscZPagxaK5Hu0tkvvHoUJ1I2rHzgadSBIpwPW3OW7bKgSORAzccOqGaCHL4AoNhoJVl5oWa5eGJNrKuyMGm38z77K99aXe6pt3bu9hz7+7pw/Zx9B6Pl1WmwxOAXEUFM+EJgToNOqDmTlKnXk+U6EdSDiR/+9Z/C6j0EP/5yY4Ru0LYeWpT2khLMm48NJbx6F91cg2z2k4dCwq69g7ym0OxPMI/SuYtwQlU8NECRAYk6CfkG+Zec8F5+0xQ5u5XW4tI9h38N8S7fgCGAgl3rDy/HLNannUJBpXd2/vRK+8xMSvlRSP3+5/y01zAXlSlqOqdzUM5Ckj06gP3ijMxaAQwZFfwRtKmHX1Ol7deGxNrpXS9jOfPqNQM+foDsMeU3K5buc8RySZlrv8/f2Fvag8OhpFlb2VsNvTdDhUw8FcpXyh4osAOU3JOar+8SHjxKSWVZOh8WSzFaSvlB57PP3F0zQF/ZLqypbQ16hNVzIVaqfKpqVkd7poq58yT99HF64s1paWSlRGgciim1S3MCU22oVpb8hQV/5ivjwhYRWL81BfWM7QvkjGux4Kind5W+XVNBLurV5j51V6CTaZKMNhXLNm0oU0veGsI/v34Gm7RavTy6rHyX096h082SY8mtUaf4bBfqnxIcvpGEPbcSwpmUOKcbiYP+r+xD0vVu8btreaqALXOdkABXbmJ6eDU1OhtamIU1lJ+HlLrrcWEKXO+hyZx5ehf5yBOmb8OpqeO/eLUiP955+zvOf3r516x5UgvAXSfT3o63J0GRoTr3BPLrBBrqcm0SXU+hyGfKazKqXJlvnzC9E9ZMOo+k06Miingxd2erVjhxRCEallVv3+K8eYxOnqM7SgEZtempzOQZpd3NqampzDV3uoMvpWXQ5Da+mNtBVbAoh9R8lSAu3ET3eu8/fffr8Frzch//zT6nzvyAk0Vc36BtsajdQGeygq4x6abJ1aZlRaXYk1qZToKszOIDOw9bQR1il+u8k29JXn9/CU2n4EQR9eDOXM5Xz7UtC40pPef7pPf7pqqFxXPE0P1zJ623NukrfUqDz5vWDl4b3Mmx1z9UPSdBLKz/dWfjq1p6h6VL3NOhKkHoLum/EYny/9PRTni895n/aN0CHJq57VVeZoGYXp6DSfnrpqXlN+unyMKfw/GFHFkzzsreygFak+3/HPzU0HQjyZTW4njPlk44qv/Rae4Q7X0LbtrDA370bhnMLeoxH7yR9MufaQxl1lZMisRxWviZRXzAvX1ErUkFqDwWEir5A0CfS1Tv3EEs1yghVDSm7PpFC97jrUDhyRVps4XCAJKsyf4mMysJe6XaJhw9Tgo56+EIwpIfLlOZVn6NcpVNQpY+rtqA/YIO7gtK6MuyVU8NlVEf2yk+aet9WZ9HSHRRiNVxGlBg9/Gk8T4b80Ku/zd8tofGGhN9X5V9dWHivkIlJoFO9inFnEo9V1D/Ygv7KGmUUwNVgR7E2Y3EE55LSbf6ePn/iaXRhpfSOFFe2zWsfnGrQrpKyf7u6cls14lC7kfD7mgY+SD2k8qNQTHtQ2MuHbJwNMRYubEC3jafDmWXwaF+tQ0df3u7deY7ZGWGAcPibowM6jV86Hdp0UutQ4ovRdOIbjeu9e5rwqyvqx/fpI34mQSUACMpAoy7XLNpuT6NQm057ONr3NuKwXycMFFMP5Zhotiimf7dgRhkJ0N+hNH4qmD6shanlERKpZOGlKvsKv6Jr3AJS9QtOEhPb/BElORA6/Wv7luPWtPQG7yZgl9Fpt45TR1r/XRtrdGhXnEgkk2nCrJmgfydZsvDU+MeVHeZFZnsa5cmdT2jhl9X7d8M48HS7pAVeRLHB7mMAudOf6HXLdhWJOvdeU3ZtcfTgla1tMTHo9jfgt7o05NE4iplL0lsDdCO0+7MkqX8/KLB7k1eLgdTpVHfUwwkOKGQ/pI8Pwnf4kqFxz3+6kPU9UpQfxVE7dkDPTPNHTcdUAO1ml+/eP1hVQX/0w/dvlBZbksd83We2jUoVW3k5MgkhfE+PAXytySumUVKyyIg7eFvUXFVh87xSRgaO9PLtV6oLpW0Qr5jZAOhZkwd0WQPwv0166Jp/y0U6NUmR3r3+zd9+8vqNIklCM+9Q8oJZA9+b4qfMpqw4wfMpTX3UjXiVnmtzyXsz3wZqWZJyIND+0YAzar1D5d+IYjRB5slJhX/4GQ/z1Q/vjq4RiS5ieoanCtY4v123PXMZezmU3SpJSpKfUJe/bdR32PU3rgVHJm1ZUgnjjbghhCS9/Fm1a3ehpj/6+s0lOcCiSehAULALUt/5D4iaEcaYx5Nk3hgo/haq2ev3b7+59v4dp0hp/u+phN3GQz5F5Rv5y/DqueOH0kkO9farDSNVumxXC0mQ5Ge0H9KJAGK60CgQngnotMDLVx9+ePT8nz68eilxCp14mNyGWkY9KRggJeCQrRW7RhX9CZ3f/1ZECqdqHJpB/zC3RT52tHDANyh3yihgcaETJrmNJjU1HmfnG0XD8Ge5U/eaAB+Zq3QyY1Q83qby5CIdyBeJq8ykFCSvXK6QZWUi1+C3aQfCtWLYlj6jRvmEqrfkM3TLa1rCNi5TB53ZpTo5B4hRNQuPzGt3L2iElPfIM0djBdehYNBl1Wy5Vr9458/m6JxniOCTBomgfIoTSHGZOqrQoHJX4eoFOhCU037qwZWhJvneRW6GP6IstNDKrcd6tPBSaDlU7tH56SKEnUg4Y/tlWsjVTADN+8OtQEW6tNC9GEPyMG0tupwC2QpyZS0dGr2FOU7LAFArKavMEqaQLFClQn3Z9QplngvJFOWLoHqIuRuxDqNx5aVZOM45xiwdXyPSdyPudi7POROQ9d/WdX3ANUeC3lU613IxMR5KRxUFiIXGEZUnB9RJsUbnp2s1wzXa3xG5xCfHnJnX3lclhjmdiRNcg/G6BTgjzvM7OZzLh0GvhTIZyzjXs/DwR3cDw6bmk0yNmk5cYIbL1M32znm7rgC6+K5VtISOQaOYTERpebXxqZe/GKBr/5euxUAOxBM+ZRiZSB9m3WhkI4rJ7QaTqSe3c2o79QouIcbD/LPQDuo8XWacPrRUPsI5SO6q7ljRCEDLMEyf4dof3tJYudzmHO/gxvfQ6LzHNVJMnpyRf3vIgK6nfucYrwdl4W0bkQHJfyQG3x/Vlh/ReeZAQbmws/yyMSRxmTrUuMkX6uZylV6twDfXwJEBcOnG12lFHyGTftkydaoLRlNxUHZX0LGhnIBr/mM6R00wztxo40YQupIZ1ZlsdXg0fpTCE1kfVl3zDzTLQD+DrPUHmN0gysWJMvVlrcHOIlOjDyeEZFJUzaSr8PagqxU/JhkNGez7pzsVz7iw3dLjF4VzfqZAyUsca2P0T8dl6kSTvDYdn1Ir3tOqifK5LkOkBxWSbEmHOosjQr0BWkyZuqpx1/XDvyyZ3tDR30YV74IbX1vzovaqIeimBXR6nsjbuTGuVbQ1rGMP6TitPqw1KitMxTTZkKHGVmiJ6cQBciC8KlgJAmrM3KgtxyTgDiBrqAsGHm5m//QKOthIb4lVZ5MwUWTgvCC6anrVahuECLP7hAuLXZrWM31X1Nu4DXM4NaPa8mSBDlwAmSyesfQGoPAst9jAaDQFTftEH6BfThTYviPIuuGhovW6tJwUoGpc1mi6d8JGy6KoYM3VplfY0BU5gWLx2M5GNt3qcocczVt29SJq4gRZW47lpRfQZbZpPbPgzHcZ2CegtTqP+zcvh0f8MVNNASJG0VBW7S1d7tpr3JrRYjDXYpV9IjXzoyvjGvULgetaU0osHZVsm2HW28SWtuOBY/jL8SOytlz7jcS87kW29QjbtN5SnQYnsu0jvzkx83M3/rHB1MYBIkKs2W1D45j+iGRbz0W2Zknolt07ZdbwdjAAQqRrl9tu6R3m0Pa1fnKp9Z8TIorH/vjONT5JPSbqFcfeFPeKwGXqNtNEpc2WE8itWZ+dnqf5napMP4JE7IWsad3qHDUuRvZ9rHVkYmYXkAWKZXZdOkOWq11JlmXusu2wt7po6ZLn2HCg3KyiVoseEYD5Z/wOvQ8C5KJ1CjCaNuB2UnbNMOtEDgGnxqFD88s+TmTNLiPUqmZjP0HuUIZJbwHoqHHzPPVy8y2UWo4ogo8PXXdtc5pDrTPLjvbAWLhx2CJc7USQWGY5S3V0QJkjNtwt3ers274utou4h6qgW6hlftP1kK2lJTz6870iiEQiQOm06dylHf3cBSvouIEOe0pgefG01715s1fF/vTk3Itny4MePG004UzM4HazVwB9flmTt9IWdAJd+1IOn6DDW221Ogq8T+cQW6jlZ7zLia67L4jeoBWtPTBrDqf0/ttmqCDBaFzMsaurQdlp7+84kNng+NpVQZ+cOzMnoJyHLWpbQJf8R7PmeKeDuNdu+GhobrQANIQ3Tn8xhN/gvdU469jj2INM0D+5IujLZ/0c3IFBFxvJ/kGHRtte3Cl+ygcMGTwUrC21DeGXnrmMJoMmY5nsACfEDAv07KYveQ3CoJutvPsBHVLMzqLO+Wnhbh4w5TbMY/66wc9vnPV/1JqV72CnVMY2+zst4cqgQ1OyvjHImbhZE01X2xrzp0NL0y7djh3IOpGO5LzEYYAe2nnxon+bukQ0pbbROGJdnPH5SmN9H85hTOBGGGA0h8jZgN5/Bn7WZ4dpkshzjtxBD+i0wJCb1xQsGaBvG6CP5HRr6pguD43bGNQl9KK6ZUUqX7US3hcZ3kthAJfxCjS1Tsy/Hho3F9TZdZam9aM5GJT007kRgp6l1vc2MRAyYKHv3AVAuJs17gfp3kd3aNSyrkgDKpGmKEbFVKwaRx/GuswHdJKasWP1BJ8xPfzibBuyNK3v4/SXwYk9islIDMIrNCa9IqgzA/NMV2mhzzyqq7ElQB/FIbBrjJE2uq9u2+zKQ4oFZF9y2hAz+6ePxLqEyvocZpz+4pE4NRSaZ61FjWlwbFmj+DrBbgDSItsYdMt54gER21V6FPN3zGIs9O1xs5W3Za2wNmj41p1y2kEG+GWPoDRfJT3Dy9LKO0DatFpoLSUJg26T5DAZzCH2Wqth/TR1eSQxAERljgJ9BNZlmbfuOZUp82KX5BAL6MzjE7T1qnpNqAfuqEhzm3TQfTVrviLZBqbULutiXA082Yb6UPZdIHQiCQCC3m9f06uR5iTrp6kLfXfa7JvmeNvomNotXQ0DOPTL1g7/CoDqLUVOiL2RRD8M2tLSU+Nif+m4g9KugyOCUsKRxskOVVxLA+/KeVIu5P8s0WGRun8N/XQQGbiTrn/KOspX60KNAx3HOJ+aPB0MLQU0YbhRvisJkTjov4vvAOQSHc/VF3+/6GxY588CctbREZxB3dmN8icnPw61KZ4Tue8DeTiGwYF+I6g7u9NSYFsFJGXcx7GHxvW/N+STxgX6VGDTFEFLL9wTM7yGud+du35pXKBfH8VcssG7o+Yl/FJAId7x2PTRgO6Zr+Wpcc+8U5gGofmAFl5eNArQcUGLI3lqnMPK6so0ej9dpVGAvullHbJeijx/FkxkfUyg74xphNHk6Z7MBrNzNybQveUdBXkLv+nSRndwGpPw878S0LNB7GYEtR3oRb8W0AOhcbmMk78E0Jf85EUHQOMC3UcJUfA0NuGDcf89aX0M0U0LjQv0cdFIwgBeNOu1evoro18E6MOj/wUHsE1YCMggnAAAAABJRU5ErkJggg==" /></div><br /><b>Symmetry pictures</b><br />Depending on your personal drawing skills you could draw half of various objects and get your child to draw the other half, keeping it symmetrical. For example you could draw half a ladybird and then pass it over for your child to draw the other half and colour it in (you may have already coloured your half in an interesting pattern ready to be copied. Children often love this as it's sitting and colouring. You could make it more fun by both of you drawing a half object and then exchanging.<br /><br />Hopefully you are now inspired with lots of things to do but are maybe unsure of what level to do this out so here is a progress chart for symmetry. I have avoided using ages this time as this is not necessarily age dependent, some children can progress along this quite quickly given lots of practice.<br /><br /><ul><li>First step is to recognise simple shapes that are symmetrical and be able to mark on the line of symmetry. Eg draw a line of symmetry through a square or a triangle and then to venture slightly further and be able to draw one through a teddy bear picture or a picture of a spider etc.</li><li>Once they can recognise this symmetry can your child draw it? If you drew half a square and the line of symmetry could they draw the other half - the reflection? Try it with a teddy bear.</li><li>Once basic symmetry has been established you need to start putting this into context by looking at regular shapes and identifying how many lines of symmetry a shape has and where they are.</li><li>Alongside the above children need to be able to draw what I would call a more random reflection. ie. They have a shape and a need to be able to reflect this in a line of symmetry that is not part of the shape.</li><li>Once they can reflect a shape in one line of symmetry can they reflect it in a diagonal line of symmetry and then across 2 lines of symmetry? eg. Imagine a hexagon with a line of symmetry drawn vertically to it and then draw a line of symmetry across the bottom so it is horizontal to it - can they draw a reflection in both these lines? </li></ul><div style="text-align: center;"><img alt="Image result for reflective symmetry" src="https://encrypted-tbn1.gstatic.com/images?q=tbn:ANd9GcQF_JygSpyZtaMW0zdsC71ws8VKBTHoTMQSRnToL8g32xRZn54o0Q" /></div><div><br /></div><div>I hope you all enjoy this weeks activity - something fun but educational :)</div><div><br /></div><div>If anyone would like to help me I would love a little feedback from you all so I can make sure I am giving you the help and inspiration needed.. Nothing detailed but I would really appreciate it if you could email me (cal@lotty.org) or comment below and let me know your favourite article or top three articles. If you would like to give reasons for these that would be an added bonus for me. Thank you</div>Charlotte Haywardhttps://plus.google.com/101613062113924736341noreply@blogger.com0tag:blogger.com,1999:blog-5343833198242744295.post-44115952353551290892015-08-14T11:03:00.003-06:002015-08-14T11:03:35.933-06:00Planes, trains and automobiles........This week I thought I would give you a fun maths craft after the last few busy posts with lots of 'lesson' style learning. This also serves a double purpose as it gives you chance to revise the work some of you might have done on sequences a few weeks ago.<br /><br /><b>What you will need</b><br /><br />A printed out train with many carriages or something else that has many of something!<br />This could be many aeroplanes, cars, beads, pictures of animals.........<br />(The one I used is <a href="https://docs.google.com/document/d/1kPyF2mAFEi_5Sihd_UaS1p0ibDrBavebttuVMOzZIL0/edit?usp=sharing" target="_blank">here</a>, you could do much bigger ones too)<br /><br />Colouring pencils or pens<br /><br />A sequence!<br /><br /><b>What to do</b><br />Choose a sequence with your child that they would like to learn / practice or revise.<br />With your child write the sequence on your train carriages (or something else)<br />Let your child colour in and or decorate their train.<br />Display your train (or other) on the wall. The more your child looks at it the more the sequence will sink in.<br /><br />I know many children that would love this activity: a little bit of learning and then some colouring and decorating :)<br /><div class="separator" style="clear: both; text-align: center;"><br /></div><div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/-9p8lC_0byaA/Vc2Hi_v-ERI/AAAAAAAAgtk/DL8jiC_y7e4/s1600/IMG_20150814_241512793.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="180" src="http://1.bp.blogspot.com/-9p8lC_0byaA/Vc2Hi_v-ERI/AAAAAAAAgtk/DL8jiC_y7e4/s320/IMG_20150814_241512793.jpg" width="320" /></a></div><br /><br /><b>Pre-school</b><br />These sequences will be the basics of numbers and you may need to start nice and easy with just the<br />Basic counting up as far as you can go<br />Counting backwards from 10 and then maybe 20<br />Counting in 2's to 20<br />Counting in 10's to 100<br /><br /><b>5, 6 and 7 year olds</b><br />These children will , hopefully, be confident counters by now but will need to be working on counting in sequences that miss out numbers, so 2's, 3's etc. The other area you may need to practice is going over 100.<br />Counting forwards - always worth practicing<br />Counting backwards - from any number below 100<br />Counting in 2's - as far as they can<br />Counting in 2's - but odd numbers<br />Counting in 5's - can they get to 50 or 100?<br />Counting in 10's - how far can they get?<br />Counting in 3's - up to 36 initially<br />Counting in 4's - up to 48 initially<br /><b><br /></b><b>7, 8 and 9 year olds</b><br />Hopefully most of these children have mastered the art of counting and can do the basic times table sequences. So the next challenge for these is to push them to know all their tables and to look slightly further afield.<br />Counting forwards - always worth practicing<br />Counting backwards - from any number below 300<br />Counting in 2's - as far as they can<br />Counting in 2's - but odd numbers<br />Counting in 5's - can they get beyond 100?<br />Counting in 10's - how far can they get?<br />Counting in 3's - up to 36 initially<br />Counting in 4's - up to 48 initially<br />Counting in 6's - up to 72 initially<br />Counting in 7's - up to 84 initially<br />Counting in 8's - up to 96 initially<br />Counting in 9's - up to 108 initially<br />Counting in 11's - up to 132 initially<br />Counting in 12's - up to 144 initially<br /><br /><b>9, 10 and 11 year olds</b><br />By now these children should be revising their times tables and pushing onto more interesting sequences:<br />Counting forwards - always worth practicing<br />Counting backwards - from any number<br />Counting in 2's - as far as they can<br />Counting in 2's - but odd numbers<br />Counting in 5's - can they get beyond 100?<br />Counting in 10's - how far can they get?<br />Counting in 3's - how far can they get?<br />Counting in 4's - how far can they get?<br />Counting in 6's - how far can they get?<br />Counting in 7's - how far can they get?<br />Counting in 8's - how far can they get?<br />Counting in 9's - how far can they get?<br />Counting in 11's - how far can they get?<br />Counting in 12's - how far can they get?<br />Can they start counting in any of the numbers above but starting from a different starting number eg. count in 6's starting on 2.<br />Counting in 13's<br />Counting in 15's<br />Counting in 25's<br />Counting in square numbers<br />Counting in triangular numbers<br />What other interesting sequences can you find? fibonacci, prime numbers, to the power of 2............<br /><br /><div style="text-align: center;"><b>Have fun with this one!</b></div><br /><br /><br /><br /><br /><br /><br />Charlotte Haywardhttps://plus.google.com/101613062113924736341noreply@blogger.com0tag:blogger.com,1999:blog-5343833198242744295.post-62589876816668333132015-08-07T13:07:00.002-06:002015-08-07T13:07:20.110-06:00Addition.......how do we teach it now?!!!So, how do you help your child when it comes to addition?<div><br /></div><div><div style="text-align: center;"><img src="http://4vector.com/i/free-vector-add-blue-clip-art_117064_Add_Blue_clip_art_medium.png" /></div><br />Throughout their time at school your child will be exposed to many different methods of doing addition. Some will be written methods and others will be what we call mental methods - worked out in your head or using jottings. As a parent the best way you can help your child with their addition is to build up their ability to do addition in their heads - what I would call mental addition. <br />This will build your child's understanding of addition in a much better way than through using pencil and paper methods. To be able to do maths in your head you have to be able to understand what you are doing. Doing the mental methods will really build your child's knowledge and understanding of numbers. The danger with using pencil and paper methods is that your child doesn't fully understand what they are doing and can't do it in their heads and so ends up relying on a method they don't quite understand and therefore does not have the knowledge to recognise if they have gone wrong. I have seen it many times when children are working through sums. They bring me them to mark and several are obviously wrong if you look at the numbers but these children, because they are relying on the method, are not actually looking at the numbers. They are just putting them through a formula and not even looking at or thinking about what is coming out the other end so can't spot their mistakes. Giving your child a really secure mental knowledge and understanding is the best thing you can do for them.<br /><br />So, now you know what to do here's how to do it.<br /><br />As with everything start easy and build up. Easy builds the confidence.<br /><br />When doing addition, your ultimate aim is for it to be done in the head or with simple jottings but you need to teach your child what to do in their head first. So, when doing the activities below you need to have something to write on so all practise can be done modelling what is going to be going on in the head and then, as time goes on, you can gradually take away how much is written down.<br /><br /><div style="text-align: center;"><img alt="Image result for add" 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" /></div><br /><div style="text-align: center;"><b>How to teach mental addition</b></div><br /><b>Level</b>: Single digit addition progressing to 2-digit add 1-digit numbers<br /><br />Find an object that you have many of! This could be crayons, books, duplos, cars............<br /><br />Create a sum on the floor with your objects ie two small piles of cars. With your small child ask them how many cars there are and then how many cars there are in total and count them out together. One thing that is really good to do is to count the individual piles and then count the cars altogether and then start with one pile and say something similar to this:<br /><br />'OK, I have 4 cars on this pile and 2 on the other pile. If I add them together I can do it by starting with the first number and then adding on the second. I know I have 4, so I don't need to recount them, I just add on the next two. So, 4, 5, 6. I have 6 in total.' Basically you are demonstrating that you don't need to count all the cars every time.<br /><br />Once you have done the sum then swap the sum round so instead of it being 4 cars add 2 cars make it 2 cars add 4 cars.<br /><br />After doing these sums write them out or encourage your child to help write them out so they can start to see how we write sums out. I would always try and use something fun for the writing like a whiteboard, a window or chalk, just makes it more fun for your child.</div><div><br /></div><div><div style="text-align: center;"><b>Really important - when writing out the sums for mental addition please always write them out horizontally, across the page</b></div><br />Once you have established basic addition you need to ensure they are starting to understand that:<br /><br /><ul><li>You don't have to count each time</li><li>Addition sums can be done either way round and give the same answer</li><li>Their fingers can help them - our number system is base 10 so having ten fingers works really well for addition</li></ul>As you progress you may find that cheerios or beads work better and eventually once the visual has been understood you can drop the objects.<br /><br /><b>Level</b>: 2 digit add 2-digit numbers<br /><br />When it comes to adding two 2-digit numbers together you need to start encouraging your child in a very visual method so they can start to internalise this and use it within their heads.<br /><br />I teach this by writing the sum across the page and then drawing a loop on top of the sum from one units number to the other, adding them in my head and writing the total above the loop. Initially I write the sum above the loop too. Then I draw a loop under the sum from one tens number to the other and then, write the total of these under the loop. Again I start by writing the sum. Please, please write the full tens number of 20 or 30 etc. please don't just write 2 or 3 to show the number of tens. They really need the visual of the full tens number to help internalise that understanding. Once I have added the units and then the tens (please always try to demonstrate by doing the units first) I then write after the sum a new sum of the tens add the units with the answer. This is very visual and can really help your child to see and understand the process they need to go through to add numbers together. Although I encourage children to add the units first (this will help them with bigger numbers and when holding numbers in their heads) when they write the new sum I encourage them to write the hundreds number first, then the tens and then the units as this can help them see the numbers fit / add together.<br /><br /> 6 + 3 = 9<br /> <img src="https://encrypted-tbn1.gstatic.com/images?q=tbn:ANd9GcTMx75EfWhz7ZXfQ85L8XMQClbNlBh78sbDsIRaqaSeYzfqCZ47FQ" /> <br />eg. 26 + 13 = 30 + 9 =39<br /><div> <img height="133" src="https://encrypted-tbn1.gstatic.com/images?q=tbn:ANd9GcTLvMbvjVQPj12XUXT6RZlX5P3KHG1TMFb2RIL55JH_RK1JwBWU" width="200" /><br /> 20 + 10 = 30<br /><br />Once you have shown this method you will need to stay visual for a while but as your child increases in confidence and ability the next step is to slowly take away the visual and encourage them to do this within their heads.<br /><br />1. Stop writing the sums on the loops, just write the answers<br />2. Next step is to take away the end sum where you add the tens and units, encourage them to do that sum in their heads and just write the answer.<br />3. Then the loops need to be dropped. As these are dropped you may want to use the final sum again, as a way of recording the answers to the mini sums eg.<br /><br />26 + 13 = 30 + 9 = 39<br /><br />Obviously the final step is then to drop that final sum and for all those steps to be done in the head.<br /><br />The above process is not quick, it will take a lot of time and practice but eventually your child will get there and will have a fab understanding of numbers.<br /><br />What you may find happens, is that every time you increase the level of the sum you will need to re-use some of the stepping stones above just to re internalise but also give your child the tools and time to learn to cope with bigger numbers.<br /><b><br />Level</b>: 3-digit numbers add 2- digit numbers<br /><br />For these sums you need to use exactly the same visual as above. All you are doing is adding in a simple 100's element. You should still have 2 loops but when you write out the second sum you will have hundreds in there too. eg.<br /><br />147 + 83 = 100 + 120 + 10 = 230<br /><br />This is going to require lots of practice as there are many areas that can confuse a budding mathematician. <br /><br /><ul><li>Suddenly they are dealing with three numbers</li><li>They may have hundreds in more than one number in their second sum and tens in more than one number.....</li><li>They have to go into much higher numbers </li></ul>If there is confusion add a third sum into the process for a while to help them break it down even more:<br /><br />eg. 147 + 83 = 100 + 120 +10 = 200 + 30 = 230<br /><br /><b>Level</b>: 3-digit numbers add 3-digit numbers<br /><br />As with above you need to take this step by step and steadily.<br /><br />Use the same method as above but this time you will need to add a third loop to add the hundreds numbers together. Likewise, add in the loop, do lots of practice and then slowly take the visual elements away until your child can add these numbers confidently in their heads.<br /><br /><b>Level</b>: Bigger numbers!<br /><br />I could go on describing the gradual increase with 3-digit add 4-digt etc. but I think you should understand what you are doing by now. Your child should also understand. If the previous levels have been taught slowly and steadily then by the time you hit 4-digit numbers your child should be able to manage very easily in his / her head without having to go through the written / visual process to practice.<br /><br /><div style="text-align: center;"><b>Activities</b></div><br />The basics you need for teaching mental addition is paper and pencil and some objects if you have a young mathematician.<br /><br />As with many aspects of maths this part of maths does initially require some sitting down and learning but we can make it more fun and interesting<br /><br /><b>Dice</b> - use these to create your sums. Each dice throw represents another digit in the sum (yes, the dice only go to 6 but this can work great when moving up a levle as it keeps the sums a little simpler)<br /><b><br />Number cards</b> - your child may love making some numbers cards 0 - 9 which you can then use to help you pick the numbers for your sums<br /><br /><b>Race</b> - children love racing / working against an adult. Write a sum and both of you race to do it<br /><br /><b>Taking it in turns</b> - write sums for each other. So you write one for your child to do, they write one for you to do. (establish rules for the sums if you do this ie. 2 digit numbers etc.)<br /><br /><b>Timer</b> - this can be used in several ways: how many sums in 1 minute or you could set a target of 'can you do 3 sums in one minute.<br /><br />Obviously there is lots of progression that can be made with this topic. My advice is to find your childs level and with that to improve it a little and then do lots of practice around it. Then in a few weeks come back to it and move them on again. Go slowly and steadily. There is no rush. The most important thing here is that you are developing a clear understanding of addition in your child.<br /><br />Once you have done the sitting down teacher bit you need to practice. Again, this can be done in may ways.<br /><br /><b>Sitting down practice</b> - every few days sitting together and working through some sums<br /><br /><b>Random</b> - every so often just ask your child what the answer to a sum is eg. What's 7 + 26 . This can be quite fun if you just add it into your everyday life.<br /><br /><b>Hide and seek numbers</b> - hide some numbers (these need to be full numbers at the level you're working at) around a room / the house. Get your child to find 2 and add them together. Hide them again and then they need to find another 2 and add them.<br /><br /><b>Bribery games</b> - some children may need more of an incentive and you could score points for every sum they get right doing the activities suggested above. When they have so many points they could earn something. Generally with my daughter when she earns something it's craft time with me or a day out of her choice (within budget) etc.<br /><br /><div style="text-align: center;"><img alt="Image result for add" src="https://encrypted-tbn3.gstatic.com/images?q=tbn:ANd9GcSH7o6Yd1XqXdjAP2M9nve4zkVDs2vEKMI5kXYXiEUemcZvG6R38Q" /></div><br /><div style="text-align: center;">So, this week is a slightly different week in that it is more teaching a skill but it's a really useful skill to have and the number confidence it will give your child is well worth it. Enjoy :)</div><br /><div dir="ltr" style="color: #222222; font-family: arial, sans-serif; font-size: small;"><br /></div><div dir="ltr" style="color: #222222; font-family: arial, sans-serif; font-size: small;"><br /></div><div dir="ltr" style="color: #222222; font-family: arial, sans-serif; font-size: small;"><br /></div><div dir="ltr" style="color: #222222; font-family: arial, sans-serif; font-size: small;"><br /></div><div dir="ltr" style="color: #222222; font-family: arial, sans-serif; font-size: small;"><br /></div><div dir="ltr" style="color: #222222; font-family: arial, sans-serif; font-size: small;"><br /></div><div dir="ltr" style="color: #222222; font-family: arial, sans-serif; font-size: small;"><br /></div><div dir="ltr" style="color: #222222; font-family: arial, sans-serif; font-size: small;"><br /></div><div dir="ltr" style="color: #222222; font-family: arial, sans-serif; font-size: small;"><br /></div><div dir="ltr" style="color: #222222; font-family: arial, sans-serif; font-size: small;"><br /></div><div dir="ltr" style="color: #222222; font-family: arial, sans-serif; font-size: small;"><br /></div><div dir="ltr" style="color: #222222; font-family: arial, sans-serif; font-size: small;"><br /></div><div dir="ltr" style="color: #222222; font-family: arial, sans-serif; font-size: small;"><br /></div><div dir="ltr" style="color: #222222; font-family: arial, sans-serif; font-size: small;"><br /></div><div dir="ltr" style="color: #222222; font-family: arial, sans-serif; font-size: small;"><br /></div><div dir="ltr" style="color: #222222; font-family: arial, sans-serif; font-size: small;"><br /></div><div dir="ltr" style="color: #222222; font-family: arial, sans-serif; font-size: small;"><br /></div><div dir="ltr" style="color: #222222; font-family: arial, sans-serif; font-size: small;"><br /></div><div dir="ltr" style="color: #222222; font-family: arial, sans-serif; font-size: small;"><br /></div><div dir="ltr" style="color: #222222; font-family: arial, sans-serif; font-size: small;"><br /></div><div dir="ltr" style="color: #222222; font-family: arial, sans-serif; font-size: small;"><br /></div><div dir="ltr" style="color: #222222; font-family: arial, sans-serif; font-size: small;"><br /></div><div dir="ltr" style="color: #222222; font-family: arial, sans-serif; font-size: small;"><br /></div><div dir="ltr" style="color: #222222; font-family: arial, sans-serif; font-size: small;"><br /></div><div dir="ltr" style="color: #222222; font-family: arial, sans-serif; font-size: small;"><br /></div><div dir="ltr" style="color: #222222; font-family: arial, sans-serif; font-size: small;"><br /></div><div dir="ltr" style="color: #222222; font-family: arial, sans-serif; font-size: small;"><br /></div></div></div>Charlotte Haywardhttps://plus.google.com/101613062113924736341noreply@blogger.com1tag:blogger.com,1999:blog-5343833198242744295.post-53955522115686308042015-07-31T12:27:00.004-06:002015-07-31T12:27:58.054-06:00Problem Solving - where do I start?Problem Solving - is this a phrase that you have heard many times in conjunction with your childs maths work but are actually unsure what it means?<br /><br />I would imagine that you are not alone. In the good old days, where teaching was more traditional this phrase would generally mean giving children some pre-written word problems that were linked to some of the work they were doing. These were very staged and mostly unrealistic. However, these days problem solving means something entirely different and requires and a very different way of looking at maths.<br /><br /><div style="text-align: center;"><img alt="Image result for thinking pictures" src="data:image/png;base64,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" /></div><br />Over the past few years maths teaching has developed and changed and there is now a strong belief of teaching for understanding. Basically we really want your children to understand what they are learning and how it works, rather than just to know a formula and how to put the numbers through it. Part of this teaching for understanding is problem solving. These days we want to teach children through problems and discussion. By doing this your child has to think about what they know and apply this to the problem and can often extend their own learning and what they know by working through a problem. Initially, this can be quite a difficult thing to understand and get our heads around, as parents. But once you start to get into it this can be great fun and a learning curve for all. The great thing about problem solving is it can be a learning adventure for everyone at any level.<br /><br />There are a wide range of methods for using problem solving to teach. Children can solve collaboratively or independently. New ideas can be taught or old ones consolidated. Problems can extends a child's knowledge of a particular concept or just give them the vision to understand what they thought they knew.<br /><br />I thought that today I would introduce problem solving to you as a parent / tutor and start showing you how this can be used to help your children.<br /><br />As I mentioned above, problem solving is very open ended and, I believe, the part that we, older people, struggle with the most is the fact there are no answers! We were brought up on the concept of maths being right and wrong. Problem solving is all about exploring and experimenting with numbers, a very different way of looking at things.<br /><br />So, here is today's activity.<br /><br /><div style="text-align: center;"><b>Explore the numbers: 1, 2, 3, 4, 5, 6, 7, 8, 9 and 0.</b></div><div style="text-align: center;"><b><br /></b></div><div style="text-align: center;"><img alt="Image result for thinking pictures" 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" /></div><div style="text-align: center;"><b><br /></b></div><br />This is an incredibly open ended problem which makes it a fab problem as there is so much that can be done with it but also one where lots of encouragement could be needed as it's quite easy to be lazy on this problem.<br /><br />When it comes to doing this problem with your child you may be lucky and have a child that is used to this kind of thing and will just get stuck in and play with those numbers. I would expect though, that most of you will have children that will look at you blankly and not know how to start. Below I have given you some question that will hopefully get the problem started and then just go from there. You will need paper and pens for all the jottings you might do.<br /><br />When you introduce this problem keep it very simple and try not to give too much info and see what your child does. If they are not sure how to start, use some of the questions to help. The idea behind the questions is that they will spark other ideas and thoughts and hopefully you and your child, together, will start to explore the numbers without the aide of my questions. The questions are there purely to get you going enough to get the ideas and conversation flowing with these numbers. I have only given questions and not broken this down into levels this week as it is so open ended. Go with the flow, start with the very simple questions whatever level your child and just keep nudging the conversation deeper and deeper depending on what level your child is. I have added in some more difficult question to really push that thinking if some children are struggling to do this on their own.<br /><br /><b>Number</b><br />What's the biggest number you can make using all of these digits?<br />What's the smallest number you can make using these digits?<br /><br /><b>Counting</b><br />Can you count with them?<br />Can you count forwards? backwards?<br />Can you count every other number? What are those numbers? What about the ones you missed out?<br />Can you join one of the numbers to each of the other numbers and make a sequence? What sequence did you make? Can you count further than you made?<br /><b><br /></b><b>Adding</b><br />Can you add any of the numbers together?<br />Can you add the first number to each of the other numbers? What happens to them? What about if you add the second number to each of the others? the third? etc.?<br />Can you add all the numbers together?<br />What happens if you add 1, 2 and 3 together? Now add 2, 3 and 4, what do you get? What about 3, 4 and 5? Continue.........look at all the answers.<br />Can you add any of these numbers together to make 10? Do any of the other numbers add together to make 10? How many different ways can you make 10? What about doing the same for 11, 12 etc.<br /><br /><b>Subtracting</b><br />Can you start at 9 and take each of the the numbers before it away? eg 9 - 8 - 7 - 6.......... (you may get 'no you can't' or you may get 'yes' and be able to start exploring the negative numbers they go into - particularly good with 9, 10 and 11 year olds)<br />Which numbers can you pair up so that you can take one away from the other and stay with positive numbers?<br />Can you take more than one of the numbers away from any of the numbers? What's the highest numbers of these numbers that you can take away from one of these numbers?<br /><br /><b>Multiplying</b><br />Can you multiply any of these numbers together?<br />What happens if you multiply the numbers all by the last number: zero?<br />Can you multiply more than 2 of these numbers together?<br />Can you multiply all these numbers together?<br />What happens if you multiply all the numbers by one of the numbers? Now do this again with another of the numbers?<br />Can you multiply the numbers together in groups of three? Are there any patterns? What about if you multiply them together in groups of 4?<br /><br /><b>Dividing</b><br />Can you divide any of these numbers by one of the other numbers? Which ones? Did you develop a system to help you work this out methodically? If not, would this help?<br />Can you find a number that all of these numbers divide by? Can you find a number that none of these numbers divide by?<br />Can you put all the numbers together except one. The ones that are together should make a number that divide by the one not included (eg. 123467890 divided by 5)<br /><br /><b>Playing</b><br />Can you find another way to explore / play with these numbers?<br /><br />Have fun and enjoy this weeks problem. I would love to hear about some of the discussions you have with this problem and how far into number exploration it took you.<br /><br /><br /><br /><br /><br /><br /><br /><br />Charlotte Haywardhttps://plus.google.com/101613062113924736341noreply@blogger.com0tag:blogger.com,1999:blog-5343833198242744295.post-62557675895632362142015-07-24T13:34:00.002-06:002015-07-24T13:34:46.760-06:00Number Bonds<div dir="ltr" style="color: #222222; font-family: arial, sans-serif; font-size: small;">Number bonds: a phrase that can bring confusion to many! What are they? How do they work? How can we help our children with them?</div><div dir="ltr" style="color: #222222; font-family: arial, sans-serif; font-size: small;"><br /></div><div dir="ltr" style="color: #222222; font-family: arial, sans-serif; font-size: small;">From the time your child starts school you will hear the phrase 'number bonds', possibly from your child but more often from their teacher and in information sent home from school. Surprisingly this information often works on the assumption that we all know what number bonds are! Sadly we don't.</div><div dir="ltr" style="color: #222222; font-family: arial, sans-serif; font-size: small;"><br /></div><div dir="ltr" style="color: #222222; font-family: arial, sans-serif; font-size: small;">Number bonds are the addition pairs that make a particular number so, for example, if you were looking at the number bonds to 10 you would be looking for all the pairs of numbers that add up to 10:</div><div dir="ltr" style="color: #222222; font-family: arial, sans-serif; font-size: small;"><br /></div><div dir="ltr" style="color: #222222; font-family: arial, sans-serif; font-size: small;">0 + 10<br />1 + 9<br />2 + 8<br />3 + 7<br />4 + 6<br />5 + 5<br />6 + 4<br />7 + 3<br />8 + 2<br />9 + 1<br />10 + 0</div><div dir="ltr" style="color: #222222; font-family: arial, sans-serif; font-size: small;"><br /></div><div dir="ltr" style="color: #222222; font-family: arial, sans-serif; font-size: small;">The most frequently looked at sets of number bonds are the bonds to 10 and 20. Once children have understood and discovered these ones it is assumed that they understand how these patterns work and should be able to work the rest out as and when needed. However, there have been many times when teaching the older primary children when I have brought up the subject of number bonds and I get blank looks from students. This is mainly because number bonds are covered in Infants ( Kindergarten and 1st Grade) and often not revisited as there is so much more curriculum to cover in the older years. As a maths specialist, I feel they should be revised at least once a year, in the later years. The knowledge of these patterns and how to use them in all aspects of number is a brilliant skill to have and many children lack it. You will often find that the first ti e children do this, they write down the sums randomly and it's only when looking at them that they start to understand the patterns involved - the ones that are obvious to us!</div><div dir="ltr" style="color: #222222; font-family: arial, sans-serif; font-size: small;"><br />As a parent/guardian/ tutor this is one area you can really help your children. It's such a fun topic to teach and can bring amazing rewards, not least your child's confidence with numbers.</div><div dir="ltr" style="color: #222222; font-family: arial, sans-serif; font-size: small;"><br /></div><div dir="ltr" style="color: #222222; font-family: arial, sans-serif; font-size: small;">So, this week, play with the number bonds and have some fun looking at the patterns and how they link across our number system.</div><div dir="ltr" style="color: #222222; font-family: arial, sans-serif; font-size: small;"><br /></div><div dir="ltr" style="color: #222222; font-family: arial, sans-serif; font-size: small;"><div style="text-align: center;"><b>Preschool</b></div><div style="text-align: center;"><img alt="Image result for numbers" src="https://encrypted-tbn1.gstatic.com/images?q=tbn:ANd9GcQWhcaOBr1DaBHeA1pkz8yzSmak3n0IuiVSyM3OHkfCaBoZRWhnJg" /></div></div><div dir="ltr" style="color: #222222; font-family: arial, sans-serif; font-size: small;"><b><br />What:</b> number bonds to any number up to and including 10 if they're ready. Start with 3 and move on from there.</div><div dir="ltr" style="color: #222222; font-family: arial, sans-serif; font-size: small;"><br /><b>How</b>: start by using some blocks (or something similar that will do the same job: pencil crayons, cutlery, apples.........) and ask your child to find 3. Once they've done that hold up one block and ask them to find the other blocks you need to make 3. Once they have done this say the sum '1 block and 2 blocks makes 3 blocks'. After making sure your child has understood this and you've repeated it several times then do the same but with 2 + 1. Finally show the two different sums next to each other using the blocks and encourage your child to talk about what he / she sees. He / she might repeat the sums and tell you what each number is. Hopefully the will also notice that the sums are the same but written the opposite way round.<br /><br /></div><div dir="ltr" style="color: #222222; font-family: arial, sans-serif; font-size: small;">If three is easy then your next step is to progress up the numbers and do something similar to above. I wouldn't do much more than one number and all it's bonds in a session, if you're going to move forward to another number then do it the next day. If you want to write the sums down you can do but it's not essential. The important thing is starting to recognise the bonds for each number and to see the patterns with how they work.</div><div dir="ltr" style="color: #222222; font-family: arial, sans-serif; font-size: small;"><br /><br /></div><div dir="ltr" style="color: #222222; font-family: arial, sans-serif; font-size: small;"><div style="text-align: center;"><b>5, 6 and 7 year olds</b></div><div style="text-align: center;"><img alt="Image result for numbers" src="https://encrypted-tbn2.gstatic.com/images?q=tbn:ANd9GcQYFMf0mZefj-JL1Y6Eidrjzkhwsku59BolV7yd6_lweO1VzkvH9g" /></div></div><div dir="ltr" style="color: #222222; font-family: arial, sans-serif; font-size: small;"><br /></div><div dir="ltr" style="color: #222222; font-family: arial, sans-serif; font-size: small;"><b>What:</b> number bonds to 10, 20, some of them may be able to extend this to 30 and 40. Another extension is to do the whole tens number bonds to 100 (10 + 90, 20 + 80.......)<br /><br /><b>How:</b> start by using some blocks (or something similar that will do the same job: pencil crayons, cutlery, apples..........) and ask your child to find 10. Once they've done that hold up one block and ask them to find the other blocks you need to make 10. Once they have done this say the sum '1 block and 9 blocks makes 10 blocks'. After making sure your child has understood this and you've repeated it several times then do the same but with 2 + 8. Continue doing this until you have all the sums. If you have enough equipment it would be great to have all the sums laid out on the floor / table. If you can't do this then as each one was 'discovered' write it down (or get them to) so they're all written down together. Then encourage your child to talk about what he / she sees. He / she might repeat the sums and tell you what each number is. They need to start to notice that the each number is each sum is one less / more than the previous and some of the sums are the same but the opposite way around. Once you've had a discussion I would finish for the day and let the info sink in. As a follow up activity next day ask your child if they can write all the number bonds to ten. If they can, great. If not, then just briefly go over some of the areas they may find hard. The most common problem in repeating this is children know there's a pattern but can't remember what it is. If they need a nudge then write the first two sums for them and see if they can continue.<br /><br />If ten is achieved then your next step is to progress up the numbers with number bonds to 20, 30 and higher if you're both enjoying it and it's understood. I wouldn't do much more than one number and all it's bonds in a session, if you're going to move forward to another number then do it the next day.<br /><br /><br /><div style="text-align: center;"><b>7, 8 and 9 year olds</b></div><div style="text-align: center;"><img alt="Image result for numbers" src="https://encrypted-tbn0.gstatic.com/images?q=tbn:ANd9GcRQUlASt-i_pKQCuQeYjsBcQzAbuvRkWnJRw19EJFmLa3s319qG" /></div><br /><b>What:</b> number bonds to 10, 20, 30. Then extend using the 10's and 100's.(10 + 90, 20 + 80..........., 100 + 900, 200 + 800....., 1000 + 9000, 2000 + 8000.........) You may find that you can also start looking at all the number bonds to 100 too.<br /><br /><b>How:</b> If you're starting with the number bonds to 10, which you probably should as revision, then follow what I have written for the 5,6 and 7 year olds.<br />Once you've covered the basic number bonds to 10, 20 and 30 etc. then you need to move onto the bigger numbers. Initially there is little alternative but to do it with paper and pencil. I try to make this more exciting by either using a white board and pen, or a huge sheet of paper and coloured pens or lots of sheets of paper; one for each sum and then put together in order...........you know what your child likes so use whichever of these works to make it more interesting for them.<br /><br />By this point your child should have a good idea of what number bonds are and what the patterns are. What you are doing now is showing them how these bonds work across the whole number system and not just with the small numbers. So, maybe using one piece of paper get all the bonds to 10 written down, on the next sheet of paper get your child to write all the (10's) bonds to 100, then on the next sheet, the bonds to 1000 etc. Go as far as your childs knowledge of the number system will let you. Then look at all the sheets of sums and discuss the pattern and how it works.<br /><br />The next step is to look at all the number bonds to 100. My favourite way of starting this is to give them 3 or 4 sums to work out and then discuss how they're working it out and if there is an easier way. So, ask your child to find what number they need to add to 25 to make 100. Then try 52 and then try 93. While this is happening just watch and see how your child does this. I suspect there will be a lot of finger use! Once they have done these three sums talk to them about how they did them, if they found it difficult or if they found them easy. If they found them difficult you need to show them there is an easy way. Ask them to look at each pair of numbers and for each pair add the units numbers together and then add the tens numbers together. What they should discover is that the units add up to 10 and the tens add up to 90. The next step is to try and encourage your child to explain why this is and then show them how they can use this knowledge to work out the number bonds easily. eg. 45 + ? = 100<br />So, I need to add something to my units number to make 10 and something to my tens number to make 90.<br />If I add 5 to the units number I have 10 and if I add 50 to my tens number I have 90. So I need to add 55. Check the sum works :)<br />Initially your child may need some paper to record these numbers on but as you practice then, hopefully, he / she will be able to do it in their heads. A good way to practice is to every so often just ask 2 or 3 sums or set a nightly challenge of 3 sums one night, 4 the next etc. You could time them and set the challenge of improving their time each night.<br /><br /><br /><div style="text-align: center;"><b>9, 10 and 11 year olds</b></div><div style="text-align: center;"><img alt="Image result for numbers" src="https://encrypted-tbn1.gstatic.com/images?q=tbn:ANd9GcQeOzAqkO7KHz5zRIvZTc0Oc7vIvyZqkAlErZNtMYSBQyO7-wwZ" /></div><br /><b>What</b>: revision of all number bonds mentioned above. Then moving forward with bigger numbers 10000 + 90000, 20000 + 80000..........., 100000 + 900000, 200000 + 80000.........and then number bonds to 1000.<br /><br /><b>How:</b> With these children I suspect you will find that a lot of them don't really know the number bonds but with some quick revision they will soon pick up on the patterns. Use the info above and look at all the multiple of 10, 100 and 1000 bonds, they are fun and quick and easy to do and you may be able to get up to and beyond 1000000.<br /><br />Once you've had fun with the big numbers then revise how they work out the number bonds to 100. Again, you may find they can do it but have never really noticed the pattern mentioned above of the units making 10 and the tens numbers making 90. If they haven't found this, try and help them to discover it. Once these are secure move onto the number bonds to 1000. It's a great skill to be able to find pairs of numbers that make 1000 and, if you know the patterns it's not difficult. As with above, I would give them 3 sums to work out, so ask them to find the number that you add to 295 to make 1000, then 507 and then 989. Once they have done this write the sums down and discuss how they did it and if they can find any patterns that will help them.Hopefully they will notice that the units add to 10, the tens add to 90 and the hundreds add to 900.<br />eg. 368 + ? = 1000<br />So, I need to add something to my units number to make 10, something to my tens number to make 90 and something to my hundreds number to make 900. So 8 + 2 makes 10, 60 + 30 makes 90 and 300 + 600 makes 900. So the number I am adding is 632.<br />As you practice you could turn this into a little competition to try and increase the speed and efficiency of working this out. You could race each other or do sums against own speed or within a certain time.<br /><div style="text-align: center;"><b><br /></b></div><div style="text-align: center;"><b>Whatever you do, have fun :)</b></div><br /><br /><br /><br /><br /></div>Charlotte Haywardhttps://plus.google.com/101613062113924736341noreply@blogger.com0tag:blogger.com,1999:blog-5343833198242744295.post-69298000761552309292015-07-17T11:48:00.000-06:002015-07-17T11:48:15.497-06:00Holiday MathsSo, the children are on holiday from school and, as a parent, you are keen to keep at least some of what they learnt last year working in their brains. What to do?<br /><br /><div style="text-align: center;"><img alt="Image result for number" src="https://encrypted-tbn0.gstatic.com/images?q=tbn:ANd9GcQUVG4AS0BvPc0wZXIydxnwJVmX2i5ZxxXNC4haykQCLBZGFCr3" /></div><div style="text-align: center;"><br /></div>Some parents like the idea of buying workbooks or printing out work sheets and every week sitting your child down and doing some work. As a teacher, my recommendation is not to do the above but to do what I would call incidental maths. Children are on holiday from school to have a break from work and to let everything they have learnt sink in and be processed. So, sitting them down and working through books doesn't give children the break they need. However, doing some incidental maths can keep those skills consolidating and give your child a break from the more formal work. It also teaches them that learning can be fun and takes the pressure off both of you having to sit and do school work when 'everyone else is having fun!!'<br /><br />What is incidental maths? Incidental maths is maths that you can make happen as you go about your every day life. For example, you may be sitting at the dinner table and everyone has a drink. As you're eating dinner why don't you ask a few questions about the drinks? How much water do you think is in your glass? Why? So, if you put all our glasses together how much water do you think we'd have altogether? If I drank half my water, how much would I have left?<br /><br />This is quite a difficult thing to describe as every child is at a different level and every child's day is different. As a parent it is your chance to really have some fun with the maths and just let it happen within the day, without it being a big thing. You will just have to grab the opportunities and make them work for you and your child.<br /><br />Below I have described some of the more obvious scenarios that could happen to most of us to get you going and inspire you to do more. I have tended towards the higher level of student as sometimes it is harder to think of more challenging activities. I hope those of you with younger children can find ways to make the suggestions simpler. I would love to hear some of the things that you do end up doing as your incidental maths.<br /><div style="text-align: center;"><img alt="Image result for number" src="https://encrypted-tbn3.gstatic.com/images?q=tbn:ANd9GcReELSypeMCfDTZzBu0ss0NRcL3rZqepVqXJ0PDWGR-XO2AQReC" /></div><div style="text-align: center;"><br /></div><div style="text-align: center;"><b>Number work</b></div><b>Traveling</b> - It was this many miles from a to b and then we did this many miles, how many have we traveled in total? We are traveling at 60 mph and have 6 miles left to do, how long will it take us? The journey is x miles long, how long will it take us to complete traveling at 60mph?<br /><b>Car registration plates</b> - how many different numbers can you create with what you see. Write down the next 6 plates you see and use the digits to create the biggest number you can or the smallest. can you take the smallest away from the biggest? Or add all 6 numbers together, or find the smallest of the six and take it away from the biggest of the six.<br /><b>Numbered lamp posts, bollards etc</b>. - Have you seen anything on a local walk with numbers that you can add, take away, multiply, spot the pattern in?<br /><b>House numbers</b> - add them, take them away, swap the numbers around to make the biggest / smallest etc.<br /><br /><br /><div style="text-align: center;"><b>Measure / Capacity</b></div><b>Drinking</b> - how much liquid have you drunk today, let's keep a record and add it up? How much is everyone drinking at the table? How much is left if two of us drink everything in our glasses? How much wine is Mummy drinking? What is the capacity of her glass?<br /><b>Water Play</b> - mine have a tea set they play with in the bath so more questions about how many cups would fill the teapot? or the pan? How many spoonfuls fill the cup? How many cups fill the bucket? How much water does it take to water the plants, how can you work it out?<br /><b>Suitcases</b> - how big is my suitcase? Does it follow the airlines regulations? If not, by how much is it out? Whose suitcase is the biggest? Heaviest? What makes it the heaviest?<br /><div style="text-align: center;"><b><br /></b></div><div style="text-align: center;"><b>Money</b></div><b>Foreign Currencies</b> - what is the exchange rate? How does it work? So, how much will you get in the local currency if you exchange 10 pounds / dollars? When shopping encourage your child to spend their money and either just count it out or work out how much it is costing them in English / American money using the exchange rate. They could also add up how much you are spending as you go around the store, or they could add up by rounding up or down each item so they have an estimate of how much your shopping will cost. Alternatively you could give them 10 pounds / dollars and ask them to get the food for dinner with that money, adding up as they go as they can not over spend.<br /><div style="text-align: center;"><b><br /></b></div><div style="text-align: center;"><b>Shape work</b></div><b>Shape spotting</b> - what shapes can you see? Do they fit together? Why do you think it is that particular shape?<br /><br /><div style="text-align: center;"><b>Time work</b></div><b>Day to day</b> - we are leaving in 10 minutes, so when the big hand gets to........ Lunch will be at 12:30, can you tell me when it is that time? If it takes 45 minutes to get to Denver and it's 9:30 now, what time will we get to Denver?<br /><b>Calendar</b> - Have a calendar displayed with the monthly activities on so you can discuss how many days until........, how many weeks until........, when you are next going swimming.<br /><br /><div style="text-align: center;"><b>Data Handling</b></div><b>Long journeys</b> - give them a piece of paper and a pencil, can you record how many different coloured cars you can see in the next 5 minutes? How many different kinds of animals can you see in the next 30 minutes? Can you now sort what you have seen and tell me which animal was the most common, least common etc.?<br /><b>Holiday</b> - Record what we do each day on holiday and then create a table showing how many shops we went into, how many times we went swimming, how many museums we visited, how many restaurants we went to?Charlotte Haywardhttps://plus.google.com/101613062113924736341noreply@blogger.com0tag:blogger.com,1999:blog-5343833198242744295.post-15998758361647397802015-07-10T11:11:00.001-06:002015-07-10T11:15:00.017-06:00What's the time Mr Wolf?<div style="text-align: center;"><b>The Faces Of The Clock</b></div><div style="text-align: center;"><br /></div><div style="text-align: center;">The Big Hand is busy</div><div style="text-align: center;">But the Small Hand has power.</div><div style="text-align: center;">The large one counts the minutes.</div><div style="text-align: center;">But the Little One names the hour.</div><div style="text-align: center;"><br /></div><div style="text-align: center;">When both Hands stand at the top together,</div><div style="text-align: center;">It's sure to be Twelve O'clock. But whether</div><div style="text-align: center;">That's twelve at noon or twelve at night</div><div style="text-align: center;">Depends on if it's dark or light.</div><br /><br /><div style="text-align: center;"><img src="https://encrypted-tbn0.gstatic.com/images?q=tbn:ANd9GcQEnKHNnOEL5sraVeQAcBPNtQ0rMf9A8wZYJ7MHq_rpo99A5co-ew" /></div><br /><br />Teaching time can, literally, feel as if you are going round and round in circles. Every child learns about time in their own time and not necessarily when you would expect. I have always found that you are far better to work at teaching time little and often than trying to achieve a lot in a small amount of time. If you gently plug away at this in the background children will eventually start to make sense of it all and then be able to use time within their every day lives.<br /><br />This week I thought it would be fun to get crafty again. So, your first activity is to make a clock.<br /><br /><br /><b>You will need:</b><br />A paper plate<br />Two long thin pieces of cardboard (cardstock)<br />A split pin (or a bent paperclip!)<br />Whatever you want to use for decoration: felt pens, crayons, sticky numbers, jewels, stickers.........<br /><br /><b>What you need to do:</b><br /><br /><ul><li>Start by writing or sticking on the numbers 1 - 12 around the outside edge of the back of your paper plate. </li><li>Using the two pieces of card make your big hand and little hand and stick them in the middle with the split pin. </li><li>You may want to add small lines between the numbers to show the minutes </li><li>Decorate! </li></ul><br /><div style="text-align: center;"><a href="http://2.bp.blogspot.com/-4kOEtWu-l6s/VZ_zKKsgQJI/AAAAAAAAfb8/_nuwOyAivIg/s1600/IMG_20150710_102543248.jpg"><img border="0" src="http://2.bp.blogspot.com/-4kOEtWu-l6s/VZ_zKKsgQJI/AAAAAAAAfb8/_nuwOyAivIg/s320/IMG_20150710_102543248.jpg" /></a></div><br /><br />Once you have your clock you can then do some fun time telling activities. Start by doing a very brief review on telling the time at your child's level and then do some of the games I have added to the bottom of this article to practice that skill. Please, this is a little and often subject, so I would teach and do an activity for no more than 10 minutes and then choose another activity to do the following day for 10 minutes. Again, the next day do 10 minutes. Then leave it for a few days and come back to it. You will find the knowledge has either stayed put and you can move forward or there is a little confusion and you will need to do some more activities at the same level to consolidate.<br /><br />Normally I differentiate by age. For time I am just going to list the skills that need to be taught starting with the easiest and ending on the hardest. This is because every child learns time at a different pace of learning and does not always fit within the typical parameters for this. I would suggest everyone starts at the beginning and works their way down the list of skills, gradually building them up. For those with children really needing to start at the beginning this is something that will happen slowly, please don't feel you need to be at the bottom of the list by the end of the summer!!<br /><br />The last two skills are using knowledge of time rather than telling the time. When your child can confidently tell the time they then need to be able to use this knowledge to survive every day life - hence the final two skills.<br /><br />1. o'clock - can your child confidently read the whole hours on the clock not in chronological order? eg. 1 o clock, 2 o clock, 3 o clock.......<br /><br />2. Half past - can your child confidently read the clock when it is half past the hour? eg. half past 2 (2 thirty), half past 6 (6 thirty) etc<br /><br />3. Quarter past and quarter to - can your child confidently read the clock when it is quarter past or quarter to the hour? eg. quarter past 4 (4 fifteen), quarter past 7 (7 fifteen), quarter to 6 (5 forty five), quarter to 10 (9 forty five)<br /><br />4. 5 minute intervals - can your child confidently show how many minutes past each big number represents? eg. 1 means 5 minutes past, 2 means 10 minutes past, 3 means 15 minutes past - they can show this by counting round the clock using the hands on the clock to help. (You may want to mark the minutes on your clock at this point)<br /><br />5. Minutes and hours - can your child confidently read how many minutes past a particular hour it is? eg. It is 10 minutes past 4, It is 45 minutes past 6...........<br /><br />6. Minutes to the hour - can your child confidently read how many minutes to the next hour it is? eg. 20 minutes to 8, 10 minutes to 9, 5 minutes to 2.......<br /><br /> 7. Can your child confidently read the television guide and work out when a program will finish?<br /><br />8. Can your child confidently read a train or bus timetable and work out how long a certain part of the journey may be or what time you would arrive at a particular destination?<br /><br /><b>Activities</b><br /><br /><b>What's the time Mr Wolf?</b><br />One of you close your eyes while the other sets the clock to a certain time. The one that has set the time then asks 'What's the time Mr Wolf?' and the other person opens their eyes and reads the time.<br /><br /><b> Drawing the time</b><br />Find something to write on and write with that is a novelty eg. chalk on the driveway, whiteboard pen on the window or mirror, paint........ Draw a clock face and then ask your child to draw a specific time on the clock. If it's white board pens this works really well because you can rub the time out and reuse the clock face.<br /><br /><b> Dice Time</b><br />Use two dice. Choose each time whether to throw one or two dice. When they have been thrown add the total and then your child has to show the time on the clock using the number shown on the dice as the hour. eg. dice show 10 then 10 o clock needs to be created. If you are also using minutes throw the dice again and use that number to show where the minute hand needs to go and then your child needs to read the time they are showing on the clock. eg. a 10 was thrown first and then 2. The 10 is for the hour and the 2 is where the big hand needs to be so the time would read 10:10 or 10 past 10.<br /><br /><b>Challenge</b><br />Have somewhere to keep score. Ask your child to show a particular time on the clock. If they get it right they get the point, if they get it wrong you get the point. You may find your child then wants to swap round and give you some times to show on the clock - they love challenging us adults. Give it a go and have some fun.<div style="font-family: Verdana, Arial, Helvetica, sans-serif; font-size: 12px; line-height: 20px;"><br /></div>Charlotte Haywardhttps://plus.google.com/101613062113924736341noreply@blogger.com2tag:blogger.com,1999:blog-5343833198242744295.post-67929999191862392912015-06-30T22:16:00.004-06:002015-07-15T21:55:13.008-06:00Number PatternsSometimes it is fun to just sit down and colour some pretty patterns and that is what this weeks activity is all about.<br /><span style="font-family: Times, Times New Roman, serif;"><br /></span><span style="font-family: Times, Times New Roman, serif;">As I have mentioned on many previous occasions, children need to sometimes just play with numbers and see what they can discover for themselves. Although it can look like they are not doing much their brains are doing a lot of processing as they have chance to look at a number and use the number however they want so they can puzzle over it and their brain can logically work through what that number means and what it can do.</span><br /><br />So this week , I am keeping the activity simple and fun. All I would like you to do is print out some <a href="https://docs.google.com/document/d/1EL1MISDFXJ_IhMBohbZh_whboB2oFwjJTKzbs-HfO5E/edit?usp=sharing" target="_blank">100 squares</a> and let your child play with them.<br /><br />Initially I would sit with your child and maybe take a 100 square each and talk about the numbers on it.<br /><br />What number does it start on?<br />What number does it finish on?<br />Can you find the number ___?<br />Can you find a single digit number?<br />Can you find a 2-digit number?<br />Can you see any patterns? What?<br /><br />Once you move onto discussing patterns you need to be very open minded and guide the conversation but not lead it. When a child sees a pattern the pattern could be what we would deem a pattern to be or it could be a completely new idea to us but something very interesting to your child. Go with it and talk about why it is a pattern, what makes it a pattern, where the pattern begins, where it ends etc. I always find this bit fascinating as children's minds are less restricted than ours, everything is still new enough to them that they will explore in every direction they can think of and are not limited by the parameters of what we are now trained to see as normal. We really want to encourage this open minded thinking. When you are talking about the patterns please encourage your child to explain the patterns in their words. Explaining their maths is actually something children find really difficult and the more practice they can get, the better. Help and hint but try not to put works in their mouths.<br /><br />Once you have discussed the square, the numbers and anything interesting about it find some coloured pencils or pens and colour some patterns. This may be something you do together or something your child is happy to do alone. However it works, keep popping along and chatting about the patterns that are being coloured. Try to keep the conversations light and interesting but not too pressured or heavy. This is supposed to be a fun activity where the children are discovering for themselves. These patterns can be patterns with the numbers or they might be patterns with the squares which you could follow up by looking at the numbers in the squares. Make sure you have multiple copies of the 100 square so multiple patterns can be coloured.<br /><br />I am going to keep the differentiation simple this week. This is a very open ended task that looks like it could be very simple for the older children. However, what often happens with this activity is the older children love it because they don't get to play with numbers any more, they're too busy manipulating big numbers. Often, being given this chance can really help them to make sense of some of the more difficult concepts they are studying.<br /><br /><b>Pre-school</b><br />Keep it simple, fun and interesting and finish before your child gets bored. You will more likely be working at the first half of the 100 square, don't push them too far if they're not ready but there's nothing wrong with taking a look at the higher numbers and seeing how they work. This is a fab activity for this age as they can really explore some numbers. One way of working through this with them is to look at a new pattern every day for a week.<br /><br /><b>5, 6 and 7 year olds</b><br />You will hopefully be looking at the whole square with these children. This activity is great for this level as it can really help them consolidate their knowledge of numbers to 100 and possibly beyond. At this age the number square often helps make sense of what they're learning. Hopefully when doing this your child should be able to come up with patterns that fit across the whole square and be able to explain the patterns her / himself without too much guidance.<br /><br /><b>7, 8 and 9 year olds</b><br />I would imagine these children will enjoy just being able to play with numbers with no pressure. They should be able to work with the whole square and make predictions about higher numbers and patterns. Something to encourage at this level is talk of place value and how the numbers are made up of tens and units and how this is the basis for some of the patterns they will find. The visual of the number square should help them to really see how the place value works. (place value is something I intend to discuss in a later article, if you are not sure about discussing this with your child then don't worry, we will go over this later.)<br /><br /><b>9, 10 and 11 year olds</b><br />Use what I written above but then extend them with some different number squares. These can be really fun as they start to encourage thinking away from our base ten number system. Most of all with these children let them have fun and rediscover the joy of playing with numbers.<br /><a href="https://docs.google.com/document/d/1OTxoQGyoSHQG_pvKGcXqaapTFucshQwcAhDye-xK6p0/edit?usp=sharing" target="_blank">5's number square</a><br /><a href="https://docs.google.com/document/d/1YoGvpSN86IVnwkyZpSKYQwtYkflXKrO5yBRsPxYGw_w/edit?usp=sharing" target="_blank">6's number square</a><br /><a href="https://docs.google.com/document/d/11Debj6uXdUGF_POhgO_jlswTlNkI-TCiw_4WMcfj9UM/edit?usp=sharing" target="_blank">7's number square</a><br /><a href="https://docs.google.com/document/d/12ejmIucBvBJI16hVsTiz8X2ROafu0Bw6owRGnjiMHyA/edit?usp=sharing" target="_blank">8's number square</a><br /><a href="https://docs.google.com/document/d/1MSeihKQoWKKKqcChJbTpNtX7oY6kzsPqjS8ovgqK0po/edit?usp=sharing" target="_blank">9's number square</a>Charlotte Haywardhttps://plus.google.com/101613062113924736341noreply@blogger.com0tag:blogger.com,1999:blog-5343833198242744295.post-6003290492632894602015-06-23T20:37:00.003-06:002015-06-23T20:37:53.111-06:00Gathering information and playing :)<div dir="ltr" style="color: #222222; font-family: arial, sans-serif; font-size: small;">This week I thought it would be fun to have a look at some data. Children are such curious creatures and love finding out about the world around them. What better way to do this that through collecting information and looking at what the results can tell us.</div><div dir="ltr" style="color: #222222; font-family: arial, sans-serif; font-size: small;"><br /></div><div dir="ltr" style="color: #222222; font-family: arial, sans-serif; font-size: small;">Data handling is actually a fairly simple part of the curriculum initially and so can get overlooked by tutors, parents or anyone else doing extra work with your child. I find it is a great way to have some fun, find out something interesting and to learn to use numbers to help us. This can also be a great bonding session as you and your child work on this project in search of an answer together. This activity is something that you can work on towards a shared goal rather than the normal teacher / student style of helping with maths.</div><div dir="ltr" style="color: #222222; font-family: arial, sans-serif; font-size: small;"><br /></div><div dir="ltr" style="color: #222222; font-family: arial, sans-serif; font-size: small;">The joy of this week's activity is it can be entirely open ended, you can choose what to do, how to do it and how far to take it and have lots of fun in the process.</div><div dir="ltr" style="color: #222222; font-family: arial, sans-serif; font-size: small;"><br /></div><div dir="ltr" style="color: #222222; font-family: arial, sans-serif; font-size: small;">So, here it is:</div><div dir="ltr" style="color: #222222; font-family: arial, sans-serif; font-size: small;"><br /></div><div dir="ltr" style="color: #222222; font-family: arial, sans-serif; font-size: small;"><b>Data Handling</b> - keep your ears and eyes open and when an appropriate topic appears in your life grab it and do some data gathering around it and then follow it up with some data analysis.<br /><br /></div><div dir="ltr" style="color: #222222; font-family: arial, sans-serif; font-size: small;">For example: my daughter loves books and was trying to work out if I had read more to her or her brother one day. So I suggested we recorded who I read books to each day for a week. We created a tally chart which we put on the wall and then every time I read her, her brother or them both a book a tally was added to the chart and at the end of the week we looked at the results, drew a simple graph and then I got her to answer some questions about the results.<br /><div style="text-align: center;"><img alt="Image result for books" 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" /></div></div><div dir="ltr" style="color: #222222; font-family: arial, sans-serif; font-size: small;">Another example: many years ago with my Year 3/4 ( 2/3 Grade) class the children were complaining that the playground equipment wasn't very good and that they would like some new stuff. So I suggested they did a bit of data gathering about what equipment we already had and what state it was in and then they could present their findings to the head teacher as evidence that we needed new equipment. The children had a fab time without really realising that they were doing data handling.<br /><div style="text-align: center;"><img alt="Image result for outdoor toys clipart" 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Owa5dkHX6StKQeappHRwAjnoy31q1Lb02vVOjnsjJlJ8AgJrL7S3tZn6KAMrH6gkmP8AdwD1PtS6QOw0rTlOTahDL3v36Mol4mRsExGo7Mr+6xX7qebrlRcmZ/UtYZLh/EKUQe9z+zWf2USYVJzk6ufP1jzpzaLiz0/OvZ8n/lrU/BpOH7daOLV4uH9zy/ff/G7PVY3E9VgY96X6e19TvYhujBf12y7/AG3Jdvex8qtJMRyNfFFQep83cm3csre9op/uTbale5I/TYEWf1KZ0t+0xZvDTWT2XZflsvRg4tlP5+Qcnx/URnv+c3UOHM16hGAAAuAAAAByAHAAd1N0aGRZmtzbwFCSXWT+h911gu2T1T7OY8q40Uwm1sajSe43t9sA8HGO8cRTBWBGRxHdWYrtb3TIeB8R1Gr41mtxeeHT+E0dFV7S8Eg4cD1j/XVVimU09UJtNOzIooqjtK/0+ivrH3f51yUlFXZ2MXJ2R9X20QnBeLfDxpFdOxViDlyG05+lg6ffivrNFJzm5M0IU1BaHm24dwI41U8GYcSefSBjrB79RPlW5/LTjlxrObybrOsrT26llc6poh62rrliHWT85evmOOQUg3qK+iZlUjgQ5VWHcQ/pCvS0ZU8TBOLSaVmn3HisTCtgqkozi3FttNd/PvNJvBcAREE8WIx5gk+6sJsofnrlhy6VR7VjXPvNM4pZLpvzOZCecjZ6NO8t877K+7nTjZ+41tGPTXpnyWZpSWBYnJIj9VePd51OpiIULRWrWvlYnhei6+OzTfYi0krrvvt9BR/TSrwMkftdQfjXaPa6tyKnwYH4VqobCNBhI41HYqKB5AVxm2Jbv60EJ8Ykz54zVf8AMP8Ap5j3/GGlpW/x/Jn/AMvP0ffXyb49grU7O+Tq2l9Iw6E+o0iFvDSw86aH5MbH6Mw8Lq4/86ql0xRg7OL+gjV6ArRdlVT+gq2tMehwevA+/wC6sRudeqtxEFbOuFo3xkgFcSKGI4Z4OMd9ezpuzbjH5vVjlrZ39zE1n9oWg/odWRQDAqzqAMfom1sAB2oHHtrGx2IValOmo/EreHFeZs4XDdVOE3L4XfxurDCx/Rr4Vlb4f7zP9tT5xqaf7Hv0eLKMGHUVIIweI5Uq23baZg/U6gH7SZI81P8ADXl2s1BPwPS0tKpldoWkL7SsVnQOsvTREHvUFGBHEMHxxFaefcmJeEVxeRjsW5LAd35wMffWb2hKrtM6EM1pHBcEqQdGi6UsOHImISV6CTUcRUnTo07cU/1/IhibOtL3wM6+5cOD0slzKOyS4kx7VTSD7a+oLGK3iboo0jUKzEIoXOATxPX7ab3cnDFJ9uN/u8o+kugeMhEY/mpWnOdRqMm9WKStfQ8y2dA0iwwxkBpFGW6o0xqklY9QVcnxxTxblGYyjCRBEitwxA0wR8EJz1ucuftCvU9rbv7Ngi1z29siABc9EoLdigKMsTjkAaxX9N2kmTs/YbXK8QJDAiRnBxwJDEjyr0bpdZLN7139PDXmXY+tLFpR2SSVt9vf6Gd/pdGOmINM/wBGFS/mR6I9pphZ7rz3HG5PQxfqo2zI47JJBwUdy8e+mXR7Yb9Fs2CBOpWmU48FDA+6qnSbXPzLJfbJn+Y09Rw9KOq1ZVh8HRjrrJ+Bp7W1SNFSNQqKMKqjAA7qsRzFeRrGPtTa0Xr2sEw/sXIPkWJ91Ft8pEYYJdQzWzHrdSV88A49hpx2e5qdbDZ6eKPQ7e6Ddx7PwrtSK1uldQ8bBlPFWUgg+BFOLafUvf10nVp5dUEo8UdaKKKoIH3FIVII4EU/tLkOufMdhrO1d2VPpfHU3D29X+u+rqU7OxRWhmjfiOJpdKlj1Cs47kkk8zTna7Yj8SPvP3Ulrtd62I4eOlwoooqgZCle0CrtggHHaAePtpmx4Gk2aYoRu7lkEFFL9sbegtV1TyBM8hxLN9lRxPjypEd/y/6Cyu5R1HRpB+NNkpVIx0bNbTXY2ytfpv6o5D6R/CsDHt++c/8ABdEPrapD7ioFaGDau1xGojtosYGMxLy7cm7HwpavVyqy/RlNWo8vZPQAKmvPf6Z26P8A0duw8EB912a7x777QjP+8bKmYdbW7B/bo4/zVn5G9jPehvzSjYUYazjDAEFMEHiCDkEEeFVV38tAdMknQt9GYaCO49Vdd1L6OW0iMbo4CgHQwbByeBxy9tW1U0kcQqtPkxs4ZWkt+lgLDDLFIdB45HosDjHdjmat3m4ME0ZSaSeRWHEGTHgRgZzWhr5YsOK4PceGfA9RrkKr+YLchFZ7i2tvazW9vEsazIyOfSYtqQqCzMSTjNZ3d/ajSWkJIw/Rqr55h0/NuD36lNbwbTjzhjobsf0fIng3sJpJcbssGZ4Gj0szPoZPRyx1MQy8eJJPtpfFYT+Ijo9b8Tl2hQTmqG1VybdOqS7tUPgJRIfdGafNs65H9VbJ3s5IqpNGNcbSTrLLHIjxRQKSoYHBLY+oXHHtpaj0dKnJTm1pqRWpX+UjZEjtHMFMkapgph2VWEqyN0qoCxjkRejZlBKgDgQTXSz+UqLowpjiRlGAi3VuFGOoaypA/Zrb1DRg8wD4jNMu/Bl3iYE/Krk+hbo/2LpHPlGjUtv98Xd9f5I6Z58Zjk9ZGIK9QUY5cPCke8lxxVesZJ9vAffTGHvnsi2jfP2TASb2Pjhbn2mcf/hXOXeiKRCtxAdJ5glHHlJoPurUZqJJQASxwAMkk4AA5kk8hWjll/d78h7LLn5HnuyNpw2sszQEpbAxMyuw5OSkmhNRJKnQ4I44LDjwxvdg7fgmfTFKjEj1c4bt9Q4PurG3iR39wypGrBljXWUBKQo7O0xJGVL50IOZGW5Yp3J8nlvLkJrhxxXo2JVT1EI+QP2cHvqhOTU77X9FtvxuUrMk7WsbaisVsrbFzYyGC+bpYgMpcDOQmQuqTrKgkBjzXUpOVORtQaoBO4V9xHDDxHxr5rtZxapFHeD5caFuEnZDbaseYz3EH/XnSKsttv5U5pJnjsI4TEpKmWfWRIc4JjVSMJnIyc5xnGKiDbN7p9L8kJ7VWfH8/H3VbWcc25yhQqqCbjo9UaqprA3VhcTMWmvJQDySAmFB3DByfaTVRt3wpyt3coe0XD/+VUZo8xtYabV7rz9Ez0g0pkjIJBrOCeXo9D30zDtXo1b99U1e+snfk20glgeR5dXoqWdjJx4IwBy2eWPwq6jVipWLIYaai5O2np9B3tnZskd1+UdD0yh9ecF8DQFCMoBZdBBZSFYekcgHjTzYm8cdzqVQVZRkqSDwzjKkdh4EHBHWONKjf7RlT0YBCSOvTkftOx0/4Zq5u5u40DNLK4eVwQcZPMgsWduLsdKjOAAFAAFMxTUtNu8Vje+mw1vtoJEAWzljhFUFnc89KIOJPw68VUtN97ufENnCCVyNS6ZSuOppGZYFYdgaTw4Uj29cqlyfyjV0bkLwBGqHo1IjR+AwZdetQQzDRzANXxvraxKunWoX1VWPRjHLTkgD2VTP+o2pOyW3N/j3crqWno3axoE2PtaTi86x93TBj5R26jyNff8AsttH/wB7/wByb7waV23ytSkehs+6mA5Pp0Z9xBp3u58pEdzKIZIZreUsFCyDI1FWcITzUlVYjIAOk4NJzoyhvt4v9xJpr/QuutzL986poZM8+l6N8+Ou1bNZZvke2gk3TW00Fu/bFK6+QSJR7OVe00VGM3Db1IvU8T27vttvZ8giuOibqSTogVlx9FxgFu1cA91Ptjb07ZnjEkKWM69ehsMp61dHeMo3ca9Gv9nxzxtHMiyRsMMrgMD7D8a8/wBofJlNbSdNsyZlI/qpHIIH0Y58HK/UlDL4VZnjJbK5yx3fejaqjE2zgR1hVZwf8OST4GqUm9ig/ntnRp25e4h/nt1Hvqzs/wCU6SBxDtOB4n5BwhGe8x5Icd8TN9kVvNn7UinQPDIsidqMCB3HsPcarkmiSZgLTfGxJwbeIH/moG9zOPhTu335tkGEgkA/svyZh/BLn3Vp57GNxh40b7SK3xFL5N0bJudpanxt4fjpqHa5+X5RK8eXn+Cgu/0P6q7/AOnc/wApNQ+/8I/qbs//AFnH82K6yfJ9s9udnB7E0/DFJdqbn7NTKpaQlus+lhf4uJqcKcpuyfl+TsY5nZJ/f8Fm6+UlAp0W9xq/tOgjA7zrlFZq938hBJdl1nmGmhznwRmPkKsJujZj/wBND7UDfzZq/bbOij/Rxxp9hFX4Cn6dCcPmX2/LHYUnDb3+hlH3wupTi1tdX1isun95xGB51K7uXt0Qb2dUjznooQD559HPjqrZV9RxFjgUxay1ZLq7/EypszZSQroiXAJyeZLE82djxY95p9bw6RjzqILcKO/rNfG0NoRwRtJKwRF5k9vUAOZY8gBxNK1KmbRbHJSWy2Em90oD2xOCQ07MDjBiW2k6UNn5pJjHlTXYKsLS3DesIYs9x0LwrJWkcm0Lly6lU9FZQf6qFWDi1zyM0jBWkx6qgLzrd0pBXk587L7X18/K/ErWuoU42TaYGo8zy8K42Gzc4Z+XUO3vNNqdpU/mYtWq/KjxjanyX3ltK5tAJ4SzFAHRJEUknQ6uQrYzgEH2VR/oTaY4fkc3lF8ekxXuteYfKptmRrmOyDtFD0Iml0nSZdTsix6h80aGJHXkVKpTh8UkO4XH4mTjRjZ8Fde9jE3aXaErIIYSOfTXVsmPHDsaXTyy8lnSU9lqsk+PGT0Y/fWktbeziUYijB7SqEk9uo12k3ljUYQDwH4DhSmePyxNfq8VN2zfZJeZnLWxmPr295J4yQwDy0uffWl2EhgbXHs9VfGA8t6ZGHbp9A6c9wFJ7rfPjpXi3Uq8W/dXJqzZ7O2lccVhaNfpTsI8+CHU/mBUrzfBIpq0oLSrVfg3fySLe09vX7SeiLaEDmAGlLfaY4HkBVa23pvZpehjijDqup3X0uGoLkI7qBxI5k866ncnaJ+fAO/pZPuStFujuY1pI8ssoeR00YRSEVdQY4LcWJIHE45cqsjOUVq/sUVXh+rtTbzfX19BS1resPSLnPMa7RR+70TfE1xtdkXin0ejj7825P8ABbVvpLNT3HuqpJYsOXH/AF2VOGR8X92KqKfFmVm2DdyevesB1hFA/iQIw86s7G3XjtyGyXcEspOAFYjBcAcS2OGpiTjgCKckUUxkjuWKnG9xla7dkXg3pjv5+dN7XbUb9ek9jfceVZaiqp4eEu4hOhCRuKKyFttB4/VY47DxHlTOHeX6ae1T9x/GlJYWa21FZYeS21Gt7YRzIUlRJEPNXUMp9h4Vito/JLEH6Wxnns5f7N2ZD3FSdWO4NjurUrvFH16h7P8AOht4YvrH2f51CMKsdkyrqZ8jHC425a8GSK8QfOULqx34KMD+y3jX0flYaH/i7C5h7SvEDv8Azix+7NaebeX6KfvH7h+NLLraUknBm4fRHAe0dftq6FCUviViyOGm99BVP8sFnKNMcjx55l43B8BpBA8a4R7y2rDIuIfa6j411utiQS/pIYm72jUnzxmqce59qpykbIfqSzL8HpqMMitEZhCcFZWLg23Af6+H/FT8ahtu24/r4v8AEX8arNupbE5ZGb7U0x+L1btN0Lc/1Kgd+o+WTXXKSV3YsvNcjkN4YM8HZvsRTSeWhDUz77wxDhFJ4ymGDP8AiuG91M33TtDwNvEfFc1YstgW8JzFBDGe1IkU+YGaTnUnPj5fkqlKTM9FvPdz/wDDwKB1ORJIPYzCJD7GaucG5k80okvJySOQRssM8xGQAkI70Bb69bM19JGScAZJqu3Ahl5leyskiRY4kCovBVUcB+J7+unthszHpPz6h2ePfXWx2eE4ni3w8KuU5TpW1kK1a1+zEKKKKvFiazu9248G0AhkLpImQkkZGoA4yrAghlyAcEdVaKiglGTi7xdmeXx/Il6XpXrlexYI1b94sw91P7H5KLCP143mPbNIzD9xcKfaK2NFcyovni69RWlNv6sWwbuW8a4ihjiH9kip/KK4T7IYer6Q8jTmioSpxluVQqyjsZhkIOCCD31FaWWFWGGAPjVCfYw+Ycdx5edUSotbDUcRF76Cmius1qyesPb1edcqpatuXpp7HxJEG5iqsuz/AKJ9h/GrtFSjOUdiak0KJIivMYr4pyRVeSxU8uHw8qYjXXEmp8xdRVh7Jh3+FcGUjmKvUk9mTTTIoooqR0KKK+lQnkCa4B80VYjsWPPh41bitAvee/8ACqpVYoi5JFa2s88W5dnbV8CiilJzcnqVNtk0VFd7W0MhwOXWeyopX0RBtJXZ8wQFzhR/l407tLIRjtPWfw7q6W9sEGB7e/xrrTlOnl1e4jVquWi2CiiirSgKKKKACioooAmioooAmioooAmioooACKqT7MRuXonu/CrdFcaT3JKTjsJJ9luvL0h3c/KqZFaeuU1qr+sAe/r86olQXAYjiH8xnaKZT7GPzD7D+NUJbdl9YEf67aolBx3GY1Iy2Z8VFFFQJnyYl7B5VH5Ov0R5V90V3Mztz5EQ7B5Cvqiii5wmooorgBRViCxduQ4dp4CmVtslV4t6R93l11ZGnKRXOrGJQstnl+J4L29vhTuKIKMAYFfVFNwgoiNSo5k0VFFTKyaKiigCaKiigAqaKKACiiigAooooAKKKKACiiigAooooAKgiiigCvJs9D80Dw4fCq77FXqYjyNFFQcIvgWKpJbMpzbP0/O93+dVmTFFFKzik9B2nJyWpKRZq5DsvV873f50UV2nFPcjVm47FlNjIOZJ91WorNF5KPifM0UU0oRWyE3OT3Z1oooqRAKmiigCKKKKACiiigAqaKKAP//Z" /></div>Some other ideas:<br />How quickly do fruit / veggies appear on our plants?<br />How long does Mummy actually need to spend doing jobs instead of playing with us?<br />When does it get dark each day?<br />How much of the different types of food do we eat each day?<br /><br />Here's a brief 'what to do next'<br /><br /><ol><li>Once you have an idea you need to turn it into a question to investigate.</li><li>Discuss with your child how you can do this including what info you need to gather and how often</li><li>Together create a chart to gather the info on</li><li>Gather the info you need over whatever time frame you decided on - most helpful is a week</li><li>Look at the info you have gathered and discuss how this can be recorded to best show the results for discussion</li><li>Discuss what the results show</li><li>Answer your original question</li></ol><div>You could extend this activity to the computer and have a go at some graphing software together. Please can I ask that you do it on paper first as the exercise of having to sit and draw a graph really helps develop that understanding. Remember children are practical learners and they learn so much more through doing something than just being told about it or watching it happen. The computer is a fun extension.</div><div><br /></div><br />I hope you have fun with this activity and thoroughly enjoy exploring and investigating something together and coming up with an answer<br /><br /><b>Preschool</b><br />Keep it simple and interesting with these small people. A basic tally and then a very simple pictogram is all these children need, they will love exploring and finding out the info. Doing the counting of the tallies and moving that info to another graph will keep them busy and teach them how we can investigate something and record the results in a very simple way. (When tallying you can either do the proper tally in 5's or you can just do lots of lines without going in 5's. This depends on your child and what would work best for them )<br /><br /><b>5, 6 and 7 year olds</b><br />Hopefully you can tally properly with these children (what a great way to follow on from last weeks counting) and when you write up the data you could use a simple block graph or a pictogram or both. Really look at the info with them and make sure they understand how the data worked, and that they clearly understand where the answer came from. They should be able to answer simple questions around their data. You could always do the analysis on the computer with them too.<br /><br /><b>7, 8 and 9 year olds</b><br />These children should easily be able to tally and gather their information. Where you are going to challenge these is in the analysis. When they do the graph they should be able to do bar charts where the intervals are counted in 2's or 5's or a pictogram where the picture represents either 2, 5 or 10 or something. Really try to push their understanding of the data by asking lots of questions and maybe getting them to make some predictions. Again computer graphing could be fun.<br /><br /><b>9, 10 and 11 year olds</b><br />Before any data is gathered start by encouraging your child to make a prediction of the results. Then gather the data using a tally chart. When looking at the data these children can really extend their knowledge of graphs. As well as pictograms they can do bar charts, line charts and pie charts. A good discussion here is which is the most appropriate for your set of data and why. Once they have graphed their information as well as answering basic questions these children need to be encouraged to know what the mean, mode, median and range of their data is. Then when you ask them about their data and discuss it really push those questions and encourage them to answer the question but also be able to explain why they came up with that answer.</div>Charlotte Haywardhttps://plus.google.com/101613062113924736341noreply@blogger.com0tag:blogger.com,1999:blog-5343833198242744295.post-34071993480216613642015-06-16T20:13:00.004-06:002015-08-27T20:31:19.028-06:00Number sequencesThis week I thought I'd look at one of the more obvious places to help your children at home: Times Tables!<br /><br /><div style="text-align: center;"></div><br />Some of you will read this and want to close the page as it doesn't sound very interesting and you may or may not have already tried times table learning. Please don't close the page, please take the time to read what I say, it will really help your child.<br /><br /><a href="https://www.blogger.com/blogger.g?blogID=5343833198242744295&pli=1" imageanchor="1" style="clear: right; float: right; margin-bottom: 1em; margin-left: 1em;"><img alt="Image result for numbers" border="0" 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" style="cursor: move;" /></a>When I mention times tables I know people can experience a whole range of emotions. Some people love them and get quite excited when this subject is brought up because it's one place they can shine at maths. Other people, however, start to feel absolute dread and fear when times tables are brought up because of the pressure they feel at needing to come up with answers straight away. Then there are the teachers who all have their own opinions on times tables and where they fit within maths teaching!<br /><br />Back in the day, when I taught full time, I did teach times tables but I taught them as a sequence of numbers rather than a list of multiplications. The reason behind this is I feel very strongly that students gain much more confidence within maths and therefore improve their ability when they have a very good number agility. If they can play with numbers then they have the number knowledge to build on when learning new concepts.<br /><br />In all my years of teaching maths I found that the children that found maths difficult were the ones that were really unsure of their number skills. The problem they have then is that when learning a new concept they are so busy trying to do the simple number manipulations that they are unable to keep up with learning how the new concept works. When tutoring these children I would initially focus on their number skills and it was amazing to watch them grow in confidence and ability.<br /><br />So, back to the number sequences, if your child can mentally count in 2's, 3's, 4's, 5's etc. then they have the ability to work almost anything out.<br /><br />When teaching these number sequences I would ask the child to work out the sequence with me and write it out on the white board or piece of paper etc.<br /><br />2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24<br /><br />Then we would play games that involved reciting the sequence of numbers. I would always do this with the correct sequence in front of the child. This is so they learnt the correct sequence. It takes the pressure off the child and their ability while they are learning and it means the correct pattern is absorbed by the brain. If they are constantly reciting a sequence incorrectly then it will take much longer to learn.<br /><br />Once the sequence was learnt then we would play with those numbers and look at the patterns that happen as we go through the sequence and really learn about how this sequence works and then take the sequence further mentally. For example when looking at counting in 7's we would break up how the addition is done. Most times instead of adding 7 we would then add two numbers: 7 to 14 we would do the sum 7 + 3 + 4 = 14, then to 21 we would do 14 + 6 + 1 etc. to really look at how those numbers work. When looking at counting in 3's we would look at how the number sequence repeats itself 3, 6, 9 ........33, 36, 39.<br /><br />For those people that do like to have the times tables known we would link it back. I would encourage the child to use their fingers and for every number they said in the sequence put another finger up. For example if I wanted the child to tell me 4 x 5 I would ask them to count in 5's and for each number hold a finger up so when 4 fingers were up they knew they had the answer to 4 x 5.<br /><br />There you have the gist of how I teach times tables and some of my reasons for this method. Below I have listed some games and activities to do to help learn the sequences and below that I have differentiated for each group as normal.<br /><br />Please, have a go. This is great for number confidence for weaker mathematicians and also a fab activity for extending the knowledge and understanding for those stronger mathematicians. I guarantee your child will have better number knowledge if you start learning a new number sequence each week and spend 5/ 10 minutes each day playing with it.<br /><br />Enjoy!!<br /><br /><br /><b>Throwing a ball</b><br />Play catch with your child and as you throw the ball say the first number in the sequence and then your child will say the next number when he / she throws it back (have the sequence written somewhere you both can see it - mirror, window)<br /><br /><b>Marching</b><br />March around a space and every time you put a foot down say the next number in the sequence (you could get your child to do this on their own but it's much more fun to both do it)(have the sequence written somewhere you both can see it)<br /><br /><b>Marching up and down the stairs</b><br />Like just marching but up and down the stairs and when you step on a new step you say the next number in the sequence.(have the sequence written somewhere you both can see it)<br /><b><br />Hand tapping</b><br />Tap hands on a table or another surface that makes a noise and every time you tap say a number in the sequence.(have the sequence written somewhere you both can see it)<br /><br /><b>Writing</b><br />Get your child to write the sequence on something they are not normally allowed to write on. For example: a white board (with a white board pen), a mirror (with a whiteboard pen), a glass table top if you have one or anything else that can be written on and cleaned off but gives a feeling of fun and excitement while doing it.<br /><br /><b>Saying numbers in a funny way</b><br />Encourage your child to say the sequence in different voices. You could say the first number in a loud voice and child has to copy with the next number. Then you could use a quiet voice, a squeaky voice, low pitched voice, growly voice.........<br /><br /><b>Talking to a teddy (or any other stuffed animal)</b><br />Ask your child to teach teddy a particular sequence. Or you could just get child to count with teddy - to make this even more fun you could join in too.<br /><br /><br /><b>Pre-school</b><br />The best number sequences to work on with these little people are:<br />Basic counting up as far as you can go<br />Counting backwards from 10 and then maybe 20<br />Counting in 2's to 20<br />Counting in 10's to 100<br /><br /><b>5, 6 and 7 year olds</b><br />Counting forwards - always worth practicing<br />Counting backwards - from any number below 100 <br />Counting in 2's - as far as they can<br />Counting in 2's - but odd numbers<br />Counting in 5's - can they get to 50 or 100?<br />Counting in 10's - how far can they get?<br />Counting in 3's - up to 36 initially<br />Counting in 4's - up to 48 initially<br /><br /><b>7, 8 and 9 year olds</b><br />Counting forwards - always worth practicing<br />Counting backwards - from any number below 300 <br />Counting in 2's - as far as they can<br />Counting in 2's - but odd numbers<br />Counting in 5's - can they get beyond 100?<br />Counting in 10's - how far can they get?<br />Counting in 3's - up to 36 initially<br />Counting in 4's - up to 48 initially<br />Counting in 6's - up to 72 initially<br />Counting in 7's - up to 84 initially<br />Counting in 8's - up to 96 initially<br />Counting in 9's - up to 108 initially<br />Counting in 11's - up to 132 initially<br />Counting in 12's - up to 144 initially<br /><br /><b>9, 10 and 11 year olds</b><br />Counting forwards - always worth practicing<br />Counting backwards - from any number <br />Counting in 2's - as far as they can<br />Counting in 2's - but odd numbers<br />Counting in 5's - can they get beyond 100?<br />Counting in 10's - how far can they get?<br />Counting in 3's - how far can they get?<br />Counting in 4's - how far can they get?<br />Counting in 6's - how far can they get?<br />Counting in 7's - how far can they get?<br />Counting in 8's - how far can they get?<br />Counting in 9's - how far can they get?<br />Counting in 11's - how far can they get?<br />Counting in 12's - how far can they get?<br />Can they start counting in any of the numbers above but starting from a different starting number eg. count in 6's starting on 2.<br />Counting in 13's<br />Counting in 15's<br />Counting in 25's<br />Counting in square numbers<br />Counting in triangular numbersCharlotte Haywardhttps://plus.google.com/101613062113924736341noreply@blogger.com0tag:blogger.com,1999:blog-5343833198242744295.post-36056554895614765572015-06-09T20:52:00.001-06:002015-06-09T21:00:46.809-06:00Fun with waterSummer has definitely arrived here in Colorado which has inspired me to use water play for this weeks activity.<br /><br /><div style="text-align: center;"></div><div style="text-align: center;"><img alt="Image result for water play images" src="data:image/jpeg;base64,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" /><br /><br /></div>Capacity is an area that can be difficult to teach in school. Ideally you want to give the children lots of containers and lots of water and just let them explore, while you, as teacher, hover in the background prompting their exploring and learning. Take a class of 24 +children and a classroom full of books, art work and many other piles of things to keep dry and you can start to see why this idea may not always be a sensible one in the classroom.<br /><br />However, take a sunny day, one or two children and a garden that loves water and this activity can be lots of fun.<br /><br />So, ready for some fun?<br /><br /><b>You will need:</b> lots of containers of varying shapes and sizes, these could include spoons, bowls, cups, plastic boxes, buckets etc.<br /><br /><b>Location:</b> Best place for this to happen is outside but it can be done in the kitchen or bathroom<br /><br /><b>Activity:</b> Set your child / children up in the garden with lots of containers and several buckets of water or a paddling pool full. Encourage your child to play with the water and containers. Tip water from one container to another. Count how many of one container may fit into another. As your child plays then your job is to prompt with thoughts, ideas and suggestions.<br /><br /><b>Preschool</b><br />The best way of doing this activity with these little munchkins is to give them as many different sized containers as you have and do lots of comparisons with them. There are two main objectives for this age range. The first one is to expose your child to the language of capacity; capacity, volume, biggest, smallest, more, less, least. The other objective is to introduce the idea that liquid can fill a container and different containers hold different amounts. If you do have a measuring jug and / or spoons then briefly introduce these with their units of measure and ensure you include these as you play.<br /><br /><ul><li>Which container is the biggest? So, which container holds the most liquid?</li><li>Which is the smallest contained? And therefore holds the least liquid?</li><li>If we tipped the contents of this contained into that one, how many times do you think we would need to do that before it was full? Let's see if you're right.</li><li>Can you estimate how many of these will go into this container? Let's see if your estimate was right? </li><li>If I tipped this half empty cup into this bucket as one of the cups we are measuring can we count it? Why not? What do we need to make sure we do with every cup before we tip it in?</li></ul><div style="text-align: center;"><img alt="Image result for water play images" src="https://encrypted-tbn1.gstatic.com/images?q=tbn:ANd9GcTfj_NexWFjJ154cnI6s3R2v9q0sJl_zwPUugdh9fLfYAAV5guC_w" /></div><br /><b>5, 6 and 7 year olds</b><br />These children are starting to use units of measure and therefore using equipment with units of measure marked on. When using measuring jugs it is useful for them to understand and know what the scale sare on the side but they only need to be able to work with litres, half litres and quarter litres to begin with.They also need to be able to compare different containers and amounts of liquid. It is very important that they understand that when measuring we have to use a full unit of whatever that unit may be.<br /><br /><ul><li>To warm up and get going I would use the questions for the preschool children and then extend into these questions:</li><li>If I tipped this half empty cup into this bucket as one of the cups we are measuring can we count it? Why not? What do we need to make sure we do with every cup before we tip it in?</li><li>Shall we use the measuring jug to measure roughly how much is in this cup?</li><li>Why don't we estimate how much is in this pot and then measure to see if we are right?</li><li>How many litres are in this pot? </li><li>If I used two of these pots how many litres of water would I have altogether?</li></ul><div style="text-align: center;"><img alt="Image result for water play images" src="https://encrypted-tbn2.gstatic.com/images?q=tbn:ANd9GcTPe-U7wQ-KhUmVxgnLXjqHUXAA9uHUUmwWhPhg707Kc-A0SztG" /></div><br /><b>7, 8 and 9 year olds</b><br />With these children we should be starting to really use the units on the side of measuring jugs in details. They need to understand litres and millilitres and be aware of the other units too. An extension that is good for these is to use part litres and discuss the quantity in litres so using the decimal point. These children also have the knowledge and ability to start to mulitply amounts and play with the numbers a little more. It is very important that they understand that when measuring we have to use a full unit of whatever that unit may be.<br /><br /><ul><li>To warm up and get going I would use the questions for the previous two groups children and then extend into these questions:</li><li>If I tipped this half empty cup into this bucket as one of the cups we are measuring can we count it? Why not? What do we need to make sure we do with every cup before we tip it in?</li><li>How many of these cups do you think will go into this big pot? Why? (needs to be a well thought answer, not just a guess). Let's measure the capacity of the cup and then work it out and see if you were right? Let's do it and check our calculations were right?</li><li>How much water does this bottle hold? Can you tell me in ml? and now litres?</li><li>If this many cups go into this pot and this pot goes into this bucket 2 times, how many cups will go into the bucket?</li></ul><div style="text-align: center;"><img alt="Image result for water play images" src="https://encrypted-tbn1.gstatic.com/images?q=tbn:ANd9GcRhqs-Gce6blO9KmfxSWu326j7tj57tX9WyqsAujCn4k2xHdwS6cg" /></div><br /><div style="text-align: center;"></div><b>9, 10 and 11 year olds</b><br />These children generally need a lot of consolidation on capacity. In school they will now be solving problems using capacity but may not have the practical skills and knowledge to be able to solve these well. My advice here is to use the previous groups questions and have lots of fun answering those and playing with capacity. Include lots of practice with those measuring jugs and make sure you have a go with all possible units of measure.<br />If your child proves to be confident at this and / or is ready for more throw some fun problems at them that you can have fun solving together.<br /><br /><ul><li>The outside tap drips at a rate of 1 drip, every two seconds. How long will it take to waste a bucket of water?</li><li>A young friend / cousin has been playing with the water table? How much water has she / he wasted during the course of the day?</li><li>The plants need a cup of water each morning and evening. How much water does it take to water the plats each day?</li></ul><br /><br /><br />Charlotte Haywardhttps://plus.google.com/101613062113924736341noreply@blogger.com0tag:blogger.com,1999:blog-5343833198242744295.post-64759428906765265732015-06-02T21:24:00.003-06:002015-06-02T21:24:40.101-06:00Let's get creative with 3D shapesWhen helping your children with maths at home how often does some 3D shape work feature? I sometimes feel that it can slip off the radar and not always be looked at. When our children are little we spend a lot of time going over basic shapes but as they get older we tend to focus more on numbers and forget the other aspects of the subject.<br /><br />Shape is as important as the number work and is much more effectively taught if done little and often. Children know the shape names but often don't get enough practice at looking at those shapes and putting names to shapes so end up with a vague knowledge on something that should be secure.<br /><br />As a parent it is always useful to bring shapes into the conversation on a regular basis. Sometimes just identifying different shapes and giving them names, whether it be 2D or 3D. Another time you could focus on one shape and discuss the properties. For example: choose one shape and spend a day identifying it where ever you go and asking 'what makes it that particular shape?' Why do you think it's a ...?'. Nothing too serious or heavy, just simple identification to keep the knowledge of shapes fresh.<br /><br />Anyway I thought this week would be a good week to do something with 3D shapes.<br /><br />The activity is going to start off the same for all ages:<br /><br />make a 3D shape!<br /><br />I have attached various shape nets so you can use these to get started:<br /><a href="https://docs.google.com/document/d/1nMd30VffzttBaQzwCPCyBv8D7eXxyoAFBWClJRaRH1g/edit?usp=sharing" target="_blank">Cube</a><br /><a href="https://docs.google.com/document/d/179Uzz_ELYd6r4-r8Hocr8KHJu4R0Mreat85z0WAIV0o/edit?usp=sharing" target="_blank">Alternate cube</a><br /><a href="https://docs.google.com/document/d/1mJwG-P9pJwyvRjlfdh4dLPOIUwijEcK61qwxpwPsAVc/edit?usp=sharing" target="_blank">Alternate, alternate cube</a><br /><a href="https://docs.google.com/document/d/13QgG5Rifd86KYu2o-l6kf5RhaSrsosTko3pUNo7GuSU/edit?usp=sharing" target="_blank">Rectangular prism / cuboid</a><br /><a href="https://docs.google.com/document/d/1Y92_vLDzzVRG9J2YaLj43WrU0bpwZUpQHsEZrgIzWRk/edit?usp=sharing" target="_blank">Cylinder</a><br /><a href="https://docs.google.com/document/d/12jb3t4u40UC8KcQEb_nvVzGj8mw6WyWNbW3INQkSF3Q/edit?usp=sharing" target="_blank">Triangular Prism</a><br /><a href="https://docs.google.com/document/d/1nVgcBAuq6uVLc_dBCr4gGVMARFMgU9ntEJLHu55q3XI/edit?usp=sharing" target="_blank">Pentagonal Prism</a><br /><a href="https://docs.google.com/document/d/1MyhryAEOmStdltprS2wwHUN8j-F6HKeBfmjsir2zWFw/edit?usp=sharing" target="_blank">Tetrahedron</a><br /><br />On this activity the differentiation comes in with each individual child and their interests and abilities. Some children love the creativeness in making the net, others love the arty, crafty decoration at the end etc. Below I have listed some different ways you can make this activity fun, interesting and mathematical for your child. Choose the variation that you and your child will get the most from and then alter it according to your child's age, ability and enthusiasm! Generally these activities become increasingly more difficult and challenging so my advice would be Pre-school for the first one and much older children for the last but they can all be tweaked and altered to suit your child.<br /><br /><br /><ul><li>Talk about different 3D shapes, including some comparisons. Discuss which is your childs favourite shape and then make a model of that shape together. As you go discuss how the net works and the properties of the shape. Let your child have fun decorating it once it is complete. You could do a cube / cuboid and make it into a little treasure box for them.</li></ul><br /><br /><br /><ul><li>Cut out and score along the folds of three different nets for the same shape. Demonstrate to your child how one of these can be folded together to make a shape and then see if they can fold the other two. Let them play with all three for a while and just explore how they work. An extension for an older child might then be to create their own net for the same shape.</li></ul><br /><ul><li>Make nets for three cubes, each one slightly bigger than the previous. Together fold the nets and make the shapes. Once the shapes have been made explore them together. Talk about their differences and similarities, the number of faces, vertices and edges. A final activity you can do here is to decorate. Stack them one on top of the other and draw four different faces on the outward faces of the top one, four different bodies on the middle faces and four sets of feet and legs on the bottom faces. Twist and turn and have fun creating people!</li></ul><br /><ul><li>Make nets for three prisms the same apart from that each one is slightly bigger than the previous. Fold and make the 3D shape for each one and then, as in the above activity, spend time looking at the different shapes and compare using the language of shape. This is a great activity for developing an understanding of prisms, which can be quite difficult. Once they have compared the prisms then ask your child to create their own net for a similar prism.</li></ul><br /><ul><li>Go shape hunting around the house and see what interesting 3D shapes you can find. Encourage your child to choose their favourite and try to recreate it. For younger children, obviously you would need to provide the basic net but older children could have a go at creating their own net to recreate the shape.</li></ul><br /><ul><li>For older children a favourite activity from my classroom days was to do a little bit of warm up work on nets to remind them how they work. Then I would give them a piece of cardboard and tell them to go and make any 3D shape they chose. This was such a creative and fun activity. At the same time it was really good in encouraging children to learn about 3D shapes and their nets.</li></ul><br /><div style="text-align: center;">Have fun with your shapes this week</div><br />Charlotte Haywardhttps://plus.google.com/101613062113924736341noreply@blogger.com0tag:blogger.com,1999:blog-5343833198242744295.post-69282351827376116552015-05-26T21:07:00.001-06:002015-05-26T21:07:12.392-06:00Scavenger HuntingHave you ever done a mathematical scavenger hunt?<br /><br />If you haven't here's your chance and if you have enjoy doing another.<br /><br />This weeks activity follows the same guidelines as any other scavenger hunt: find the objects listed on a piece of paper.<br /><br />The difference between this and any other one though, is this is mathematical. I love this kind of activity because it's maths, it's fun, it can be done outdoors and it requires a little bit of imagination. ie. it's not always obvious and can require some thinking 'outside the box' which is great practice for any young, budding mathematician.<br /><br />For those that have not heard the expression ' thinking utside the box' it means that where maths is completely literal this is not and is sometimes going to take a little bit of thinking with imagination - which is not always easy for young mathematicians.<br /><br />For example one of the objects could be 'Find a double'. This tests your childs understanding of double but let's them have some fun with it. They might find two trees stood next to each other (double 1), they might find 2 plants, each with 3 flowers (double 6) etc.<br /><br />So, this week, as normal, I have broken the activity down into the four age ranges and produced a list of objects for each group.<br /><a href="https://docs.google.com/document/d/103uItW7P5FSTkYhrGmUKt9eR4LiPLnTHbYB7NgSbqPE/edit?usp=sharing" target="_blank">Preschool</a><br /><a href="https://docs.google.com/document/d/1em1zZyBWK_wSVZeXtnsdQESKq_vveGNlWkjn_TiqhL8/edit?usp=sharing" target="_blank">5, 6 and 7 year olds</a><br /><a href="https://docs.google.com/document/d/1uGOykxHHFXm_FHSHp3trtiqpoOHJzu2-5p2_zGwTxQM/edit?usp=sharing" target="_blank">7, 8 and 9 year olds</a><br /><a href="https://docs.google.com/document/d/1z6ZeVIfxVTgFMpXnh2fA1l5goGAMUHSlWI9SB3cisl0/edit?usp=sharing" target="_blank">9, 10 and 11 year olds</a><br /><br />Please remember these age ranges a wide so you may need to alter the sheet (create another document with it and then alter it however you like).<br /><br />My advice would be to start the hunt together and discuss what was found to tick a particular item off the list. With the older children you could then give them a time limit and get them to complete the rest of the sheet on their own and then go through it afterwards. You could always invite a friend round for your child and get them to do the hunt together.<br /><br />I would suggest that for the younger children you work through this together, discussing and having fun.<br /><br />A final suggestion: you could bring a camera with you or send older child off with a camera and take pictures of each item and then discuss the pictures together the next day.<br /><br />I envision this happening outside but if you are stuck inside on a wet day I think this could be lots of fun to do round the house.<br /><br />Enjoy!Charlotte Haywardhttps://plus.google.com/101613062113924736341noreply@blogger.com0tag:blogger.com,1999:blog-5343833198242744295.post-36419596806476431202015-05-18T22:28:00.003-06:002015-05-18T22:28:44.215-06:00CookingThose that know me well have probably been wondering how long it will take for cooking to appear in one of my posts. I love cooking, mainly baking, and spend a lot of time creating things in the kitchen with the children, using the excuse that it's educational. So, in order to justify my claims, I thought I would look at how we can make cooking educational for this weeks activity.<br /><br />I'm assuming many of you may do cooking with your children and already pull out the educational opportunities without realising it. Others of you may cook but, like me, are often in a rush so don't manage to make it as educational as it could be and, I suspect, there are others out there that avoid the kitchen with the children.<br /><br />For those that already cook with your children I'm sure you have lots of good recipes that you already use and have fun with. For those that don't get in the kitchen much or need some inspiration I will add two of my favourite 'cooking with children' recipes to the end of this post. We regularly make Shortbread biscuits, courtesy of Delia Smith, and the other 'go to' for us is a basic sponge cake. These recipes are simple, fun to do with all ages, have the flexibility to pull out all sorts of mathematical learning and produce tasty treats.<br /><br />Living in the US I am slowly learning to cook with cups and finding the conversions very interesting! However, in the interest of mathematical learning I would like to encourage everyone to use scales for this exercise, if at all possible. There is a lot more maths involved in weighing ingredients out, multiplying recipes using the weights rather than the cups and understanding how capacity, weight and measure all work. I know this isn't always possible but if it can be done I would recommend it (I have spare scales if anyone local wants to borrow them). Please anyone that is using scales, weigh your ingredients in grams and kilograms. This is the standard measure recognised across the UK now and what children in the UK are taught at school.<br /><br />Rather than break this weeks learning into age groups I am going to work through the process logically and discuss the different ways you can be mathematical as you work through your recipe.<br /><br /><b>Weighing</b> - the most obvious activity with cooking is to weigh and measure the ingredients. This can be done right from little children up to big children with varying levels of expectation. My daughter (4 yrs old) spoons the ingredients in until I screech stop and then we talk about what the scales say. With older children, you can ask them to spoon in the ingredients and to monitor themselves how much they are putting in.<br /><b><br /></b><b>Measuring</b> - a lot of recipes use liquids and this again is another great thing for the children to do. This can work from asking them to pour, while you monitor the amount or vice versa, asking them to monitor the quantity while you pour. Or they could do both. Sometimes only small quantities are used and you need measuring spoons. We have fun counting the number of spoonfuls that we need as we put them in. An older child could count the quantity that has gone in, rather than the number of spoonfuls. eg. 15ml, 30ml, 45ml.....<br /><br /><b>Converting Units</b> - I mentioned above that all weighing should be done in grams and kilograms but if you have an older child (9, 10 or 11) they can really benefit from being aware of other units of measure, being able to work in them and converting the units. One day you could try cooking but using pounds and ounces. A step further would be to get them to convert a recipe from grams to ounces. This is difficult and will need support but can be fun. You could also convert between grams and cups. I have found this particularly interesting. If you're really keen and have lots of time then try cooking a recipe using grams and then cooking it again using cups and see if the results are the same. If they're not the same, a really fun extension of this would be to then play around with the conversions until you can get the two recipes to create the same product.<br /><b><br /></b><b>Filling the pans / tray</b> - this is always fun time to get mathematical. When we put the shortbread onto the trays we always do some kind of counting / adding exercise. You could just count them. Or you could count them in twos or threes etc. Or, like we did today, we counted both baking trays and added together how may we had.<br /><br /><b>Time</b> - When your product is cooking you can time it in various ways to help the maths. With little ones I would encourage them to set a digital timer, if you have one. This is fun for them and is starting to give them an awareness of time. With older children look at what time it is and ask them to calculate what time the cooking will be complete. With children not quite ready to do this on their own you could work it out with them.<br /><br /><b>Sharing out the finished product</b> - this can be a great fractions activity, particularly with a cake. I'm assuming you're not going to eat the completed cake / shortbread / other tasty bites in one sitting but you could have a really good discussion on how you would divide it if you were going to and how many others were going to join you or if it was to be split between the same number of people but over two sittings........<br /><br /><b>Changing the recipe</b> - once you have made your cake / cookies / something else there is much fun to be had in creating variations. I've mentioned some possibilities for these under each recipe but ask your child for ideas too. Once they've decided how they want to alter the product then they need to decide how much of the extra ingredient they need. This could be as simple as you pouring and asking your child to call stop when they think there is enough and then weighing to see how much that was. Or you could make it really mathematical and ask your child to work out what quantity they think would be appropriate. You could even turn it into an experiment and make several batches to decide. Some fun mathematical thinking.<br /><div style="text-align: center;"><span style="color: #674ea7; font-family: inherit; line-height: 1.38; white-space: pre-wrap;"><br /></span></div>Sometimes an activity like this may not look particularly complicated or difficult and, as parents, you want something to challenge your child. This may not challenge in the way that number equations will but it will give them much needed practical experience with measure and capacity and throw in some good old life experience. Also, it will meet my aim, to make maths fun and enjoyable and to show children it can be this and not always working in a book. Please enjoy your cooking this week. I would love for you to share any recipes that you love to cook with your children or to see some photos of you doing some mathematical cooking added in the comments.<div style="text-align: center;"><span style="color: #674ea7;"><span style="line-height: 22.0799999237061px; white-space: pre-wrap;"><br /></span></span></div><div style="text-align: center;"><span style="color: #674ea7; font-family: inherit; line-height: 1.38; white-space: pre-wrap;"><br /></span></div><div style="text-align: center;"><span style="color: #674ea7; font-family: inherit; line-height: 1.38; white-space: pre-wrap;"><br /></span></div><div style="text-align: center;"><span style="color: #674ea7; font-family: inherit; line-height: 1.38; white-space: pre-wrap;"><br /></span></div><div style="text-align: center;"><span style="font-family: inherit; line-height: 1.38; white-space: pre-wrap;"><b>Shortbread Cookies</b></span></div><span id="docs-internal-guid-15c54745-6a56-08af-468a-251388339264"><span style="font-family: inherit;"><br /></span></span><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; font-style: normal; font-variant: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-family: inherit;">150g plain flour (For anyone American that is All Purpose!)</span></span></div><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; font-style: normal; font-variant: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-family: inherit;">100g butter or marg</span></span></div><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; font-style: normal; font-variant: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-family: inherit;">50g caster sugar (For anyone American that is granulated sugar)</span></span></div><span style="font-family: inherit;"><br /></span><ul style="margin-bottom: 0pt; margin-top: 0pt;"><li dir="ltr" style="background-color: transparent; font-style: normal; font-variant: normal; list-style-type: disc; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; font-style: normal; font-variant: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-family: inherit;">Cream butter and sugar together.</span></span></div></li></ul><ul style="margin-bottom: 0pt; margin-top: 0pt;"><li dir="ltr" style="background-color: transparent; font-style: normal; font-variant: normal; list-style-type: disc; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; font-style: normal; font-variant: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-family: inherit;">Work in flour</span></span></div></li></ul><ul style="margin-bottom: 0pt; margin-top: 0pt;"><li dir="ltr" style="background-color: transparent; font-style: normal; font-variant: normal; list-style-type: disc; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; font-style: normal; font-variant: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-family: inherit;">Roll out mixture until Â½ inch thick and cut out with cookie cutters</span></span></div></li></ul><ul style="margin-bottom: 0pt; margin-top: 0pt;"><li dir="ltr" style="background-color: transparent; font-style: normal; font-variant: normal; list-style-type: disc; vertical-align: baseline;"><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; font-style: normal; font-variant: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-family: inherit;">Place on a large baking tray.</span></span></div></li></ul><ul style="margin-bottom: 0pt; margin-top: 0pt;"><li dir="ltr" style="background-color: transparent; font-style: normal; font-variant: normal; list-style-type: disc; vertical-align: baseline;"><span style="background-color: transparent; font-style: normal; font-variant: normal; vertical-align: baseline; white-space: pre-wrap;"><span style="font-family: inherit;">Cook on 150Â°c / 300Â°f / gas mark 3 for about 30 minutes, until the cookies are turning golden</span></span></li></ul><div><span style="white-space: pre-wrap;"><br /></span></div><div><span style="white-space: pre-wrap;">Once you've mastered the basics you can make these more interesting by adding chocolate chips, dried fruit, nuts, spices............</span></div><br /><br /><div style="text-align: center;"><b>Basic Sponge Cake </b></div><br />113g caster sugar (granulated sugar in the US)<br />113g butter or marg<br />2 eggs<br />113g self raising flour (self rising in the US)<br />(if you're living at altitude, like me, then you will need to add about 100ml of milk and cook for longer)<br /><br /><br /><ul><li>Cream butter and sugar together</li><li>Beat in the eggs one at a time</li><li>Fold in the flour</li><li>Divide the mixture between two small sandwich tins</li><li>Cook on 180<span style="white-space: pre-wrap;">Â°c / 350</span><span style="white-space: pre-wrap;">Â°f / gas mark 4 for about 20 minutes, until cake is golden, coming away from the edges of the tin and springs back when gently pressed.</span></li></ul><br /><span style="white-space: pre-wrap;"><br /></span><span style="white-space: pre-wrap;">Depending on the size of your tins you may need to increase this recipe. I do double this for my tins which are</span><br />Variations: chocolate (I add 100g melted chocolate and 20g cocoa to my doubled recipe), coffee, orange, lemon......<br /><br />Of course once you have made this cake you will need to ice it.......<br /><br /><br /><div style="text-align: center;"><b>Buttercream</b></div><br />113g butter / marg<br />225g icing sugar<br />drop of milk<br /><br /><br /><ul><li>Add all ingredients to a bowl and gently blend together.</li></ul><br /><br />Charlotte Haywardhttps://plus.google.com/101613062113924736341noreply@blogger.com0tag:blogger.com,1999:blog-5343833198242744295.post-15061479709464336192015-05-11T21:59:00.000-06:002015-05-11T21:59:03.402-06:00Bribery, a tidy house and a child that can work with money........So, who has longed for a house that can be organised and yet still be inhabited by children?<br /><br />What feels like many years ago I had a similar longing but it was for a tidy classroom. I had a class that were particularly messy and disorganised, as is fairly typical with year 5 (4th grade) students. At the time I worked in a school where we had three classes per year group and so myself and my colleagues put our heads together to try to solve this problem.<br /><br />The answer: The Belongings Shop!<br /><br />In essence what we did was to give each child some imaginary money (this particular year group had 10 pounds recorded on a sheet). Then, each time a child came to a lesson particularly well organised they were 'given' some money. For example, if someone arrived to the lesson with everything they needed and was sat ready with it we would verbally give them 50 pence. It was then the child's responsibility to record this on their sheet and get it checked by me or whoever was teaching them, by the end of the lesson, without interrupting the lesson. However, if a child was missing something they needed for a particular lesson then they were 'fined'. For example, if someone came to my maths lesson without their ruler then they would be fined 10 pence. Again it was then the child's responsibility to record this on their sheet and then get it checked.<br />We also used this for belongings that were left lying around. If they had been lying around long enough we would scoop them up and then 'sell' them back to the child for a small amount of money.<br />At the end of the half term (6 weeks) there would be small prizes for those children with the most money. Each child would then start with a fresh sheet for the new half term.<br />This was all done in a very light hearted manner and while doing it we were able to have fun with the children and laugh about it. It did get the message across though and, I felt, that year we had a year group that were very good a dealing with money and percentages (at the end of each week they were 'given' interest on the money on their sheets.)<br /><br />We found this was a fun, but practical way of learning about money that also helped to keep the children organised. From a maths teachers perspective, this was a great exercise to do as the best way to teach money is to get practical and actually play with money.<br /><br />I therefore thought that this could be adapted as this weeks activity, particularly in light of the approaching summer holidays and the chaos that then surrounds every household.<br /><br />Please note the idea behind this is to get practical and think about money and, therefore, the maths behind it. So any calculations here should NOT be done on a calculator. A lot of the learning will be lost if this happens, as it's easy and requires little thinking to put something into a calculator and copy the answer.<br /><br /><b>Preschool</b><br />These little people are only small and only just beginning to come to understand what money is and what it is used for. My instinct would be to use real money here as they are going to struggle with the concept of imaginary money plus the actual touching and playing with money will benefit them so much. So, before beginning this activity your quest is to gather pennies and I would gather lots, be prepared for a preschooler on a mission!!<br />I would start by giving your child 10 pennies in a pot and then talk to them about what they can do to gain more pennies and how they might loose pennies.<br />The activities I will leave up to you but keep it light and fun. I suspect I might give her pennies if she puts things away but she looses them if I find her things lying around. Please don't turn this into a behaviour management system, it is supposed to be fun and lighthearted.<br />We will probably do this for a couple of days maximum, I don't want her to get bored and disheartened.<br />To make the maths work for these people I suggest that periodically throughout the day you can sit with them and count the pennies they have and maybe discuss how many they might have had if they hadn't lost 'x' or how many they could have had if they had lost some. This can be a very practical discussion on simple addition and subtraction using the coins to help.<br /><br /><b>5, 6 and 7 year olds</b><br />Hopefully these children have an understanding of what money is and a basic knowledge of the coins and how much each one is worth. The older ones should also be starting to count in sequences of 2's, 3's, 5's etc. If your child has come across sequences of numbers and is starting to understand and manage this then I suggest using either 2 pence coins or 5 pence / cents. Like the preschool children I would use real money and not imaginary.<br />Again, I will leave it up to you to choose the activities you reward and fine. My thoughts run along the lines of belongings around the house and being organised for things. So give money for putting stuff away or being ready to go swimming with swimming bag etc. or take money away for leaving things lying around or not having the stuff needed to go somewhere.<br />Do this for a few days, not too many as it is supposed to be fun and not just endless. Then, periodically throughout the day sit together and count the money. This is great practice for counting in sequence. And, like the preschool children, a fab exercise in basic mental subtraction and addition if you discuss how many they might have had if they hadn't lost 'x' or how many they could have had if they had lost some. This can be a very practical discussion on simple addition and subtraction using the coins to help.<br /><br /><b>7, 8, and 9 year olds</b><br />These children should be pretty secure in their knowledge of money, coins and simple pound to penny or dollar to cents conversions. So, with these children, particularly the older ones, I would be tempted to give them a whole amount of pounds / dollars, maybe 5. But I would keep the rewards and fines simple to start off with, so multiples of 5 or 10. These children should manage imaginary money but I would recommend at this age using real money (or pretend if you have a stash or cut out paper coins if you have time....). I feel that they strongly need the visual to help with this.<br />Again, I will leave it up to you to choose the activities you reward and fine. My thoughts run along the lines of belongings around the house and being organised for things. So give money for putting stuff away or being ready to go swimming with swimming bag etc. or take money away for leaving things lying around or not having the stuff needed to go somewhere.<br />Do this for a few days, not too many as it is supposed to be fun and not just endless. Then, periodically throughout the day sit together and count the money. I suspect the hardest part of this for this age group will be taking away an amount from a whole pound. This is a difficult concept and why I suggest having real money on front of them. (If you find life is particularly busy and you don't want to focus on this then work in pence / cents (not pounds / dollars) and give them amounts in pennies - these could be quite high and you can just use this as an exercise on adding and subtracting but using numbers in the hundreds) If you do have time to sit and go over the taking away of small amounts from a whole pound / dollar then my advice would be to use pennies or 10 pence / cent pieces and very visually do this before slipping in some actual pounds / dollars.<br />You can also introduce the idea of interest at this point. I wouldn't get into percentages but maybe give them a penny for every pound / dollar they have at particular times during the activity.<br /><br /><b>9, 10 and 11 year olds</b><br />This was the age group we originally created this activity for. Start them with 10 pounds / dollars and make it imaginary but maybe also have a pot of money sitting on the side that they can use to help them with their calculations. When you reward / fine these children make sure it is obscure amounts of money like 27 pence or 53 pence so they really have to use their brains.<br />Again, I will leave it up to you to choose the activities you reward and fine. My thoughts run along the lines of belongings around the house and being organised for things. So give money for putting stuff away or being ready to go swimming with swimming bag etc. or take money away for leaving things lying around or not having the stuff needed to go somewhere.<br />With this age group you could run this for a week or more, depending on how it's going. Do remember to periodically check how much they have and maybe give them interest, every morning or week depending on length of activity.<br />If adding interest I would keep it simple. If they've heard the term percentages then they should have a basic knowledge that 1% of 100 is 1 and 2% is 2 etc. You could just give interest for whole pounds / dollars and ignore the extra pence / cents they have or, particularly the older ones could work the whole thing out with some help. My advice here is to gently suggest and proceed as long as your child is comfortable and seems to know what they are dong with a little guidance. I would recommend not pushing this part if your child is at all unsure as it can be quite a difficult concept to teach and trying to teach it to them at home may confuse what they are doing at school.<br /><br /><br />When you are finished doing the activity you could go out and let your mathematical child spend the money they earnt?<br /><br />So, there you go, a fun activity that could help you keep a tidier house. Please do remember that this is to be fun and light hearted and not a behaviour system.<br /><br />Many thanks and happy memories to Linda Wild and Di Jones, my amazing colleagues, for the fun we had with this 'system' of organisation!!<br /><br />Charlotte Haywardhttps://plus.google.com/101613062113924736341noreply@blogger.com0tag:blogger.com,1999:blog-5343833198242744295.post-22861238598218566322015-05-04T22:26:00.003-06:002015-05-04T22:26:47.261-06:00Measure, measure, measure......When it comes to maths many of us automatically think of numbers and don't always consider the other parts that make up the whole subject. Measure is a huge part of learning mathematics; it needs knowledge and understanding of numbers to be able to measure and then you need to be able to manipulate those numbers to complete measurement calculations.<br /><br />Over the years I have found the best way of teaching measure is to get out and do some practical work on it. There is only so much theory that you can go over with the children. What they actually need is practical practice in real life situations.<br /><br />Therefore I thought for this weeks activity I would set you all measuring and doing one of my favourite classroom activities.<br /><br /><b>You will need:</b><br />ruler / tape measure<br />post it notes<br />pen / pencil<br /><br />Once you have the above things ready it's easy. You and your child need to go round the house and measure as many things as you can with the ruler / tape measure. Once you have measured something the measurement needs to be written on a post-it and the post-it stuck on the item.<br /><br />For example: You might decide to measure the height of the toaster. Write that measurement on the post-it and stick it to the toaster.<br /><br />Once this gets going there are two ways you can follow this activity through.<br />1. You can either let your child go mad and post-it everything first and then do some discussion work after.<br />2. Or you can discuss each measurement as the post-it goes up.<br /><br />Generally I do number 1 as children love the whole post-it activity and need time to just have some fun with it.<br /><br />Once you're ready for the discussion part here's how it works:<br /><br /><b>Preschool</b><br />Most importantly with these little ones you want to be using a very basic measure that just has single numbers and no millimeters or fractions of inches. We have a very simple learning resources one that we use.<br />http://www.amazon.com/Learning-Resources-Simple-Tape-Measure/dp/B00B99ET4Y/ref=sr_1_1?ie=UTF8&qid=1430797163&sr=8-1&keywords=children%27s+tape+measure<br /><br />With pre-schoolers you are simply introducing the idea of measuring to them, encouraging them to start measuring at the beginning of the tape / ruler and recognising and writing numbers. This can be lots of fun, as for the main you are going to be playing with the tape measure. If I was doing this with my daughter I would really be focusing on the measuring and reading the tape measure and let the writing on the post-its take a secondary role. This may mean that what is on the post-it does not really resemble a number but they've had a go which is sometimes just as important.<br /><br /><b>5, 6, 7 year olds</b><br />Again, with these children I would stick to a simple tape measure that works with single digits and no fractions of units. They hopefully now understand the basic principles of measuring and have a good knowledge of reading and writing numbers. The main focus with these children is to really start to understand measure and what it means. So as well as measuring objects and recording this, a really good focus is to compare what you are measuring. As you go around the house pick an object and encourage your child to find another object in the house, that they have already measured, that is longer / shorter than the original object. Talk about why this is so and possibly bring the objects together to physically compare them. Once you've done this and if you're child is confident with these comparisons you could introduce the idea of predicting and ask your child to find an object they THINK is longer or shorter than a particular object.<br /><br /><b>7, 8, 9 year olds</b><br />I would encourage these children to use a ruler with the basic units on but showing the fractions of units too. Something like this for UK children:http://www.amazon.co.uk/Helix-Folding-Ruler-Shatter-Resistant/dp/B009NKV804/ref=sr_1_5?ie=UTF8&qid=1430798142&sr=8-5&keywords=ruler<br />and this for American children: http://www.amazon.com/Westcott-Non-Shatter-Ruler-Inches-13862/dp/B00309RVJ6/ref=sr_1_1?s=office-products&ie=UTF8&qid=1430798199&sr=1-1&keywords=ruler<br /><br />This was my favourite age for this activity as these children are really starting to grasp measure and how it works and I was able to move them onto the next step and look at changing the units they were working with. So, the first thing they would do would be to measure in their basic unit (cm or inches) and maybe do a little bit of comparison of objects discussion to ensure their understanding. Once this is done the next thing to do would be to get them to go round and write on each post-it the same measurement but in a different unit. So, if the original is in cm they could write the conversion in mm or if they have originally used inches they could then use cm. Please let them use their rulers to help with the conversions and not expect them to do this in their heads. It can be a difficult concept to understand. After the conversions have been done use this as a discussion point and talk about the different units, how they compare and how the conversions were done - particularly cm to mm.<br /><br /><b>9, 10, 11 year olds</b><br />These children again need to be encouraged to use the rulers mentioned for the 7, 8, and 9 year olds.<br /><br />You will find that, hopefully, these children have secure knowledge of measure but are still a little confused on changing from one unit to the next. Follow the above activity but I would encourage all children to work in metric units and to write three measurements in total on their paper. Can they write it in cm, mm and m? This is tricky and they may well need a ruler / tape measure or meter stick to help but it is really good to help them understand how to convert the units and to realise that different things need to be measured using different units and equipment. When your child is doing the conversions I find the best way is to let them work it out for themselves using the equipment and possibly some help but once it is done talk about other ways you could do the calculations ie. multiplying and dividing by 10.<br /><br /><b>A few final words</b><br /><br />I loved doing this activity in class as we had lots of fun practicing measuring and working together and discussing what we were doing. Please don't measure every item in your house and then do the follow up with every single item. You will find that initially for that first measurement there will be lots of post-it notes but then attention and concentration of your child will not last to convert / discuss them all. You don't need to. Follow your instincts and stop before it becomes a chore and boring. This activity is supposed to be fun and not leave a lasting memory of boredom!Charlotte Haywardhttps://plus.google.com/101613062113924736341noreply@blogger.com0tag:blogger.com,1999:blog-5343833198242744295.post-84761197221723202662015-04-30T21:01:00.003-06:002015-04-30T21:01:27.581-06:00CountingHow many of us practice counting with our children once they start school?<br /><br />When your children are little a lot of time is spent counting between 1 and 20. Then, once they have grasped this and can then master the next few sets of tens we tend to leave the counting alone and move onto sums and manipulation of numbers.<br /><br />As a maths teacher I say count, count and count some more. Counting is the basis of the maths we learn and without this skill we can find maths difficult. A lot of children can count chronologically fairly well. But ask them to vary what they are counting and you may find that they have to think a while first. Our aim is to get your children counting confidently with whatever variations we throw at them. This will build their confidence with numbers, make maths a little more fun for them and build the foundations for good mathematics learning.<br /><br />Here are some starting points for counting:<br /><br />Can your child count in ones starting on different numbers (count for 20 to 30 numbers from each of these starting points)?<br />13<br />42<br />67<br />81<br />95<br />106<br />119<br />137<br />151<br />183<br />194<br /><br />Often a child, particularly when they are just mastering numbers, can give the impression they can count in ones but ask them to count over a 'sticky point' and you may find they struggle a little. The starting points above take you over the more obvious 'sticky points'.<br />For the majority of children the 'sticky points' are as follows: going past the 10's number, using the 'teens' numbers and going over the 100's number.<br /><br />For early elementary / primary counters then getting to 200 successfully is a fantastic achievement and you will find you should have a confident counter that can then probably count mostly successfully to 900 or thereabouts.<br /><br />Once your child is in the later elementary years he / she should be confident counting in the thousands and beyond. I find at this level that once they get beyond 1000 very little counting practice is done. If your child can count beyond 1000, can they count beyond 5000, 10000, 15000, 50000, 100000, 140000? Obviously this can't be done starting at 1 but choose some different starting points and play some counting games (using some of the activities listed in the Activities post).<br /><br />Alongside counting in ones it is really good to practice counting in 2's, 3's, 4's .........etc. It continues to build your childs mathematical agility and can also be lots of fun. When doing these the obvious place to start is from zero and keep it simple but once these have been mastered and your child is growing in confidence with manipulating numbers mentally then try going beyond 100, try a different starting point or try backwards.<br /><br />A word of advice. If you are doing this at home and it's a new sequence or one that your child is not so good at write the sequence down for them to read as they do an activity on it. Better for them to recite it correctly and fix the correct pattern in their brain than for them to recite it incorrectly and teach their brain the wrong sequence.<br /><br />I'm keeping this one short after Monday's mammoth article but will expand on some of the points here in following articles.<br /><br />But for now keep counting and having fun.<br /><br /><br />Charlotte Haywardhttps://plus.google.com/101613062113924736341noreply@blogger.com0tag:blogger.com,1999:blog-5343833198242744295.post-17077924788545903492015-04-27T21:15:00.002-06:002015-04-27T21:15:36.888-06:00Maths WalkHere's a fun activity to do as the weather gets a little warmer.<br /><br />The basis of the activity is to go for a walk and discuss any maths that you can find along the way. This doesn't need to be a particularly long walk, we tend to walk around the garden. Or we have a short loop we can do from our house that can be good too. Basically as you go for a walk use what you see as discussion points around maths. For example, you might see some tulips / daffodils. You could ask your child to count them. You could look at several plants and add up how many flowers there are in total. Pushing it further you could find two different types of flower and work out which types has more flowers. It doesn't just have to be number work. You could spot shapes; what shape is the patio / decking? Can you see any symmetry there? Once you have spotted something to talk about ask questions, discuss and do something fun with it (take a photograph of your child imitating a shape at a shape, or holding up the same number of fingers as flowers, skip round the perimeter of a shape etc).<br /><br />For each age group I have listed some questions and ideas of things that you might like to look at. Obviously everyone's garden is different and therefore questions will be different but hopefully I have given you enough ideas of how to do it that you can adapt them to your own gardens / walks. Please be careful this doesn't become a walk with lots of questions. Make it a walk with lots of conversation, discussion, questions and games. Also make sure you give your child chance to spot things / discover things without you always starting the discussion with something . I love children's minds, they are so free and open and they may surprise you and come up with some amazing facts, information or just stuff! You could try taking it in turns to ask questions and talk about what you see. This will definitely keep it a little more fun for both of you.<br /><br />The level of the maths and what you discuss depends on the level of your child. Below I have detailed the level and some discussion points for the various age groups.<br /><br /><b>Pre-school</b><br />With Preschool children you are looking for things they will recognize, counting, shapes and maybe some simple sums. Your discussion will be quite repetitive but should be good fun. Throw in some difficult concepts too if you think they will cope and extend that learning. I've also added in some fun bits to break what could seem like an endless stream of maths.<br /><br /><b>Trees: </b>How many trees can you see? Can you run and touch 3 trees? Pull down a branch (if you can) and look at the leaves; what shapes are they? Do they have and points? How many? Are the leaves tickly? Can you find any loose leaves or branches to test out how tickly they are?<br /><b>Planters / Plant pots: </b>Look at any plant pots, what shapes are they? How many are there? Can they be rearranged to make a shape /a line / a funny pattern? What plants are in them? What shapes? How many? Compare - which planter is the biggest / smallest?<br /><b>Flowers: </b>Can you see any flowers? What colours are they? What shapes? How many petals do they have? Are they symmetrical? (A pre-schooler may not understand this word but will understand 'the same on each side') Try putting the flowers against your hand / chin, do they change the colour of your skin?<br /><b>Steps into your house: </b>How many steps are there into the house? What shapes are they? We have 3 steps out the back and four round the front, how many in total? Jump up and down them and count as you go. Maybe talk about double: 2 jumps down and then 2 jumps up.<br /><b>Driveway: </b>How many giant steps does it take to walk around the driveway? How many jumps? Do both and compare, which took more, less?<br /><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="http://2.bp.blogspot.com/-2qsdssA7MSg/VT75IHz-1TI/AAAAAAAAcvc/xffyo6-CbXM/s1600/IMG_1095.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="http://2.bp.blogspot.com/-2qsdssA7MSg/VT75IHz-1TI/AAAAAAAAcvc/xffyo6-CbXM/s1600/IMG_1095.JPG" height="320" width="240" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">My daughter striding around the drive</td></tr></tbody></table><br /><b>Sticks: </b>There are always sticks or leaves lying around. Gather a pile and make a visual sum. Lie three next to each other and then 2 next to each other a little way apart from the first pile. Count the two piles separately, put them together and then count again to see how many you have altogether. This could be extended to subtraction: have a pile of 5 sticks, together take 2 away and count how many are left.<br /><b>Fences / Railings: </b>Can you see any picket fences / railings? Look at how they are made? Are they made from posts? Which direction do the posts go in? Can you count 8 posts? How many posts can you count? Let's count some together?<br /><b>Houses / Buildings: </b>Look at your house. What shapes can be seen on your house? Look at the windows? Is there a triangle up by the roof as it slopes down either side? How many windows are there? Can you see any interesting shapes?<br /><b>Visual representation: </b>Can you find anything that represents a number or sum in maths? For example are there 3 sticks just lying around? Then you've found 3.<br /><br /><br /><b>5, 6 and 7 year olds</b><br />This is going to be very similar to Pre-school. Children this age are really gaining confidence with numbers. Playing with numbers whilst outside will help to build their confidence and ability. We are looking at counting, basic number manipulations, introducing the idea of counting in 2's or 3's if you're at the top end of this level and maybe a little bit of sharing. Lots of shape work and maybe a little data collection is also worth doing with these ones.<br /><b><br /></b><b>Trees: </b>How many trees can you see? Can you run and touch 5 trees? Are all the trees the same type? How many of each type? Which one is the most common / least common? Which is the tallest / shortest tree? Which tree looks like it has the most leaves? Pull down a branch (if you can) and look at the leaves; what shapes are they? Do they have and points? How many? Are the leaves tickly? Can you find any loose leaves or branches to test out how tickly they are?<br /><b>Planters / Plant pots / Flower beds: </b>Look at any plant pots, what shapes are they? How many are there? Can they be rearranged to make a shape /a line / a funny pattern? What plants are in them? What shapes? How many? Compare - which planter is the biggest / smallest? How many plants / flowers are in them in total?<br /><div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/-XPU5wUFOFdA/VT755R3VarI/AAAAAAAAcvk/zcRJWHO64w0/s1600/IMG_1098.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://1.bp.blogspot.com/-XPU5wUFOFdA/VT755R3VarI/AAAAAAAAcvk/zcRJWHO64w0/s1600/IMG_1098.JPG" height="240" width="320" /></a></div><br /><b>Flowers: </b>Can you see any flowers? What colours are they? What shapes? How many petals do they have? Are they symmetrical? (Your child may not understand this word but will understand 'the same on each side') How many flowers in total in the garden / a section of the garden? Which type of flower is the most common? Are the flowers bigger or smaller than your hand? Is there another body part they can be compared to? Try putting the flowers against your hand / chin, do they change the colour of your skin?<br /><b>Steps into your house: </b>How many steps are there into the house? What shapes are they? We have 3 steps out the back and four round the front, how many in total? Jump up and down them and count as you go. Maybe talk about double: 2 jumps down and then 2 jumps up. Or count as you walk up the steps. You could count in ones, two's or threes.<br /><b>Driveway: </b>How many giant steps does it take to walk around the driveway? How many jumps? Do both and compare, which took more, less?<br /><b>Sticks: </b>There are always sticks or leaves lying around. Gather a pile and make a visual sum. Lie 10 next to each other and then 2 next to each other a little way apart from the first pile. Count the two piles separately, put them together and then count again to see how many you have altogether. This could be extended to subtraction: have a pile of 15 sticks, together take 2 away and count how many are left. You could also do some counting in two's with sticks. Make lots of piles of two and count. If you're child is doing well with this push the language a little. 2, 4, 6, 8, 10, how many lots of two did we just count?<br /><b>Fences / Railings: </b>Can you see any picket fences / railings? Look at how they are made? Are they made from posts? Which direction do the posts go in? Can you count 8 posts? How many posts can you count? Let's count some together? How tall is the fence? Stand child next to it - is it taller than you or shorter than you? How many hands tall is the fence? (use childs hands to measure the fence)<br /><b>Houses / Buildings: </b>Look at your house. What shapes can be seen on your house? Look at the windows? Is there a triangle up by the roof as it slopes down either side? How many windows are there? Can you see any interesting shapes? Is there any symmetry?<br /><b>Visual representation: </b>Can you find anything that represents a number or sum in maths? For example are there 3 sticks just lying around? Then you've found 3.<br /><br /><br /><b>7, 8 and 9 year olds</b><br />Children this age are really starting to see numbers and develop the ability to play with them and find maths interesting and fun, if it is made interesting and fun for them. We are really playing with numbers outside with these children and taking their knowledge of shape and measure and putting it into context to consolidate that knowledge. Your child may not be able to take the concept of cm / m or Inches / feet out into the real world without a tape measure but they should be able to understand the concept of measure so can measure things in hands, bodies, arms etc. and should be able to compare and estimate heights, widths etc.<br /><br /><b>Trees: </b>Are all the trees the same type? How many of each type? Which one is the most common / least common? Which is the tallest / shortest tree? Which tree looks like it has the most leaves? Pull down a branch (if you can) and look at the leaves; what shapes are they? Do they have and points? How many? Are the leaves tickly? Can you find any loose leaves or branches to test out how tickly they are? How tall do you think the tree is? Taller than one person? 2 people?<br /><b>Planters / Plant pots / Flower beds: </b>Look at any plant pots, what shapes are they? How many are there? Can they be rearranged to make a shape /a line / a funny pattern? What plants are in them? What shapes? How many? Compare - which planter is the biggest / smallest? How many plants / flowers are in them in total?<br /><b>Flowers: </b>Can you see any flowers? What colours are they? What shapes? How many petals do they have? Are they symmetrical? How many flowers in total in the garden / a section of the garden? Which type of flower is the most common? Are the flowers bigger or smaller than your hand? Is there another body part they can be compared to? How tall do you think the stems on the flowers are? Are they taller than your forearm? Whole arm? Try putting the flowers against your hand / chin, do they change the colour of your skin?<br /><b>Driveway: </b>How many giant steps / pidgeon steps does it take to walk around the driveway? Can your child make an estimate first? Do both and compare, which took more, less? How long do you think the driveway is? What shapes is the driveway made out of?<br /><b>Sticks: </b>There are always sticks or leaves lying around. Gather a pile and make a visual sum. Lie 16 next to each other and then 12 next to each other a little way apart from the first pile. Count the two piles separately, put them together and then count again to see how many you have altogether. This could be extended to subtraction: have a pile of 21 sticks, together take 14 away and count how many are left. If you wanted to talk multiplication you could lay out an 'array' This is basically a square / rectangle made of sticks with rows and columns. For example lay out a row of 5 sticks, then add another row directly underneath and another and another. This should look like a 5 x 4 rectangle. Once you have done this talk about it with your child, how may rows? How many columns? How many sticks in total? They may even be able to understand that this shows the multiplication sum 4 x 5 = 20.<br /><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="http://1.bp.blogspot.com/-F0hthXwptHU/VT76ii4NAVI/AAAAAAAAcvs/MD105uo81qw/s1600/IMG_1097.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="http://1.bp.blogspot.com/-F0hthXwptHU/VT76ii4NAVI/AAAAAAAAcvs/MD105uo81qw/s1600/IMG_1097.JPG" height="240" width="320" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">A array representing 3x3</td></tr></tbody></table><br /><b>Fences / Railings: </b>Can you see any picket fences / railings? Look at how they are made? Are they made from posts? Which direction do the posts go in? How many posts can you count? Let's count some together? How tall is the fence? Stand child next to it - is it taller than you or shorter than you? How many hands tall is the fence? (use childs hands to measure the fence)<br /><b>Houses / Buildings: </b>Look at your house. What shapes can be seen on your house? Look at the windows? Is there a triangle up by the roof as it slopes down either side? How many windows are there? Can you see any interesting shapes? Is there any symmetry? How many different shapes can you see in the house? Can you see any 3D shapes or just 2D?<br /><b>Visual representation: </b>Can you find anything that represents a number or sum in maths? For example are there 3 sticks just lying around? Then you've found 3. Maybe you can see three planters next to one bucket; you've found the sum 3+1. What else can you find?<br /><br /><br /><b>9, 10 and 11 year olds</b><br />These children are pretty good an number manipulation, shape, measure within the classroom but the key skill for them with this walk is to bring their classroom knowledge outside and see if they can still do all these things out of context. If they can't let's encourage them to do it using a fun maths walk.<br /><br /><b>Trees: </b>Are all the trees the same type? How many of each type? Which one is the most common / least common? Which is the tallest / shortest tree? Which tree looks like it has the most leaves? Pull down a branch (if you can) and look at the leaves; what shapes are they? Do they have and points? How many? Are the leaves tickly? Can you find any loose leaves or branches to test out how tickly they are? How tall do you think the tree is? Estimate using proper units.<br /><b>Planters / Plant pots / Flower beds: </b>Look at any plant pots, what shapes are they? How many are there? Can they be rearranged to make a shape /a line / a funny pattern? What plants are in them? What shapes? How many? Compare - which planter is the biggest / smallest? How many plants / flowers are in them in total? How high are the planters (in units)? If we stacked them all on top of each other how tall do you think our tower would be? Is there an empty one? How many buckets of water do you think would fill it? Try it and see if you were right?<br /><b>Flowers: </b>Can you see any flowers? What colours are they? What shapes? How many petals do they have? Are they symmetrical? How many flowers in total in the garden / a section of the garden? Which type of flower is the most common? Are the flowers bigger or smaller than your hand? Is there another body part they can be compared to? How tall do you think the stems on the flowers are? Try putting the flowers against your hand / chin, do they change the colour of your skin?<br /><b>Driveway: </b>How many giant steps / pidgeon steps does it take to walk around the driveway? Do both and compare, which took more, less? How long do you think the driveway is? What shapes is the driveway made out of?<br /><b>Sticks: </b>There are always sticks or leaves lying around. Gather a pile and make a visual sum. Lie 16 next to each other and then 12 next to each other a little way apart from the first pile. Count the two piles separately, put them together and then count again to see how many you have altogether. This could be extended to subtraction: have a pile of 21 sticks, together take 14 away and count how many are left. It would be fun to lay out an 'array' This is basically a square / rectangle made of sticks with rows and columns. For example lay out a row of 5 sticks, then add another row directly underneath and another and another. This should look like a 5 x 4 rectangle. Once you have done this talk about it with your child, how may rows? How many columns? How many sticks in total? Mention that this is a pictorial way of showing the multiplication sum 4 x 5 = 20.<br /><b>Fences / Railings: </b>Can you see any picket fences / railings? Look at how they are made? Are they made from posts? Which direction do the posts go in? How many posts can you count? Let's count some together? How tall do you think the fence is? Stand child next to it - is it taller than you or shorter than you? You stand next to the fence and ask child to stand 10 meters (or another amount in a different unit) further down the fence. Can they estimate that far?<br /><b>Houses / Buildings: </b>Look at your house. What numbers can you read on the houses? Can you add two or three house numbers together? What shapes can be seen on your house? Look at the windows? Is there a triangle up by the roof as it slopes down either side? How many windows are there? Can you see any interesting shapes? Is there any symmetry? How many different shapes can you see in the house? Can you see any 3D shapes or just 2D?<br /><table align="center" cellpadding="0" cellspacing="0" class="tr-caption-container" style="margin-left: auto; margin-right: auto; text-align: center;"><tbody><tr><td style="text-align: center;"><a href="http://4.bp.blogspot.com/-jWMYtpUQNwk/VT7682DaFwI/AAAAAAAAcv0/mV_UA3MPOKI/s1600/IMG_1104.JPG" imageanchor="1" style="margin-left: auto; margin-right: auto;"><img border="0" src="http://4.bp.blogspot.com/-jWMYtpUQNwk/VT7682DaFwI/AAAAAAAAcv0/mV_UA3MPOKI/s1600/IMG_1104.JPG" height="240" width="320" /></a></td></tr><tr><td class="tr-caption" style="text-align: center;">We found lots of shapes within our climbing frame</td></tr></tbody></table><br /><b>Visual representation: </b>Can you find anything that represents a number or sum in maths? For example are there 3 sticks just lying around? Then you've found 3. You might notice that a patio is a square made up of square slabs that show the array 9x9 and therefore a multiplication. What else can you find?<br /><br />Enjoy your walkCharlotte Haywardhttps://plus.google.com/101613062113924736341noreply@blogger.com0tag:blogger.com,1999:blog-5343833198242744295.post-54661212418311950972015-03-03T20:49:00.000-07:002015-04-22T13:51:41.553-06:00Number Flowers<span style="font-family: Arial, Helvetica, sans-serif;">I thought it was time to have some fun and get crafty do so here's a little numbers project for those wet / snowy days.</span><br /><span style="font-family: Arial, Helvetica, sans-serif;"><br />A long time ago (back in the distant past when my life was teaching and being with other people's children) someone introduced me to 'Number Flowers'. I thought they were a brilliant idea and have used them many times since, within my classroom.</span><br /><span style="font-family: Arial, Helvetica, sans-serif;"><br />All you need are:</span><br /><ul><li><span style="font-family: Arial, Helvetica, sans-serif;">A centre for your flower - I usually use a small paper plate for this but a circle of card will do</span></li></ul><ul><li><span style="font-family: Arial, Helvetica, sans-serif;">Some petals for your flower (between 6 and 12 depending on how enthusiastic your little mathematician is feeling) - I cut these out of coloured paper / card</span></li><li><span style="font-family: Arial, Helvetica, sans-serif;">Coloured pens</span></li><li><span style="font-family: Arial, Helvetica, sans-serif;">Stapler</span></li></ul><div class="separator" style="clear: both; text-align: center;"><a href="http://2.bp.blogspot.com/-ye4L9YjFxmU/VQhSEey75hI/AAAAAAAAb3Y/Crp7NM-Y_AI/s1600/IMG_0809.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://2.bp.blogspot.com/-ye4L9YjFxmU/VQhSEey75hI/AAAAAAAAb3Y/Crp7NM-Y_AI/s1600/IMG_0809.JPG" height="320" width="240" /></a></div><div><span style="font-family: Arial, Helvetica, sans-serif;"><br /></span></div><span style="font-family: Arial, Helvetica, sans-serif;">(For those that would rather not do a flower then a spider could be made or any other alternative you can think of)</span><br /><span style="font-family: Arial, Helvetica, sans-serif;"><br />Ask your child to choose their favourite number and then get them to write this on the centre of the flower and colour it in.</span><br /><span style="font-family: Arial, Helvetica, sans-serif;"><br />Once they have done this they need to write a fact about their number on each petal.</span><br /><span style="font-family: Arial, Helvetica, sans-serif;"><br /><b>5, 6 and 7 year olds</b></span><br /><span style="font-family: Arial, Helvetica, sans-serif;">Please encourage a small number that they can use with confidence.</span><br /><span style="font-family: Arial, Helvetica, sans-serif;">These facts can be as simple as addition sums of numbers that make their number, possibly branching to subtraction, multiplication and division depending on the level of your little mathematician.</span><br /><span style="font-family: Arial, Helvetica, sans-serif;">They could also write facts linked to dates or any other simple fact they know linked to the number. eg. 7 - my birthday, or my Mum and Dad's wedding anniversary, or the number of bikes in my Dad's garage</span><br /><span style="font-family: Arial, Helvetica, sans-serif;"><br /></span><br /><span style="font-family: Arial, Helvetica, sans-serif;"><b>7, 8 and 9 year olds</b></span><br /><span style="font-family: Arial, Helvetica, sans-serif;">Again they need to choose a number they can manipulate with confidence.</span><br /><span style="font-family: Arial, Helvetica, sans-serif;">Their facts can be a little more advanced. They could do 3-digit sums to make their numbers, definitely include all four operations. They could also do some simple (supervised) internet research on their number to see if they can find something interesting (that they can understand)</span><br /><span style="font-family: Arial, Helvetica, sans-serif;"><br /><b>9, 10 and 11 year olds</b></span><br /><span style="font-family: Arial, Helvetica, sans-serif;">This is the age that I most love doing these things with as you can really discover some interesting things. I used to set the fact finding as a homework and would let them do 2 petals with simple sums on, 2 petals with simple facts like birthdays etc and then the rest had to be stuff they had researched on their number. The only stipulation I had was that they had to understand what they were writing as you can find some very complex number stuff that could just get copied straight onto a flower!</span><br /><span style="font-family: Arial, Helvetica, sans-serif;"><b><br />Pre-school</b></span><br /><span style="font-family: Arial, Helvetica, sans-serif;">This can be done with pre-school but instead of choosing a number I would get them to write their name on the middle.</span><br /><span style="font-family: Arial, Helvetica, sans-serif;">The petals can be their favourite numbers. I got my little girl to write the numbers 1-8 and then draw the same number of dots / flowers or some other unidentifiable drawing on the petal too. We also added the right number of stickers. You could add pasta, fuzzy balls or anything else you can think of that might work.</span><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/-8odt1moi_Jk/VQhStjQE1gI/AAAAAAAAb3g/BKp0XyTktk8/s1600/IMG_0817.JPG" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://1.bp.blogspot.com/-8odt1moi_Jk/VQhStjQE1gI/AAAAAAAAb3g/BKp0XyTktk8/s1600/IMG_0817.JPG" height="320" width="240" /></a></div><span style="font-family: Arial, Helvetica, sans-serif;"><br /></span>Charlotte Haywardhttps://plus.google.com/101613062113924736341noreply@blogger.com0tag:blogger.com,1999:blog-5343833198242744295.post-81227490867397957622015-02-24T21:38:00.002-07:002015-03-03T20:49:28.571-07:00Doubling Numbers<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Arial, Helvetica, sans-serif; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Doubling is often one of those maths concepts that everyone assumes everyone can do. However, you'd be surprised at the number of Primary / Elementary students that find this difficult or have just never bothered to learn. In my experience it is so important in building basic mathematical knowledge and giving children number knowledge they can build on.</span></div><span style="font-family: Arial, Helvetica, sans-serif;"><b style="font-weight: normal;"><br /></b></span><br /><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Arial, Helvetica, sans-serif; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">When doubling with your child I would recommend starting with the basic numbers: 1, 2, 3, 4, 5, 6, 7, 8 and 9. Starting easy builds confidence and ensures you have checked they know their doubles.</span></div><span style="font-family: Arial, Helvetica, sans-serif;"><b style="font-weight: normal;"><br /></b></span><br /><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Arial, Helvetica, sans-serif; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Here is a mini 'Lesson Plan' for you to work through with your child.</span></div><span style="font-family: Arial, Helvetica, sans-serif;"><b style="font-weight: normal;"><br /></b></span><br /><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Arial, Helvetica, sans-serif; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Start with a quick warm up. Use one of the number activities and choose a sequence of numbers to work with. Depending on the level of your child you could just count. This could be anything from 0 - 20 or 150 - 180. Do one or two of the activities with either the same set of numbers or two different sets. Make it fun, have a giggle and get both of you in the right frame of mind for learning something.</span></div><span style="font-family: Arial, Helvetica, sans-serif;"><b style="font-weight: normal;"><br /></b></span><br /><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Arial, Helvetica, sans-serif; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Briefly talk about doubles. Ask your child what doubling means and the throw some examples at him / her.</span></div><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Arial, Helvetica, sans-serif; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">I would suggest using the units to start with (1, 2, 3, 4, 5, 6, 7, 8, 9)</span></div><span style="font-family: Arial, Helvetica, sans-serif;"><b style="font-weight: normal;"><br /></b></span><br /><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Arial, Helvetica, sans-serif; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">If this is the level you need to work at then I would suggest you use some of the number activities and practice doubling all the units over again until your child is done practicing or can do them. Throwing and catching a ball is really good for this as you can give the unit and then your child can double it. This will need to be revisited several times before you can safely say he / she is confident with them.</span></div><span style="font-family: Arial, Helvetica, sans-serif;"><b style="font-weight: normal;"><br /></b></span><br /><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Arial, Helvetica, sans-serif; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">If you find single digits are too easy then use higher numbers. Keep getting higher until your child is having to think about the numbers and then play some games and practice. (This can be great fun with really high numbers too, so parents of high ability children go for it, push the numbers harder and harder)</span></div><span style="font-family: Arial, Helvetica, sans-serif;"><b style="font-weight: normal;"><br /></b></span><br /><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Arial, Helvetica, sans-serif; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Once your child has mastered doubling the units I always found it useful to show students a visual that can help them double 2, 3,4 or more digit numbers.</span></div><span style="font-family: Arial, Helvetica, sans-serif;"><b style="font-weight: normal;"><br /></b></span><br /><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Arial, Helvetica, sans-serif; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Start with something fairly easy so they're not having to think too much about the numbers.</span></div><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Arial, Helvetica, sans-serif; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Write your number down and then draw little arrows from each digit and underneath each arrow write what the double of that part of the number is.</span></div><span style="font-family: Arial, Helvetica, sans-serif;"><b style="font-weight: normal;"><br /></b></span><br /><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Arial, Helvetica, sans-serif; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> 12</span></div><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Arial, Helvetica, sans-serif; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> / \</span></div><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Arial, Helvetica, sans-serif; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> 20 4</span></div><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Arial, Helvetica, sans-serif; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> \ /</span></div><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Arial, Helvetica, sans-serif; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"> 24</span></div><b style="font-weight: normal;"><br /></b><br /><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Then draw arrows underneath these doubles to show putting these numbers together and the answer you will get.</span></div><b style="font-weight: normal;"><br /></b><br /><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">It is important initially to make sure that when you double the tens digit you don't just write an individual number but the correct double. So for the above example you need to write 20 and not 2. This ensures your child is clearly understanding how doubles work. If you used 2 then you risk the answer being 6 if your child is a little unsure on place value and how that works.</span><br /><span style="background-color: transparent; color: black; font-family: Arial; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><br /></span><span style="background-color: transparent; color: black; font-family: Arial; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">If you're starting to double 3-digit numbers then use the same visual as above but with three numbers and please remember to keep all the zero's in the numbers to ensure full understanding of place value.</span></div><b style="font-weight: normal;"><br /></b><br /><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Hopefully by using this visual your child will soon be able to do this in their head using the visual which just helps them to break the numbers down and quickly work out that double.</span></div><b style="font-weight: normal;"><br /></b><br /><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Do some more examples with the visual with your child until they have clearly mastered it. Once they've done this you will need to alternate for a while between using the head and using the visual on paper to consolidate. For example you could play a variety of games over the next couple of days. Just do a game for 5 minutes or so and then leave it and do another game later that day or the next day for another five minutes or so.</span></div><b style="font-weight: normal;"><br /></b><br /><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Some games you could play:</span></div><b style="font-weight: normal;"><br /></b><br /><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Have a race - see who can double a number first, on paper or in your heads.</span></div><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">When driving along every time one of you spots a number somewhere call it out and the rest of the car have to double the number.</span></div><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Start a number sequence by alternating between you (throwing a ball or marching etc) but the sequence is doubling eg. 2, 4, 8, 16, 32........</span></div><br /><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Once doubling is a secure skill that your child has you will be able to very quickly build this knowledge to doubling higher numbers. It is something that you will need to keep revisiting for a while as you gradually increase the numbers. At some point you will suddenly realise that your child can do this and no matter what numbers you throw at them (within reason) they can double them.</span><br /><br /></div>Charlotte Haywardhttps://plus.google.com/101613062113924736341noreply@blogger.com0tag:blogger.com,1999:blog-5343833198242744295.post-13514397798987880412015-02-24T21:37:00.003-07:002015-03-03T20:49:19.417-07:00Mental Maths Activities<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Arial, Helvetica, sans-serif; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Before I list any number work I wanted to introduce you to some of the basic activities I use for helping children improve their mental maths skills.</span></div><span style="font-family: Arial, Helvetica, sans-serif;"><b id="docs-internal-guid-f1424840-bf06-7832-6692-c969555d559f" style="font-weight: normal;"><br /></b></span><br /><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Arial, Helvetica, sans-serif; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">I tend to do a lot of practical activities with children. From experience, I have found that many children are kin-aesthetic, audio or visual learners so a lot of my activities are geared towards these learning styles. The children then find they have absorbed new knowledge, had fun and improved their maths skills all in one go. It makes for a happy maths learner (and a happy teacher).</span></div><span style="font-family: Arial, Helvetica, sans-serif;"><b style="font-weight: normal;"><br /></b></span><br /><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Arial, Helvetica, sans-serif; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">A lot of my activities can be used for learning most of the basic mental maths skills. The main focus of these is to work at something together and take it in turns. Children love sharing an activity, plus it takes the focus off them a little. In their mind then the work is not all up to them, someone else is doing some of the work.</span></div><span style="font-family: Arial, Helvetica, sans-serif;"><b style="font-weight: normal;"><br /></b></span><br /><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Arial, Helvetica, sans-serif; font-size: 15px; font-style: normal; font-variant: normal; font-weight: bold; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Throwing a ball</span></div><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Arial, Helvetica, sans-serif; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Play catch with your child and as you throw the ball say a number and then your child will say another number when he / she throws it back (what those numbers are will depend upon what number skill you are practicing / learning)</span></div><span style="font-family: Arial, Helvetica, sans-serif;"><b style="font-weight: normal;"><br /></b></span><br /><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Arial, Helvetica, sans-serif; font-size: 15px; font-style: normal; font-variant: normal; font-weight: bold; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Marching</span></div><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Arial, Helvetica, sans-serif; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">March around a space and every time you put a foot down say a number (you could get your child to do this on their own but it's much more fun to both do it)</span></div><span style="font-family: Arial, Helvetica, sans-serif;"><b style="font-weight: normal;"><br /></b></span><br /><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Arial, Helvetica, sans-serif; font-size: 15px; font-style: normal; font-variant: normal; font-weight: bold; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Marching up and down the stairs</span></div><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Arial, Helvetica, sans-serif; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Like just marching but up and down the stairs and when you step on a new step you say the number</span></div><span style="font-family: Arial, Helvetica, sans-serif;"><b style="font-weight: normal;"><br /></b></span><br /><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Arial, Helvetica, sans-serif; font-size: 15px; font-style: normal; font-variant: normal; font-weight: bold; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Hand tapping</span></div><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Arial, Helvetica, sans-serif; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Tap hands on a table or another surface that makes a noise and every time you tap say a number</span></div><span style="font-family: Arial, Helvetica, sans-serif;"><b style="font-weight: normal;"><br /></b></span><br /><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Arial, Helvetica, sans-serif; font-size: 15px; font-style: normal; font-variant: normal; font-weight: bold; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Writing</span></div><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Arial, Helvetica, sans-serif; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Ask your child a question and get them to write the answer on something they are not normally alllowed to write on. For example: a white board (with a white board pen), a mirror (with a whiteboard pen), a glass table top if you have one or anything else that can be written on and cleaned off but gives a feeling of fun and excitement while doing it.</span></div><span style="font-family: Arial, Helvetica, sans-serif;"><b style="font-weight: normal;"><br /></b></span><br /><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Arial, Helvetica, sans-serif; font-size: 15px; font-style: normal; font-variant: normal; font-weight: bold; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Saying numbers in a funny way</span></div><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Arial, Helvetica, sans-serif; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Encourage your child to say and answer / sequence / what ever is required in different voices. You could ask the question in a loud voice and child has to copy with the answer. Then you could use a quiet voice, a squeaky voice, low pitched voice, growly voice.........</span></div><span style="font-family: Arial, Helvetica, sans-serif;"><b style="font-weight: normal;"><br /></b></span><br /><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Arial, Helvetica, sans-serif; font-size: 15px; font-style: normal; font-variant: normal; font-weight: bold; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Talking to a teddy (or any other stuffed animal)</span></div><span style="font-family: Arial, Helvetica, sans-serif; font-size: 15px; vertical-align: baseline; white-space: pre-wrap;">Ask your child to teach teddy a particular sequence or maths skill. Or you could just get </span><span style="font-family: Arial; font-size: 15px; vertical-align: baseline; white-space: pre-wrap;">child to count with teddy - to make this even more fun you could join in too.</span>Charlotte Haywardhttps://plus.google.com/101613062113924736341noreply@blogger.com0tag:blogger.com,1999:blog-5343833198242744295.post-15065751559585463242015-02-24T21:37:00.000-07:002015-04-20T20:46:46.667-06:00What does mental maths mean to you?<div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Arial, Helvetica, sans-serif; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Do you ever think back to your school days and the maths you did? Did you do much mental maths or was it more copying sums from text books? I find it fascinating talking to people about what they did when they were at school, everyone seems to have done completely different things.</span></div><span style="font-family: Arial, Helvetica, sans-serif;"><b id="docs-internal-guid-b94bf031-bf05-e4bf-6468-c4ac91a58744" style="font-weight: normal;"><br /></b></span><br /><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Arial, Helvetica, sans-serif; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Looking back over official curriculum, mental maths played an important role in maths lessons in the UK in the 1990's but, as the thinking has changed, so mental maths seems to have developed a less significant role within lessons. Throughout my experience mental maths is often the key to helping a child become comfortable within a mathematics lesson.</span></div><span style="font-family: Arial, Helvetica, sans-serif;"><b style="font-weight: normal;"><br /></b></span><br /><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Arial, Helvetica, sans-serif; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Most lessons start the same with the teacher standing at the front, teaching a certain aspect of maths to the class. Within each class there is always a group whose mathematical brains are fast enough to follow the teaching and do the examples along with the teacher in their heads and be first up with their hands and the answers. There is always the group that does not put their hands up. These are sometimes children that are happy to sit and watch but can do all the maths work in their heads. However, there will always be a few children in the class that are not putting their hands up because they can not keep up with the mental work of the numbers that are being used. They are so busy trying to follow the numbers that they are unable to follow the new concept that is being taught. This then builds the maths into something that they feel they can not get their heads around and it becomes something to be afraid of.</span></div><span style="font-family: Arial, Helvetica, sans-serif;"><b style="font-weight: normal;"><br /></b></span><br /><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Arial, Helvetica, sans-serif; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">If a child is happy and confident to 'play' with numbers then generally they are much happier and more confident within lessons and therefore more able to understand and follow what is happening and open to learning new ideas and concepts.</span><br /><span style="font-family: Arial, Helvetica, sans-serif;"><span style="background-color: transparent; color: black; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><br /></span><span style="background-color: transparent; color: black; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">This doesn't just happen at the beginning of lessons, it's often within the activity part of the lesson too. Children are given a task and asked to complete it and some children find they missed the beginning of the lesson because they were flummoxed by the numbers and now can't follow through. If they did manage to follow the start of the lesson there are some children that still find the work difficult to follow as they are having to constantly interrupt the work they are doing to sort out the numbers. For example: when doing some multiplication with 2-digit numbers some children are having to stop half way through the sum to painstakingly work out the simple multiplications. (this is a rather extreme example to illustrate my point, hopefully nothing this extreme should be going on in any classroom!)</span></span></div><span style="font-family: Arial, Helvetica, sans-serif;"><b style="font-weight: normal;"><br /></b></span><br /><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Arial, Helvetica, sans-serif; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">As a teacher I have seen this happen to many students and have spent a lot of my teaching years trying to undo this and teach children to enjoy their maths lessons.</span></div><span style="font-family: Arial, Helvetica, sans-serif;"><b style="font-weight: normal;"><br /></b></span><br /><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Arial, Helvetica, sans-serif; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Along with teaching whole classes I have tutored many students. When tutoring a student for the first time my main focus for the first few weeks would always be mental maths. I found this was a good way to have fun, it immediately boosted the childs' confidence and with this improved ability I found the student was then able to understand many more concepts and move their maths knowledge and understanding forward.</span></div><b style="font-weight: normal;"><br /></b><br /><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">So, to those of you needing help in how to work with your child to improve their mathematical knowledge and / or understanding start by working on their mental maths with them. This also has the added bonus that it's relatively easy and fun to do and probably one of the more achievable areas of maths for a parent helping a child.</span></div><b style="font-weight: normal;"><br /></b><br /><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">For those of you that would like to challenge your children and extend their mathematics capabilities I would say a very clear starting point is to really push their mental maths skills, the more these are pushed, the more they understand so the further they can take their maths knowledge and skills.</span><br /><span style="background-color: transparent; color: black; font-family: Arial; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;"><br /></span><span style="background-color: transparent; color: black; font-family: Arial; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">For those of you that are just here because your children can do some maths and enjoy it then again work on those mental maths skills, they can only make them better, happier mathematicians.</span></div><b style="font-weight: normal;"><br /></b><br /><div dir="ltr" style="line-height: 1.38; margin-bottom: 0pt; margin-top: 0pt;"><span style="background-color: transparent; color: black; font-family: Arial; font-size: 15px; font-style: normal; font-variant: normal; font-weight: normal; text-decoration: none; vertical-align: baseline; white-space: pre-wrap;">Over the next few entries I am going to detail some mental maths activities that can be used to help your child, whatever their level of maths. The key is to start at a really easy and basic level. This will build your childs confidence and make it easier for them to do as the numbers get harder. Starting easy is often the key to helping a child. As a parent, I understand, this can be really hard to do. In your mind you want your child to be as good as possible and you don't want to admit, even just to yourself that they can't do something that you feel all the other children can do. Please don't worry about this, your child is your child and special whether they can do something or not. As a parent it is our job to help them and the best way to do this is to start easy. and slowly build up. You will be amazed at how quickly they can make progress if you give them the chance with the easy numbers.</span></div><br />Charlotte Haywardhttps://plus.google.com/101613062113924736341noreply@blogger.com0tag:blogger.com,1999:blog-5343833198242744295.post-66095673309079304622015-02-24T21:31:00.002-07:002015-06-19T13:25:59.705-06:00How to use this Blog to help your child with their maths<span style="font-family: Arial, Helvetica, sans-serif;">My main objective when setting out on this venture was to create a blog that could be accessible to all, whether that be Pre-school children, 5th Grade / Year 6 children, children that need to extra support, gifted and talented children or just children that enjoy maths and want to do a little more.</span><br /><span style="font-family: Arial, Helvetica, sans-serif;"><br /></span><span style="font-family: Arial, Helvetica, sans-serif;">Therefore, in order to help as many people as I can and to keep this interesting and not have you falling asleep through boredom I am going to try to keep variety within my entries. Most entries will be one of the following:</span><br /><ul><li><span style="font-family: Arial, Helvetica, sans-serif;">Something mathematical that I found interesting and wanted to share and talk about.</span></li><li><span style="font-family: Arial, Helvetica, sans-serif;">A mini lesson - for those of you that want to work with your children, improving skills, I will be posting mini lessons that you can use as a basis from which to start the process of creating a happy and successful mathematician.</span></li><li><span style="font-family: Arial, Helvetica, sans-serif;">A Maths problem - A fun problem that the whole family can get involved in that also will promote the idea of maths being fun and achievable.</span></li><li><span style="font-family: Arial, Helvetica, sans-serif;">A fun mathematical activity - again something that anyone and everyone can do that will raise the profile of maths for your children.</span></li></ul><span style="font-family: Arial, Helvetica, sans-serif;">My recommendation, as a maths teacher, is that you use all my articles to help your child / children. If just 'lessons' are done at home (what I call the slog work) then you will both find this hard and struggle to keep motivated. Sometimes you need a break from this type of work. Adding problems in between 'lessons' can be lots of fun. They can also be used to consolidate things that have been learnt within 'lesson'. On top of that they really help your child to take their understanding of the maths they have done and apply it. Plus it can help families have fun together on those wet, rainy or cold, snowy days.</span><br /><span style="font-family: Arial, Helvetica, sans-serif;"><br /></span><span style="font-family: Arial, Helvetica, sans-serif;">Some of you may be questioning how the same thing can help children that need support and gifted and talented children. Ultimately when I work with children I spend a lot of time boosting their key skills. Children that need support definitely need to build their key skills as this is often one of the reasons they are finding maths difficult. Likewise I have found that often gifted and talented mathematicians also need help in this way. I have had many of these children say to me 'I don't know how I got the answer, I just did!'. It is great that their brains can do this but they do need to take a step back and ensure they know the key skills and how they help them with the more complex maths work. This will then ensure they have the skills for the maths work to become even more challenging. Finally the articles / activites I write about can be good conversation points, can promote the idea of maths being interesting and can be fund to share.</span><br /><span style="font-family: Arial, Helvetica, sans-serif;"><br /></span><span style="font-family: Arial, Helvetica, sans-serif;">As you read through the blog I will be writing on the articles how each particular activity can be used to help at different levels.</span><br /><span style="font-family: Arial, Helvetica, sans-serif;"><br /></span><span style="font-family: Arial, Helvetica, sans-serif;">Good luck, enjoy and please comment or email me if you have any questions: meaningfulmaths@gmail.com</span><br /><br /><br />Charlotte Haywardhttps://plus.google.com/101613062113924736341noreply@blogger.com0