Number Patterns

Sometimes it is fun to just sit down and colour some pretty patterns and that is what this weeks activity is all about.

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.

So this week , I am keeping the activity simple and fun. All I would like you to do is print out some 100 squares and let your child play with them.

Initially I would sit with your child and maybe take a 100 square each and talk about the numbers on it.

What number does it start on?
What number does it finish on?
Can you find the number ___?
Can you find a single digit number?
Can you find a 2-digit number?
Can you see any patterns? What?

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.

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.

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.

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.

5, 6 and 7 year olds
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.

7, 8 and 9 year olds
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.)

9, 10 and 11 year olds
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.
5's number square
6's number square
7's number square
8's number square
9's number square

Gathering information and playing :)

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.

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.

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.

So, here it is:

Data Handling - 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.

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.
Image result for books
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.
Image result for outdoor toys clipart
Some other ideas:
How quickly do fruit / veggies appear on our plants?
How long does Mummy actually need to spend doing jobs instead of playing with us?
When does it get dark each day?
How much of the different types of food do we eat each day?

Here's a brief 'what to do next'

  1. Once you have an idea you need to turn it into a question to investigate.
  2. Discuss with your child how you can do this including what info you need to gather and how often
  3. Together create a chart to gather the info on
  4. Gather the info you need over whatever time frame you decided on - most helpful is a week
  5. Look at the info you have gathered and discuss how this can be recorded to best show the results for discussion
  6. Discuss what the results show
  7. Answer your original question
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.

I hope you have fun with this activity and thoroughly enjoy exploring and investigating something together and coming up with an answer

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 )

5, 6 and 7 year olds
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.

7, 8 and 9 year olds
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.

9, 10 and 11 year olds
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.

Number sequences

This week I thought I'd look at one of the more obvious places to help your children at home: Times Tables!

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.

Image result for numbersWhen 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!

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.

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.

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.

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.

2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24

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.

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.

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.

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.

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.


Throwing a ball
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)

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)

Marching up and down the stairs
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)

Hand tapping

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)

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.

Saying numbers in a funny way
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.........

Talking to a teddy (or any other stuffed animal)
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.

The best number sequences to work on with these little people are:
Basic counting up as far as you can go
Counting backwards from 10 and then maybe 20
Counting in 2's to 20
Counting in 10's to 100

5, 6 and 7 year olds
Counting forwards - always worth practicing
Counting backwards - from any number below 100
Counting in 2's - as far as they can
Counting in 2's - but odd numbers
Counting in 5's - can they get to 50 or 100?
Counting in 10's - how far can they get?
Counting in 3's - up to 36 initially
Counting in 4's - up to 48 initially

7, 8 and 9 year olds
Counting forwards - always worth practicing
Counting backwards - from any number below 300
Counting in 2's - as far as they can
Counting in 2's - but odd numbers
Counting in 5's - can they get beyond 100?
Counting in 10's - how far can they get?
Counting in 3's - up to 36 initially
Counting in 4's - up to 48 initially
Counting in 6's - up to 72 initially
Counting in 7's - up to 84 initially
Counting in 8's - up to 96 initially
Counting in 9's - up to 108 initially
Counting in 11's - up to 132 initially
Counting in 12's - up to 144 initially

9, 10 and 11 year olds
Counting forwards - always worth practicing
Counting backwards - from any number
Counting in 2's - as far as they can
Counting in 2's - but odd numbers
Counting in 5's - can they get beyond 100?
Counting in 10's - how far can they get?
Counting in 3's - how far can they get?
Counting in 4's - how far can they get?
Counting in 6's - how far can they get?
Counting in 7's - how far can they get?
Counting in 8's - how far can they get?
Counting in 9's - how far can they get?
Counting in 11's - how far can they get?
Counting in 12's - how far can they get?
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.
Counting in 13's
Counting in 15's
Counting in 25's
Counting in square numbers
Counting in triangular numbers

Fun with water

Summer has definitely arrived here in Colorado which has inspired me to use water play for this weeks activity.

Image result for water play images

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.

However, take a sunny day, one or two children and a garden that loves water and this activity can be lots of fun.

So, ready for some fun?

You will need: lots of containers of varying shapes and sizes, these could include spoons, bowls, cups, plastic boxes, buckets etc.

Location: Best place for this to happen is outside but it can be done in the kitchen or bathroom

Activity: 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.

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.

  • Which container is the biggest? So, which container holds the most liquid?
  • Which is the smallest contained? And therefore holds the least liquid?
  • 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.
  • Can you estimate how many of these will go into this container? Let's see if your estimate was right? 
  • 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?
Image result for water play images

5, 6 and 7 year olds
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.

  • To warm up and get going I would use the questions for the preschool children and then extend into these questions:
  • 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?
  • Shall we use the measuring jug to measure roughly how much is in this cup?
  • Why don't we estimate how much is in this pot and then measure to see if we are right?
  • How many litres are in this pot? 
  • If I used two of these pots how many litres of water would I have altogether?
Image result for water play images

7, 8 and 9 year olds
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.

  • To warm up and get going I would use the questions for the previous two groups children and then extend into these questions:
  • 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?
  • 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?
  • How much water does this bottle hold? Can you tell me in ml? and now litres?
  • 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?
Image result for water play images

9, 10 and 11 year olds
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.
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.

  • The outside tap drips at a rate of 1 drip, every two seconds. How long will it take to waste a bucket of water?
  • A young friend / cousin has been playing with the water table? How much water has she / he wasted during the course of the day?
  • The plants need a cup of water each morning and evening. How much water does it take to water the plats each day?

Let's get creative with 3D shapes

When 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.

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.

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.

Anyway I thought this week would be a good week to do something with 3D shapes.

The activity is going to start off the same for all ages:

make a 3D shape!

I have attached various shape nets so you can use these to get started:
Alternate cube
Alternate, alternate cube
Rectangular prism / cuboid
Triangular Prism
Pentagonal Prism

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.

  • 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.

  • 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.

  • 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!

  • 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.

  • 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.

  • 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.

Have fun with your shapes this week