Doubling Numbers

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.

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.

Here is a mini 'Lesson Plan' for you to work through with your child.

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.

Briefly talk about doubles. Ask your child what doubling means and the throw some examples at him / her.
I would suggest using the units to start with (1, 2, 3, 4, 5, 6, 7, 8, 9)

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.

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)

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.

Start with something fairly easy so they're not having to think too much about the numbers.
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.

                      /   \
                   20     4
                     \     /

Then draw arrows underneath these doubles to show putting these numbers together and the answer you will get.

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.

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.

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.

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.

Some games you could play:

Have a race - see who can double a number first, on paper or in your heads.
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.
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........

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.

Mental Maths Activities

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.

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).

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.

Throwing a ball
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)

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)

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 number

Hand tapping
Tap hands on a table or another surface that makes a noise and every time you tap say a number

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.

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

Talking to a teddy (or any other stuffed animal)
Ask your child to teach teddy a particular sequence or maths skill. Or you could just get child to count with teddy - to make this even more fun you could join in too.

What does mental maths mean to you?

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.

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.

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.

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.

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!)

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.

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.

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.

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.

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.

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.

How to use this Blog to help your child with their maths

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.

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:
  • Something mathematical that I found interesting and wanted to share and talk about.
  • 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.
  • 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.
  • A fun mathematical activity - again something that anyone and everyone can do that will raise the profile of maths for your children.
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.

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.

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.

Good luck, enjoy and please comment or email me if you have any questions: