Helping a Struggling Maths Student: Number Bonds

This is my second post of our curriculum free maths journey.  For the first post see here.

My goal in teaching this wasn’t the recitation of number bonds (they could do that already), it was to ensure the girls understood them and were able to apply their understanding to word problems.  It was also to teach the girls to view number bonds as one of many tools they can use to aid with their maths

Using M ‘n’ Ms

I concentrated on the number bonds for 10 and gave them 10 peanut M ‘n’ Ms each.  They simply played with them, splitting them up into different piles and putting them back together.  The point was to visually show L10 that 10 could be a whole number or it could be split into smaller numbers:


Using Blocks

I then gave them the blocks.  These were their Mathusee blocks and are really very useful.  This time I wanted them to find out how many number bonds 10 had:

Then I sat down and we talked about how 10 (or any number) could be split into two or more different parts.  I asked them to work out 96 + 54.  As expected L10 started to work it out on her fingers.  I explained how the number bonds could help here.  Her face lit up a little (a very little!).  I then asked them what 114 +49 was and gave them the tools to work it out using the knowledge of the number bonds:



L10’s face lit up a little bit more.  C10 understood this already and was easily able to do these simple sums in her head.  I gave L10 a few more, marvelling at the fact that not once had she used her fingers (which is what she would usually have done).  She was grinning towards the end because it was obvious that she really did understand!  At dinner that night she asked me to set her some more for fun.  Well, I very nearly fell off my chair!  L10 asking for maths for fun?  It was a pleasant confirmation of my choice.

Using Basic Picture Diagrams

We talked about the idea of there being a whole in any given sum and then parts of a whole.  After demonstrating with the blocks I drew a diagram to illustrate this:


I then set some easy word problems that I knew L10 would be able to so I could demonstrate how this knowledge could be used as a tool to help her work them out.

  1. L10 went into a shop and bought £6 worth of bananas.  She had £10 to start of with, how much did she go home with?
  2. I thought of a number, added 8 to it, then took away 2.  This resulted in an answer of 19.  What was the first number I thought of?
  3. I went to the with £35 shops and bought a skirt for £5, a pair of shoes for £12 and two tops for £2 a piece.  One of the tops was stained so I took it back for a refund.  How much money did I go home with.

These were simple on purpose.  I wanted her to have success and know how it felt.  I thought harder problems may have clouded her understanding and made her panic.

Reinforcing with Lots of Games

I wanted them to have lots of practise doing mental maths each day.  We put aside a handful of times each day when they played a maths game.  Where ever possible Gary or I joined in, which they loved!

I had been surprised to find L10 didn’t truly understand the application of number bonds.  I knew she knew them as we had spent many mornings practising and taking timed tests all those years ago ( Saxon 3).  She was never too bad, and her maths grade was always high enough that I wasn’t too concerned.  However, not having understood something so fundamental meant that as she aged the higher level maths completely stumped her.

One session of hands on, full on maths, targeting her weak areas, had brought her forward in leaps and bounds.  I was hopeful for the future.


  1. I love this, and am glad you posted about it as I might use some of the ideas for Quentin. You are very wise to realize that although she got good enough grades that she wasn’t really understanding it and that higher math built on shaky foundation leads to real difficulties. You are wise to take a dramatic turn and look how quickly she has taken to it and now loves to explore this. Pat yourself on the back.

  2. Good call in slowing down for a while to build on fundamentals. You have described my nine-year old to a tee…scoring high but not understanding some of the basic concepts. I have decided to reserve every Friday as hands-on math throughout the school year to hopefully remedy this. I also did logic, puzzle type math over the summer for this reason, and would you believe when I asked her what her favorite summer subject was (I thought for sure she would say art), she said math?!

    1. He, he! You see I knew there was a reason L10 struggled with maths….it’s because of me!! Thank you so much for pointing out my mistake. I had to go back and look at the one I gave her (and I did actually give it to her correctly- phew!). I’ve changed it- easy peasy now!
      PS I’m blushing here!!

  3. Good job there, Claire! I’m sure the girls will have a very good grasp of numbers in no time. It’s hard to take a step back and do what seems to be “slowing down”, but sometimes that may be necessary to build a solid foundation for more complicated work later, so good for you to be doing this now. 🙂

    1. That is exactly what I am hoping to build: a solid foundation. I think I thought that the curriculum would be enough and I can see now that I relied on that too much. L10 needed much more 1-2-1 which she is now getting. I think she is always going to find numbers hard but hopefully the panic will go. Thanks so much for your encouraging comment.

Leave a Reply

This site uses Akismet to reduce spam. Learn how your comment data is processed.