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:

114+49=114+6+43=120+43=163

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.