This is a differentiated set of challenge sheets I made that focus on showing how the various numbers in a calculation ‘fit’ together, which is what the **bar model** is really great for. Once this is understood, it can then be shown how addition and subtraction are **inverse operations**, which allows us to use that knowledge to find **missing numbers** or to check that our calculations are right.

Resources included:

**Base Camp**, **Hill Climber** and **Mountaineer** sheets all focus on evidencing the 2017 ITAF statement for **Working At Expected Standard**: *“The pupil can recognise the inverse relationships between addition and subtraction and use this to check calculations and work out missing number problems (e.g. Δ − 14 = 28).” *The numbers that the children are using increase in size on each challenge level, and by Mountaineer the children have to segmenet up their bar model by themselves.

The **Everest** sheet focuses on the 2017 ITAF **Greater Depth** statement: *“The pupil can solve more complex missing number problems (e.g. 14 + – 3 = 17; 14 + Δ = 15 + 27).”*

NOTE:

I recently saw a lovely poem to help remember how to solve missing number problems, which looks like this:

The only issue I had with this poem is that it teaches a **procedure** without really the reasoning as to **why** it works. Also, it assumes that the calculation will be laid out in the typical fashion of:

*x** + **y = z. *

So it doesn’t work with, for example, something like this:

___ = 7 + 5

According to the rhyme I’d do the inverse and my ‘answer’ would be 2. And this is just the sort of layout you’ll see pop up in all kinds of tests in order to see how much sense of number the children really have as opposed to having memorised a procedure.

So, while this is a great way to remember a useful procedure, I think it would be best used perhaps as a plenary or after several lessons focusing on the ‘why’ stage. You could then see if the children can spot the limits of this rhyme and when it does or does not apply. It could even form the basis of a whole lesson investigating it!

If you do want to share this poem with the children, I’ve adapted it a little below just so it goes in order of missing number at the beginning to missing number at the end and so it’s a bit easier to read (no whiteboard glare):

Great rework on the poem – we had noticed the same problem but not got around to creating a different rhyme. Thanks for doing it for us – one for the working wall!