Mental Mondays #7

Here's a little gem that turns those very versatile empty number lines on their heads - figuratively speaking!

The main virtue of an empty number line is that 'emptyness' - they can be adapted to any purpose. Here, we keep them empty and challenge children to use their 'problem solving skills' and to use and apply their knowledge of number calculations to determine which numbers are missing.

A picture would save 1,000 words, so here we go:

Draw a (or better yet, display a pre-drawn) number line like the following:

This example shows two equal jumps arriving at the number 6. The question is, what number does the '?' represent?

The children clearly have to use their knowledge of even jumps, 'doubles' and multiplication facts to help them discern the solution. We found it helpful to encourage the children to work in pairs - copying the number line onto a mini-whiteboard and discussing with each other potential solutions.

Happy with that, now lets add a small level of complexity:

Two equal jumps and one small hop leads to 13 - what could the missing numbers be? Since empty number lines do not show scale there is more than one solution here... If appropriate, challenge the children to find more than one possible answer.

A further adaptation

Two equal jumps and one small hop back takes us to 12 - as before, this combination offers more than one acceptable answer.

Another alternative:

Three equal jumps leads to 21... challenge the children to identify each of the missing numbers?

A further level of complexity:

Two equal jumps and one small hop leads to 60 - challenge the children to identify each of the unknown numbers, again there is more than one possible answer.

Finally (for now):

Three jumps forward and one small hop back leads to 29 - what could the missing numbers be?

All of the above are offered simply as examples - the age and ability of your children will clearly determine your choices... However, any of the six ideas can be made easier or more tricky, as the situation demands.

Once the children are comfortable with any particular number line design encourage them to set a similar challenge for their partner - and then to explain to each other their thinking.

We hope you (and your children) have fun with this one. As always, we'd love to hear your thoughts, please post a comment below.

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