# 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.

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.

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## Comment viewing options

### What a lovely simple idea! i

What a lovely simple idea! i will be trying this with my Year 5 class in the new term. Thank you very much!
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### I love this idea! You could

I love this idea! You could add differentiation by changing the number at the start of the number line - for example one group could start on zero, another group could start on 20 - so that they might be jumping on in decimals whilst the first group are jumping on in whole numbers. The children could suggest starter numbers once they got the hang of it. I will be using this next week with a vey mixed ability group.
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### Used this today with a mixed

Used this today with a mixed ability Y6 class - very good tool for self differentiating. My HA were trying to out do each other with decimals. Lots of discussion and reasoning in a mental & oral session - excellent.
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### So glad this worked so well.

So glad this worked so well. Thank you so much for the feedback.
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### I'm supporting year 6's that

I'm supporting year 6's that lack mathematical confidence, this will be a great tool. Thanks
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### This idea really works. I've

This idea really works. I've even given my year 2 children lines with jumps and no numbers and was amazed at the resulting number sentences they they thought it might show - from a simple 1 + 3 to 71 + 30 3 x 10 and 46 + 6 all from the same number line.
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### That's terrific. Thank you so

That's terrific. Thank you so much for the feedback.
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### I'm as bad as some of the

I'm as bad as some of the kids I teach... I want to know if I got the answers right!!  What jumps do people suggest for the 60 one?
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### Plf678, That's ok. Three

Plf678, That's ok. Three jumps of 20 would reach 60 directly without the need for the extra little hop, so anything just shy of 20 would be acceptable:

19 + 19 + 19 + 3   or  18 + 18 + 18 + 5   would both be quite logical;

17 + 17 + 17 + 9   or  16 + 16 + 16 + 12  are starting to make that little hop into a bigger hop;

Anything larger would probably be questionable.... however (importantly), as I said in the post, there is no real sense of scale on an empty number line, so almost anythign should/would be acceptable. The 'teaching' is in seeing how the children justify their ideas.

John

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### Wow... that was a quick

Wow... that was a quick answer! Thank you :-) i've got a better understanding of this now. I'm planning my maths lessons for next week and will put this as a starter. I'm trying my hardest to get the kids to have a good visual image of a number line and this will help them.
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