Build it Up

'Build it Up' printed from https://nrich.maths.org/

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We start with any four numbers (not zero!):

A row of circles with the numbers 4, 1, 2, 2 from left to right.

We then add them in pairs and place the total above them:

A row of circles with the numbers 4, 1, 2, 2 from left to right. Above it, a row of circles with 5, 3, 4 from left to right, aligned so that each of these is between two numbers from the row below.

A row of circles with the numbers 4, 1, 2, 2 from left to right. Above it, a row of circles with 5, 3, 4 from left to right, aligned so that each of these is between two numbers from the row below.

And we then add in pairs the new numbers we just got:

A row of circles with the numbers 4, 1, 2, 2 from left to right. Above it, a row of circles with 5, 3, 4 from left to right. Above that, a row of circles with 8, 7 from left to right.

A row of circles with the numbers 4, 1, 2, 2 from left to right. Above it, a row of circles with 5, 3, 4 from left to right. Above that, a row of circles with 8, 7 from left to right.

We do the same with those two numbers to get our final number:

A row of circles with the numbers 4, 1, 2, 2 from left to right. Above it, a row of circles with 5, 3, 4 from left to right. Above that, a row of circles with 8, 7 from left to right. At the top, the number 15. Altogether this makes a triangle of numbers.

You need to find four starting numbers to place at the bottom so that the top number will be 15.

Try to find as many sets of four starting numbers as you can.

Think about good ways to do this. Maybe use a system!

What little change can you make to the rules to explore again?

What new ideas can you think of to make this different? Explore those!

You may like to take a look at the follow-on activity Build it up More.