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Build it Up

Stage: 2 Challenge Level: Challenge Level:1

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



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



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



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


You need to find four starting numbers to place at the bottom so that when you get to the top it's 15 each time.

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

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

Here's a pdf version of this task: BuildItUp.pdf

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!

Here is a brand new variation that has lots and lots within it to explore  No longer 4 numbers at the bottom,  but 7 and they are 1, 2, 4, 8, 16, 32, 64   build it up in the same way as before and when you've reached the top EXPLORE and CREATE other versions.

You may like to take a look at this follow-on activity: Build it up More.
The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities can be found here.
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NRICH is part of the family of activities in the Millennium Mathematics Project.