Build it Up
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
You may like to take a look at this follow-on activity: Build it up More.
Why do this problem?
This activity was initially developed for Wild Maths
, our sister site, to encourage learners to be creative mathematicians. Mathematics is certainly a creative subject. It involves spotting patterns, making connections, finding new ways of looking at things and using what you already know in new contexts. Creative mathematicians play around with
examples, draw pictures, have the courage to experiment and ask good questions. (Wild Maths is aimed at individual learners, rather than teachers so the notes below only appear on NRICH.)
When the simple rules have been outlined and the example worked through some pupils may be happy recording their trials on paper. I have found that some like to have little circles of paper/plastic/wood that they can write numbers on and so place them accordingly.
When a number of solutions have been found some good discussions may be had with the pupils sharing their observations as to what they notice and what does not work.
Tell me about what's happening with the ideas you've tried.
Tell me about what's happening here (where they are at at the moment)
Some children might enjoy having a go at Build it Up More
If some pupils do not have a steady hand or need help with keeping a record of what they've done, some adult support may be required.