What is the greatest number of squares you can make by overlapping three squares?
Age 5 to 7 Challenge Level:
You might have already had a go at Cut and Make where we take a square, cut it in two along a diagonal, then take one of those right angled isosceles triangles and cut that in half so that you end up with three pieces:
I've coloured them just to make it clearer.
This challenge is also about making new shapes out of these pieces, but it is slightly different from Cut and Make. There are some new rules:
You must join the shapes together along their sides.
You must have at least one pair of vertices touching for each join.
So this way is good:
BUT this one would not be allowed:
The blue triangle is not right - none of its vertices pairs up with a vertex of the red piece.
Here are some outlines of the three shapes fitted together. Can you work out how they fit in each one? You might find it helpful to print off this sheet - you can cut out the three triangles from the top of it and have a go at fitting them into the outlines.
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.