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Torn Shapes

Stage: 2 Challenge Level: Challenge Level:1

Jason's class cut out rectangles and some shapes which were two rectangles joined together from one centimetre squared paper.
They then counted how many squares the shapes took up.

After this they tore a piece out of some of their shapes to make a puzzle for the other groups to do.
Can you work out how many squares there were in these shapes before the bit was torn out? The orange, blue, green and yellow shapes were rectangles. The bottom two shapes, which are pale orange and purple, were each two rectangles joined together.

six torn rectangles
Courtney's group tore too much off their grey rectangle!

torn rectangle

What is the smallest number of squares it could have had?
What is the largest number of squares it could have had if it was not longer than any of the other shapes?

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.