Cut and make
Cut a square of paper into three pieces as shown. Now,can you use
the 3 pieces to make a large triangle, a parallelogram and the
square again?
Age
7 to 11
Challenge level
Problem
Take a square of paper, fold it in half from corner to corner and cut along the fold.
Take one of the triangles, fold it in half and cut along the fold.
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Use the three pieces to make a large triangle, a parallelogram and the square again.
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Student Solutions
Thank you to Meg for sending us these great diagrams! Did you make the shapes in the same way?
Here is a diagram showing how the original square should be cut.
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These pieces can be arranged to make a triangle like this:
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The parallelogram can be made like this:
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The square can be made as shown in the first diagram.
Well done Meg!
From Class 2GW, at the Bavarian International School, the teacher sent in the following:
They really enjoyed the Cut and Make activity this week. Although the challenge was to make a triangle, parallelogram and square, after a few minutes Jack discovered that you could make a trapezium with the three triangles. A bit later Ella discovered that she could make a rectangle. They were excited when they discovered that these weren't included in the solutions so far.
As an extra challenge, we tried to make a kite. Zoe discovered that you could only make one if you didn't cut the original square. Instead, she used the first diagonal fold line to fold in the other two corners too. So it became more of an origami kite.
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Thank you for that excellent work BIS. Why not try some more of the challenges?
If you enjoyed this puzzle, you might like to look at some of the Tangram puzzles on this site, for example Tangram or Tangrams - World of Tan.
Teachers' Resources
Why do this problem?
This problem
is based on the popular Tangram activities. It may help to extend
pupils' concepts of triangles and it will encourage them to use
visualisation.
Key questions
How have you done this?
What have you tried so far?
How could you join these two shapes? Where could
the third piece go?
Possible extension
Take a large square and cut it up into a variety of shapes,
for example:
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Possible support
Plastic or card shapes would be helpful.