Midpoint Triangle
Can you cut up a square in the way shown and make the pieces into a
triangle?
Age
7 to 11
Challenge level
Problem
Take a square of paper.
Put a mark half way along each side (ABCD). (You can do this easily
by folding.)
Join two midpoints (DC), as shown, then mark half way along the
new line (E).
Now join this new midpoint to the other two. (EA, EB).
Cut along these lines.
Now use the four shapes to make a triangle.
Image
Getting Started
Which part could be a corner?
Would it be helpful to draw the square on squared paper and cut out the shapes?
Would it be helpful to draw the square on squared paper and cut out the shapes?
Student Solutions
Joshua (Brooklands Primary School, Suffolk) says:
I found this one the hardest. I came back to it the next day and could then see it differently.
He drew a picture of the solution. So did Gemma (Sholing Junior School, Southampton).
Image
Teachers' Resources
Why do this problem?
This short problem is good for encouraging children to
visualise and it can be done practically by children who lack
confidence.
Key questions
Which part could be a corner?
Would it be helpful to draw the square on squared paper and
cut out the shapes?
Possible extension
Children could try
Rearrange the Square as a follow-up problem.