Square to L
Find a way to cut a 4 by 4 square into only two pieces, then rejoin the two pieces to make an L shape 6 units high.
Age
7 to 11
Challenge level
Problem
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Find a way to cut a $4$ by $4$ square into only two pieces, then rejoin the two pieces to make an L shape, $6$ units high.
Student Solutions
Cassandra (from Cambridge) and Josh (from Bedfordshire) both say to cut out the top right quarter of the square and put them on top.
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Audre (from Singapore) says to "Split the square in half horizontally or vertically then join them''.
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Arthur (from Cambridge) found a different way: "In the top right corner, cut a row of 3 joined to a row of 2 underneath. Flip it over and join it to the top''.
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Are there more ways to do it??
If you've gone further with pupils then you might like to see these results.
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Teachers' Resources
Why do this problem?
This activity
is an accessible piece of spatial-awareness work and will encourage
children to visualise.
Possible approach
Each child should be given the opportunity to start this with
some practical resources, for example paper, card, plastic squares
etc.
Key questions
How are you finding your solutions?
Show me how the cut-off piece fits so that we get an "L"
shape.
Possible extension
Try other even-sized squares - and afterwards look at the
Solutions !
Some pupils may like to have a go at 'near' solutions that do
not work, saying precisely why they do not.