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'Torn Shapes' printed from http://nrich.maths.org/
Why do this problem?
is a good way to assess children's understanding of properties of rectangles. The problem is a nice lead into area, although this is not specifically mentioned in the wording. Torn Shapes is a challenge that encourages children to adopt a different technique for finding area rather than simply counting
You could introduce these ideas by drawing a torn shape of your own, or cutting out a shape and then tearing it (perhaps part of a square or a triangle), and asking the children to decide how many small squares it takes up. This might involve you asking the group for suggestions as to how they might go about solving the problem, and probably modelling these for them.
After this you could show the group the actual problem on an interactive whiteboard or data projector. Then they could work on it in pairs with the shapes from this sheet or on screen with access to squared paper. It is important to allow plenty of time for children to share
their thinking and explanations with their partners and the rest of the group. Some children might want to count each square individually, but that is difficult with this problem. Others might count a row or column and use their knowledge of multiples. It is likely that they will spend some time discussing how best to approach this problem before reaching that conclusion.
As a plenary activity, you could have a torn piece of squared paper which is ambiguous in terms of the original shape it came from and use this to discuss the possible numbers of squares it contains. There is no reason why you should not make your own torn shapes from squared paper using the activity as an idea rather than a problem to be solved.
How many squares are there in a row that is complete?
How many rows are there altogether whether they are complete or not?
You could change the last part of the question so that, rather than it being no longer than any of the other shapes, the final shape has no more than 100 squares. Can learners find all the possible solutions? Challenge them to articulate the pattern in the answers.
Children would benefit from trying Wallpaper