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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 squares.
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.
This practical challenge invites you to investigate the different squares you can make on a square geoboard or pegboard.
How many ways can you find of tiling the square patio, using square tiles of different sizes?
Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?