Squares
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Data shapes
Sara and Will were sorting some pictures of shapes on cards. "I'll collect the circles," said Sara. "I'll take the red ones," answered Will. Can you see any cards they would both want?
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Fitted
Nine squares with side lengths 1, 4, 7, 8, 9, 10, 14, 15, and 18 cm can be fitted together to form a rectangle. What are the dimensions of the rectangle?
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Complete the square
Complete the squares - but be warned some are trickier than they look!
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Vector journeys
Charlie likes to go for walks around a square park, while Alison likes to cut across diagonally. Can you find relationships between the vectors they walk along?
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Semi-detached
A square of area 40 square cms is inscribed in a semicircle. Find
the area of the square that could be inscribed in a circle of the
same radius.
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Squares in rectangles
A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle
contains 20 squares. What size rectangle(s) contain(s) exactly 100
squares? Can you find them all?
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Seeing squares
Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.
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Let us reflect
Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?
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Torn shapes
These rectangles have been torn. How many squares did each one have inside it before it was ripped?