Squares

There are 79 NRICH Mathematical resources connected to Squares
Hidden Squares
problem
Favourite

Hidden squares

Age
11 to 14
Challenge level
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Can you find the squares hidden on these coordinate grids?
Data shapes
problem
Favourite

Data shapes

Age
5 to 7
Challenge level
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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?

Fitted
problem
Favourite

Fitted

Age
7 to 11
Challenge level
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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?

Complete the Square
problem
Favourite

Complete the square

Age
5 to 7
Challenge level
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Complete the squares - but be warned some are trickier than they look!

Vector journeys
problem
Favourite

Vector journeys

Age
14 to 18
Challenge level
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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?
Semi-detached
problem
Favourite

Semi-detached

Age
14 to 16
Challenge level
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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.
Squares in rectangles
problem
Favourite

Squares in rectangles

Age
11 to 14
Challenge level
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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?
Seeing Squares
problem
Favourite

Seeing squares

Age
5 to 11
Challenge level
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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.

Let Us Reflect
problem
Favourite

Let us reflect

Age
7 to 11
Challenge level
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Where can you put the mirror across the square so that you can still "see" the whole square? How many different positions are possible?

Torn Shapes
problem
Favourite

Torn shapes

Age
7 to 11
Challenge level
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These rectangles have been torn. How many squares did each one have inside it before it was ripped?