There are **49** NRICH Mathematical resources connected to **Squares**, you may find related items under Angles, Polygons, and Geometrical Proof.

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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.

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This activity focuses on similarities and differences between shapes.

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Can you each work out what shape you have part of on your card? What will the rest of it look like?

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What can you see? What do you notice? What questions can you ask?

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On the graph there are 28 marked points. These points all mark the vertices (corners) of eight hidden squares. Can you find the eight hidden squares?

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This problem challenges you to work out what fraction of the whole area of these pictures is taken up by various shapes.

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These rectangles have been torn. How many squares did each one have inside it before it was ripped?

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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?

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A tilted square is a square with no horizontal sides. Can you devise a general instruction for the construction of a square when you are given just one of its sides?

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These points all mark the vertices (corners) of ten hidden squares. Can you find the 10 hidden squares?

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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.

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If you move the tiles around, can you make squares with different coloured edges?

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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?

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How would you move the bands on the pegboard to alter these shapes?

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What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?

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What fraction of this square is shaded?

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Why do you think that the red player chose that particular dot in this game of Seeing Squares?

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Seeing Squares game for an adult and child. Can you come up with a way of always winning this game?

This article for teachers suggests activities based on pegboards, from pattern generation to finding all possible triangles, for example.

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Can you find the squares hidden on these coordinate grids?

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Can you recreate squares and rhombuses if you are only given a side or a diagonal?

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Have a good look at these images. Can you describe what is happening? There are plenty more images like this on NRICH's Exploring Squares CD.

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This LOGO Challenge emphasises the idea of breaking down a problem into smaller manageable parts. Working on squares and angles.

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Creating designs with squares - using the REPEAT command in LOGO. This requires some careful thought on angles

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What shape has Harry drawn on this clock face? Can you find its area? What is the largest number of square tiles that could cover this area?

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What is the total area of the four outside triangles which are outlined in red in this arrangement of squares inside each other?

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Can you dissect a square into: 4, 7, 10, 13... other squares? 6, 9, 12, 15... other squares? 8, 11, 14... other squares?

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Just four procedures were used to produce a design. How was it done? Can you be systematic and elegant so that someone can follow your logic?

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Look at how the pattern is built up - in that way you will know how to break the final pattern down into more manageable pieces.

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Can you use LOGO to create a systematic reproduction of a basic design? An introduction to variables in a familiar setting.

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Using LOGO, can you construct elegant procedures that will draw this family of 'floor coverings'?

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A Short introduction to using Logo. This is the first in a twelve part series.

Start with a large square, join the midpoints of its sides, you'll see four right angled triangles. Remove these triangles, a second square is left. Repeat the operation. What happens?

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The whole set of tiles is used to make a square. This has a green and blue border. There are no green or blue tiles anywhere in the square except on this border. How many tiles are there in the set?

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How many centimetres of rope will I need to make another mat just like the one I have here?

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ABCD is a regular tetrahedron and the points P, Q, R and S are the midpoints of the edges AB, BD, CD and CA. Prove that PQRS is a square.

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With one cut a piece of card 16 cm by 9 cm can be made into two pieces which can be rearranged to form a square 12 cm by 12 cm. Explain how this can be done.

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What is the minimum number of squares a 13 by 13 square can be dissected into?

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Can you work out the area of the inner square and give an explanation of how you did it?

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Cut a square of paper into three pieces as shown. Now,can you use the 3 pieces to make a large triangle, a parallelogram and the square again?

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What is the greatest number of squares you can make by overlapping three squares?

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Investigate how this pattern of squares continues. You could measure lengths, areas and angles.

Investigate all the different squares you can make on this 5 by 5 grid by making your starting side go from the bottom left hand point. Can you find out the areas of all these squares?

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What is the smallest number of tiles needed to tile this patio? Can you investigate patios of different sizes?

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How many ways can you find of tiling the square patio, using square tiles of different sizes?

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This activity investigates how you might make squares and pentominoes from Polydron.

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This practical challenge invites you to investigate the different squares you can make on a square geoboard or pegboard.

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Can you make five differently sized squares from the interactive tangram pieces?