Resources tagged with: Squares

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There are 48 results

Broad Topics > Angles, Polygons, and Geometrical Proof > Squares

Fraction Fascination

Age 7 to 11 Challenge Level:

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

Transformations on a Pegboard

Age 7 to 11 Challenge Level:

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

Cut and Make

Age 7 to 11 Challenge Level:

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?

A Square in a Circle

Age 7 to 11 Challenge Level:

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?

LOGO Challenge - the Humble Square

Age 7 to 16 Challenge Level:

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.

Torn Shapes

Age 7 to 11 Challenge Level:

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

Jig Shapes

Age 5 to 11 Challenge Level:

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

Inside Seven Squares

Age 7 to 11 Challenge Level:

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

Sorting Logic Blocks

Age 5 to 11 Challenge Level:

This interactivity allows you to sort logic blocks by dragging their images.

Seeing Squares

Age 5 to 11 Challenge Level:

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.

Polydron

Age 7 to 11 Challenge Level:

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

Three Squares

Age 5 to 11 Challenge Level:

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

Peg and Pin Boards

Age 5 to 11

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

Diagrams

Age 7 to 11 Challenge Level:

A group activity using visualisation of squares and triangles.

Square Surprise

Age 5 to 11 Challenge Level:

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

Seeing Squares for Two

Age 5 to 11 Challenge Level:

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

LOGO Challenge - the Logic of LOGO

Age 11 to 16 Challenge Level:

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?

Square Corners

Age 7 to 11 Challenge Level:

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?

Square Coordinates

Age 11 to 14 Challenge Level:

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?

Ten Hidden Squares

Age 7 to 14 Challenge Level:

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

Square It

Age 11 to 16 Challenge Level:

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.

Baravelle

Age 7 to 16 Challenge Level:

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

Great Squares

Age 7 to 11 Challenge Level:

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

Overlapping Squares

Age 7 to 11 Challenge Level:

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.

My New Patio

Age 7 to 11 Challenge Level:

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

Eight Hidden Squares

Age 7 to 14 Challenge Level:

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?

Tiles on a Patio

Age 7 to 11 Challenge Level:

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

Tetra Square

Age 11 to 14 Challenge Level:

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.

Dissect

Age 11 to 14 Challenge Level:

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

First Forward Into Logo 1: Square Five

Age 7 to 16 Challenge Level:

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

Coloured Edges

Age 11 to 14 Challenge Level:

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?

Making Squares

Age 7 to 11

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?

Zooming in on the Squares

Age 7 to 14

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?

Hidden Squares

Age 11 to 14 Challenge Level:

Can you find the squares hidden on these coordinate grids?

Opposite Vertices

Age 11 to 14 Challenge Level:

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

Geoboards

Age 7 to 11 Challenge Level:

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

Logo Challenge 3 - Star Square

Age 7 to 16 Challenge Level:

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

LOGO Challenge 4 - Squares to Procedures

Age 11 to 16 Challenge Level:

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

On the Edge

Age 11 to 14 Challenge Level:

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

Squares, Squares and More Squares

Age 11 to 14 Challenge Level:

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

Rope Mat

Age 7 to 11 Challenge Level:

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

LOGO Challenge 5 - Patch

Age 11 to 16 Challenge Level:

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

LOGO Challenge 7 - More Stars and Squares

Age 11 to 16 Challenge Level:

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

Squares in Rectangles

Age 11 to 14 Challenge Level:

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?

Fitted

Age 7 to 11 Challenge Level:

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?

Square Within a Square Within...

Age 11 to 14 Short Challenge Level:

What fraction of this square is shaded?

2001 Spatial Oddity

Age 11 to 14 Challenge Level:

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.

Square Areas

Age 11 to 14 Challenge Level:

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