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Resources tagged with Area similar to A Cartesian Puzzle:

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Challenge level: Challenge Level:1 Challenge Level:2 Challenge Level:3

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Broad Topics > Measures and Mensuration > Area

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Shape Draw

Stage: 2 Challenge Level: Challenge Level:1

Use the information on these cards to draw the shape that is being described.

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Overlap

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

A red square and a blue square overlap so that the corner of the red square rests on the centre of the blue square. Show that, whatever the orientation of the red square, it covers a quarter of the. . . .

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Cutting it Out

Stage: 1 and 2 Challenge Level: Challenge Level:1

I cut this square into two different shapes. What can you say about the relationship between them?

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Triangle Island

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

You have pitched your tent (the red triangle) on an island. Can you move it to the position shown by the purple triangle making sure you obey the rules?

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A Square in a Circle

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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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Two Squared

Stage: 2 Challenge Level: Challenge Level:1

What happens to the area of a square if you double the length of the sides? Try the same thing with rectangles, diamonds and other shapes. How do the four smaller ones fit into the larger one?

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Fit These Shapes

Stage: 1 and 2 Challenge Level: Challenge Level:1

What is the largest number of circles we can fit into the frame without them overlapping? How do you know? What will happen if you try the other shapes?

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Shear Magic

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?

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Triangle Relations

Stage: 2 Challenge Level: Challenge Level:1

What do these two triangles have in common? How are they related?

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Fencing

Stage: 2 Challenge Level: Challenge Level:1

Arrange your fences to make the largest rectangular space you can. Try with four fences, then five, then six etc.

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How Random!

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

Explore this interactivity and see if you can work out what it does. Could you use it to estimate the area of a shape?

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Numerically Equal

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

Can you draw a square in which the perimeter is numerically equal to the area?

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Kissing Triangles

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Determine the total shaded area of the 'kissing triangles'.

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Inside Seven Squares

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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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Cover the Tray

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

These practical challenges are all about making a 'tray' and covering it with paper.

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Ribbon Squares

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?

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Wrapping Presents

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

Choose a box and work out the smallest rectangle of paper needed to wrap it so that it is completely covered.

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Perimeter Possibilities

Stage: 3 Challenge Level: Challenge Level:1

I'm thinking of a rectangle with an area of 24. What could its perimeter be?

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Kite

Stage: 3 Challenge Level: Challenge Level:1

Derive a formula for finding the area of any kite.

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Overlapping Squares

Stage: 2 Challenge Level: Challenge Level:1

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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Cylinder Cutting

Stage: 2 and 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

An activity for high-attaining learners which involves making a new cylinder from a cardboard tube.

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Uncanny Triangles

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Can you help the children find the two triangles which have the lengths of two sides numerically equal to their areas?

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Tilted Squares

Stage: 3 Challenge Level: Challenge Level:1

It's easy to work out the areas of most squares that we meet, but what if they were tilted?

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Inscribed in a Circle

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

The area of a square inscribed in a circle with a unit radius is, satisfyingly, 2. What is the area of a regular hexagon inscribed in a circle with a unit radius?

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Pick's Theorem

Stage: 3 Challenge Level: Challenge Level:1

Polygons drawn on square dotty paper have dots on their perimeter (p) and often internal (i) ones as well. Find a relationship between p, i and the area of the polygons.

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Lying and Cheating

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Follow the instructions and you can take a rectangle, cut it into 4 pieces, discard two small triangles, put together the remaining two pieces and end up with a rectangle the same size. Try it!

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Rati-o

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Points P, Q, R and S each divide the sides AB, BC, CD and DA respectively in the ratio of 2 : 1. Join the points. What is the area of the parallelogram PQRS in relation to the original rectangle?

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Approaches to Area

Stage: 1 and 2

This article for teachers gives some food for thought when teaching ideas about area.

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An Unusual Shape

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Can you maximise the area available to a grazing goat?

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Tiling

Stage: 2 Challenge Level: Challenge Level:1

An investigation that gives you the opportunity to make and justify predictions.

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Extending Great Squares

Stage: 2 and 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Explore one of these five pictures.

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Shaping It

Stage: 1 and 2 Challenge Level: Challenge Level:1

These pictures were made by starting with a square, finding the half-way point on each side and joining those points up. You could investigate your own starting shape.

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Changing Areas, Changing Perimeters

Stage: 3 Challenge Level: Challenge Level:1

How can you change the area of a shape but keep its perimeter the same? How can you change the perimeter but keep the area the same?

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Tiles in the Garden

Stage: 2 Challenge Level: Challenge Level:1

How many tiles do we need to tile these patios?

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Tiling Into Slanted Rectangles

Stage: 2 and 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

A follow-up activity to Tiles in the Garden.

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Through the Window

Stage: 2 Challenge Level: Challenge Level:1

My local DIY shop calculates the price of its windows according to the area of glass and the length of frame used. Can you work out how they arrived at these prices?

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Dicey Perimeter, Dicey Area

Stage: 2 Challenge Level: Challenge Level:1

In this game for two players, you throw two dice and find the product. How many shapes can you draw on the grid which have that area or perimeter?

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Area and Perimeter

Stage: 2 Challenge Level: Challenge Level:1

What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.

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Growing Rectangles

Stage: 3 Challenge Level: Challenge Level:1

What happens to the area and volume of 2D and 3D shapes when you enlarge them?

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More Transformations on a Pegboard

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.

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Isosceles Triangles

Stage: 3 Challenge Level: Challenge Level:1

Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?

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A Day with Grandpa

Stage: 2 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Grandpa was measuring a rug using yards, feet and inches. Can you help William to work out its area?

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Circle Panes

Stage: 2 Challenge Level: Challenge Level:1

Look at the mathematics that is all around us - this circular window is a wonderful example.

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Making Rectangles

Stage: 2 and 3 Challenge Level: Challenge Level:1

A task which depends on members of the group noticing the needs of others and responding.

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Rope Mat

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

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

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Fence It

Stage: 3 Challenge Level: Challenge Level:1

If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?

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Exploration Versus Calculation

Stage: 1, 2 and 3

This article, written for teachers, discusses the merits of different kinds of resources: those which involve exploration and those which centre on calculation.

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The Pillar of Chios

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Semicircles are drawn on the sides of a rectangle ABCD. A circle passing through points ABCD carves out four crescent-shaped regions. Prove that the sum of the areas of the four crescents is equal to. . . .

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Torn Shapes

Stage: 2 Challenge Level: Challenge Level:1

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

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Carpet Cuts

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

You have a 12 by 9 foot carpet with an 8 by 1 foot hole exactly in the middle. Cut the carpet into two pieces to make a 10 by 10 foot square carpet.