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Resources tagged with Area similar to Garden Fence:

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Broad Topics > Measures and Mensuration > Area

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Bull's Eye

Stage: 3 Challenge Level: Challenge Level:1

What fractions of the largest circle are the two shaded regions?

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Pie Cuts

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

Investigate the different ways of cutting a perfectly circular pie into equal pieces using exactly 3 cuts. The cuts have to be along chords of the circle (which might be diameters).

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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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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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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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Being Thoughtful - Primary Measures

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

Measure problems at primary level that require careful consideration.

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Being Determined - Primary Measures

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

Measure problems at primary level that may require determination.

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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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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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It Must Be 2000

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

Here are many ideas for you to investigate - all linked with the number 2000.

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Lawn Border

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

If I use 12 green tiles to represent my lawn, how many different ways could I arrange them? How many border tiles would I need each time?

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From One Shape to Another

Stage: 2

Read about David Hilbert who proved that any polygon could be cut up into a certain number of pieces that could be put back together to form any other polygon of equal area.

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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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Being Collaborative - Primary Measures

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

Measure problems for primary learners to work on with others.

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Being Curious - Primary Measures

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

Measure problems for inquiring primary learners.

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Different Sizes

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

A simple visual exploration into halving and doubling.

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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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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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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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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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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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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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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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Tiling

Stage: 2 Challenge Level: Challenge Level:1

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

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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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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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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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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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The Pi Are Square

Stage: 3 Challenge Level: Challenge Level:1

A circle with the radius of 2.2 centimetres is drawn touching the sides of a square. What area of the square is NOT covered by the circle?

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Transformations on a Pegboard

Stage: 2 Challenge Level: Challenge Level:1

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

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Warmsnug Double Glazing

Stage: 3 Challenge Level: Challenge Level:1

How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?

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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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Square Pegs

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

Which is a better fit, a square peg in a round hole or a round peg in a square hole?

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F'arc'tion

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

At the corner of the cube circular arcs are drawn and the area enclosed shaded. What fraction of the surface area of the cube is shaded? Try working out the answer without recourse to pencil and. . . .

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Squaring the Circle

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

Bluey-green, white and transparent squares with a few odd bits of shapes around the perimeter. But, how many squares are there of each type in the complete circle? Study the picture and make. . . .

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Can They Be Equal?

Stage: 3 Challenge Level: Challenge Level:1

Can you find rectangles where the value of the area is the same as the value of the perimeter?

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Fencing Lambs

Stage: 2 Challenge Level: Challenge Level:1

A thoughtful shepherd used bales of straw to protect the area around his lambs. Explore how you can arrange the bales.

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The Big Cheese

Stage: 2 Challenge Level: Challenge Level:1

Investigate the area of 'slices' cut off this cube of cheese. What would happen if you had different-sized block of cheese to start with?

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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.

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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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Dissect

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

It is possible to dissect any square into smaller squares. What is the minimum number of squares a 13 by 13 square can be dissected into?

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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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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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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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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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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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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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Making Squares

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

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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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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Square Areas

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

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