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Resources tagged with Area similar to Pebbles:

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Broad Topics > Measures and Mensuration > Area

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Pebbles

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

Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?

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Fitted

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

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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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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Towers

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

A tower of squares is built inside a right angled isosceles triangle. The largest square stands on the hypotenuse. What fraction of the area of the triangle is covered by the series of squares?

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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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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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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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Hallway Borders

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

A hallway floor is tiled and each tile is one foot square. Given that the number of tiles around the perimeter is EXACTLY half the total number of tiles, find the possible dimensions of the hallway.

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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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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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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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Great Squares

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

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

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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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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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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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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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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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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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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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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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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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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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Tiles on a Patio

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

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

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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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Tiling

Stage: 2 Challenge Level: Challenge Level:1

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

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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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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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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?

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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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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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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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Geoboards

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

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

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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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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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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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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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Making Boxes

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

Cut differently-sized square corners from a square piece of paper to make boxes without lids. Do they all have the same volume?

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My New Patio

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

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

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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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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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Blue and White

Stage: 3 Challenge Level: Challenge Level:1

In the four examples below identical squares of side one unit contain some circles shaded blue. In which of the four examples is the shaded area greatest?

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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

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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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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Framed

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

Seven small rectangular pictures have one inch wide frames. The frames are removed and the pictures are fitted together like a jigsaw to make a rectangle of length 12 inches. Find the dimensions of. . . .

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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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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. . . .