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Resources tagged with Area similar to Tiling Into Slanted Rectangles:

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Broad Topics > Measures and Mensuration > Area

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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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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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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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Covering Cups

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

What is the shape and dimensions of a box that will contain six cups and have as small a surface area as possible.

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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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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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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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Isosceles

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

Prove that a triangle with sides of length 5, 5 and 6 has the same area as a triangle with sides of length 5, 5 and 8. Find other pairs of non-congruent isosceles triangles which have equal areas.

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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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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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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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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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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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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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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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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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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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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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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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Warmsnug Double Glazing

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

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

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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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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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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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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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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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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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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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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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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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Kite

Stage: 3 Challenge Level: Challenge Level:1

Derive a formula for finding the area of any kite.

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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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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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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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Making Squares

Stage: 2

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 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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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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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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Poly-puzzle

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

This rectangle is cut into five pieces which fit exactly into a triangular outline and also into a square outline where the triangle, the rectangle and the square have equal areas.

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Maths Filler

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

Imagine different shaped vessels being filled. Can you work out what the graphs of the water level should look like?

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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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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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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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Tiling

Stage: 2 Challenge Level: Challenge Level:1

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

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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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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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Different Sizes

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

A simple visual exploration into halving and doubling.

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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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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.