Resources tagged with: Area - squares and rectangles

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Broad Topics > Measuring and calculating with units > Area - squares and rectangles

Geoboards

Age 7 to 11Challenge Level

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

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?

More Transformations on a Pegboard

Age 7 to 11Challenge Level

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

Transformations on a Pegboard

Age 7 to 11Challenge Level

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

Tiles on a Patio

Age 7 to 11Challenge Level

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

My New Patio

Age 7 to 11Challenge Level

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

Torn Shapes

Age 7 to 11Challenge Level

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

Inside Seven Squares

Age 7 to 11Challenge Level

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

Fitted

Age 7 to 11Challenge 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?

Overlapping Squares

Age 7 to 11Challenge 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.

Through the Window

Age 7 to 11Challenge Level

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?

Tiling

Age 7 to 11Challenge Level

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

Triangle Relations

Age 7 to 11Challenge Level

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

Ribbon Squares

Age 7 to 11Challenge Level

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

Area and Perimeter

Age 7 to 11Challenge Level

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

Extending Great Squares

Age 7 to 11Challenge Level

Explore one of these five pictures.

Cover the Tray

Age 7 to 11Challenge Level

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

Tiles in the Garden

Age 7 to 11Challenge Level

How many tiles do we need to tile these patios?

Tiling Into Slanted Rectangles

Age 7 to 11Challenge Level

A follow-up activity to Tiles in the Garden.

Fit These Shapes

Age 5 to 11Challenge Level

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?

Dicey Perimeter, Dicey Area

Age 7 to 11Challenge Level

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?

Rope Mat

Age 7 to 11Challenge Level

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

Great Squares

Age 7 to 11Challenge Level

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

Fencing Lambs

Age 7 to 11Challenge Level

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

Making Boxes

Age 7 to 11Challenge Level

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

Framed

Age 11 to 14Challenge Level

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. . . .

Fencing

Age 7 to 11Challenge Level

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

Numerically Equal

Age 7 to 11Challenge Level

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

Lawn Border

Age 5 to 11Challenge Level

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?

Pebbles

Age 7 to 11Challenge Level

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?

Shape Draw

Age 7 to 11Challenge Level

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

Different Sizes

Age 5 to 11Challenge Level

A simple visual exploration into halving and doubling.

Exploration Versus Calculation

Age 5 to 11

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

A Square in a Circle

Age 7 to 11Challenge 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?

Wrapping Presents

Age 7 to 11Challenge Level

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

Shaping It

Age 5 to 11Challenge Level

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.

Cylinder Cutting

Age 7 to 11Challenge Level

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

Fence It

Age 11 to 14Challenge Level

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

Two Squared

Age 7 to 11Challenge Level

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?

Cutting it Out

Age 5 to 11Challenge Level

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

Tilted Squares

Age 11 to 14Challenge Level

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

Being Curious - Primary Measures

Age 5 to 11Challenge Level

Measure problems for inquiring primary learners.

Being Collaborative - Primary Measures

Age 5 to 11Challenge Level

Measure problems for primary learners to work on with others.

Being Resourceful - Primary Measures

Age 5 to 11Challenge Level

Measure problems at primary level that require careful consideration.

Poly Plug Rectangles

Age 5 to 14Challenge Level

The computer has made a rectangle and will tell you the number of spots it uses in total. Can you find out where the rectangle is?

Being Resilient - Primary Measures

Age 5 to 11Challenge Level

Measure problems at primary level that may require resilience.

A Day with Grandpa

Age 7 to 11Challenge Level

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

Paper Halving

Age 5 to 11Challenge Level

In how many ways can you halve a piece of A4 paper? How do you know they are halves?

Always, Sometimes or Never? Shape

Age 7 to 11Challenge Level

Are these statements always true, sometimes true or never true?