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Resources tagged with Area - squares and rectangles similar to Making Rectangles:

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

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Making Rectangles

Age 7 to 14 Challenge Level:

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

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Perimeter Challenge

Age 11 to 14 Challenge Level:

Can you deduce the perimeters of the shapes from the information given?

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Changing Areas, Changing Perimeters

Age 11 to 14 Challenge Level:

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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Completing Quadrilaterals

Age 11 to 14 Challenge Level:

We started drawing some quadrilaterals - can you complete them?

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From One Shape to Another

Age 7 to 14

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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Growing Rectangles

Age 11 to 14 Challenge Level:

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

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Tilted Squares

Age 11 to 14 Challenge Level:

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

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Shape Draw

Age 7 to 11 Challenge Level:

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

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Always, Sometimes or Never? Shape

Age 7 to 11 Challenge Level:

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

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Cylinder Cutting

Age 7 to 11 Challenge Level:

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

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Being Resilient - Primary Measures

Age 5 to 11 Challenge Level:

Measure problems at primary level that may require resilience.

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A Day with Grandpa

Age 7 to 11 Challenge Level:

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

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Fence It

Age 11 to 14 Challenge Level:

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

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Being Resourceful - Primary Measures

Age 5 to 11 Challenge Level:

Measure problems at primary level that require careful consideration.

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Tiling Into Slanted Rectangles

Age 7 to 11 Challenge Level:

A follow-up activity to Tiles in the Garden.

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How Random!

Age 7 to 11 Challenge Level:

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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Area and Perimeter

Age 7 to 11 Challenge Level:

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

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Shaping It

Age 5 to 11 Challenge 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.

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Extending Great Squares

Age 7 to 11 Challenge Level:

Explore one of these five pictures.

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Poly Plug Rectangles

Age 5 to 11 Challenge 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?

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Cutting it Out

Age 5 to 11 Challenge Level:

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

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Being Curious - Primary Measures

Age 5 to 11 Challenge Level:

Measure problems for inquiring primary learners.

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Overlapping Squares

Age 7 to 11 Challenge 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.

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Tiles in the Garden

Age 7 to 11 Challenge Level:

How many tiles do we need to tile these patios?

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Being Collaborative - Primary Measures

Age 5 to 11 Challenge Level:

Measure problems for primary learners to work on with others.

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Perimeter Possibilities

Age 11 to 14 Challenge Level:

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

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Can They Be Equal?

Age 11 to 14 Challenge Level:

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

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Framed

Age 11 to 14 Challenge 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. . . .

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Through the Window

Age 7 to 11 Challenge 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?

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Torn Shapes

Age 7 to 11 Challenge Level:

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

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Warmsnug Double Glazing

Age 11 to 14 Challenge Level:

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

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Fencing Lambs

Age 7 to 11 Challenge Level:

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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Paper Halving

Age 5 to 11 Challenge Level:

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

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Wrapping Presents

Age 7 to 11 Challenge Level:

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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Approaches to Area

Age 5 to 11

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

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Dicey Perimeter, Dicey Area

Age 7 to 11 Challenge 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?

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Transformations on a Pegboard

Age 7 to 11 Challenge Level:

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

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Different Sizes

Age 5 to 11 Challenge Level:

A simple visual exploration into halving and doubling.

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Inside Seven Squares

Age 7 to 11 Challenge Level:

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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Two Squared

Age 7 to 11 Challenge 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?

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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.

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Numerically Equal

Age 7 to 11 Challenge Level:

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

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A Square in a Circle

Age 7 to 11 Challenge 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?

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Lawn Border

Age 5 to 11 Challenge 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?

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Place Your Orders

Age 11 to 14 Challenge Level:

Can you rank these sets of quantities in order, from smallest to largest? Can you provide convincing evidence for your rankings?

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Ribbon Squares

Age 7 to 11 Challenge Level:

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

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Cover the Tray

Age 7 to 11 Challenge Level:

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

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Triangle Relations

Age 7 to 11 Challenge Level:

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

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Geoboards

Age 7 to 11 Challenge Level:

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

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Pebbles

Age 7 to 11 Challenge 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?