# Resources tagged with: Area - squares and rectangles

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### There are 52 results

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

### Poly Plug Rectangles

##### Age 5 to 14 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?

### 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.

### Transformations on a Pegboard

##### Age 7 to 11 Challenge Level:

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

### 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?

### Making Rectangles

##### Age 7 to 14 Challenge Level:

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

### 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?

### 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?

### 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?

### 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.

### 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?

### Different Sizes

##### Age 5 to 11 Challenge Level:

A simple visual exploration into halving and doubling.

### More Transformations on a Pegboard

##### Age 7 to 11 Challenge Level:

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

### 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.

### Wallpaper

##### Age 5 to 7 Challenge Level:

These pieces of wallpaper need to be ordered from smallest to largest. Can you find a way to do it?

### Tiling

##### Age 7 to 11 Challenge Level:

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

### 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?

### Extending Great Squares

##### Age 7 to 11 Challenge Level:

Explore one of these five pictures.

### Fit These Shapes

##### Age 5 to 11 Challenge 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?

### 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.

### Shape Draw

##### Age 7 to 11 Challenge Level:

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

### 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?

### Cover the Tray

##### Age 7 to 11 Challenge Level:

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

### 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?

### Always, Sometimes or Never? Shape

##### Age 7 to 11 Challenge Level:

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

### 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?

### 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?

### Numerically Equal

##### Age 7 to 11 Challenge Level:

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

### My New Patio

##### Age 7 to 11 Challenge Level:

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

### 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.

### 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.

### Fitted

##### Age 7 to 11 Challenge 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?

### Rope Mat

##### Age 7 to 11 Challenge Level:

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

### 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.

### 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?

### Cylinder Cutting

##### Age 7 to 11 Challenge Level:

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

### 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?

### Tiles on a Patio

##### Age 7 to 11 Challenge Level:

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

### Fencing

##### Age 7 to 11 Challenge Level:

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

### 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.

### Making Boxes

##### Age 7 to 11 Challenge Level:

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

### 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?

### Triangle Relations

##### Age 7 to 11 Challenge Level:

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

### Tiling Into Slanted Rectangles

##### Age 7 to 11 Challenge Level:

A follow-up activity to Tiles in the Garden.

### Tiles in the Garden

##### Age 7 to 11 Challenge Level:

How many tiles do we need to tile these patios?

### Great Squares

##### Age 7 to 11 Challenge Level:

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

### Sizing Them Up

##### Age 5 to 7 Challenge Level:

Can you put these shapes in order of size? Start with the smallest.

### 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?

### Being Curious - Primary Measures

##### Age 5 to 11 Challenge Level:

Measure problems for inquiring primary learners.

### Being Collaborative - Primary Measures

##### Age 5 to 11 Challenge Level:

Measure problems for primary learners to work on with others.