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#### Resources tagged with Area - squares and rectangles similar to A Cartesian Puzzle:

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### There are 60 results

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

### Transformations on a Pegboard

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

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

### Shape Draw

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

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

### Triangle Relations

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

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

### 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.

### Approaches to Area

##### Age 5 to 11

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

### 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?

### 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.

### 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.

### 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?

### 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?

### Extending Great Squares

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

Explore one of these five pictures.

### Always, Sometimes or Never? Shape

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

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

### 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?

### 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?

### 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?

### Perimeter Challenge

##### Age 11 to 14 Challenge Level:

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

### 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.

### 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?

### 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?

### 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?

### Numerically Equal

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

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

### 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?

### 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.

### 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?

### Cover the Tray

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

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

### 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?

### Growing Rectangles

##### Age 11 to 14 Challenge Level:

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

### Making Rectangles

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

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

### 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?

### 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.

### 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?

### 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?

### Tiles in the Garden

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

How many tiles do we need to tile these patios?

### Tiling Into Slanted Rectangles

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

A follow-up activity to Tiles in the Garden.

### Different Sizes

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

A simple visual exploration into halving and doubling.

### Tiling

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

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

### 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.

### Completing Quadrilaterals

##### Age 11 to 14 Challenge Level:

We started drawing some quadrilaterals - can you complete them?

### Great Squares

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

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

### 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?

### 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?

### 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.

### 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?

### 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. . . .

### 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?

### 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?

### 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?

### 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?

### Cylinder Cutting

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

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