Area - squares and rectangles

There are 90 NRICH Mathematical resources connected to Area - squares and rectangles

problem

Making Squares

Age

7 to 11

Challenge level

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?

problem

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?

problem

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?

problem

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?

problem

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.

article

Approaches to Area

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

article

Exploration versus Calculation

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

article

From One Shape to Another

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.

problem

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?

problem

Always, Sometimes or Never? Shape

Age

7 to 11

Challenge level

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