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?