Area - squares and rectangles

problem

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?
problem

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?
problem
Favourite

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.
problem
Favourite

Different Sizes

Age

5 to 11

Challenge level

A simple visual exploration into halving and doubling.
problem
Favourite

Always, Sometimes or Never? Shape

Age

7 to 11

Challenge level

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

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.
problem

Great Squares

Age

7 to 11

Challenge level

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

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?
problem
Favourite

Transformations on a Pegboard

Age

7 to 11

Challenge level

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

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?