Area - squares and rectangles

problem
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?
problem
Cylinder cutting

Age

7 to 11

Challenge level

An activity for high-attaining learners which involves making a new cylinder from a cardboard tube.
problem
Alison's quilt

Age

11 to 14

Challenge level

Nine squares are fitted together to form a rectangle. Can you find its dimensions?
problem
Arc area

Age

14 to 16

Challenge level

What is the area of the shape enclosed by the line and arcs?
problem
Place your orders

Age

11 to 14

Challenge level

Can you rank these sets of quantities in order, from smallest to largest? Can you provide convincing evidence for your rankings?
problem
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
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.
problem
Extending great squares

Age

7 to 11

Challenge level

Explore one of these five pictures.
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
Making rectangles

Age

7 to 14

Challenge level

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