This activity investigates how you might make squares and pentominoes from Polydron.

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?

Look at the mathematics that is all around us - this circular window is a wonderful example.

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

A thoughtful shepherd used bales of straw to protect the area around his lambs. Explore how you can arrange the bales.

Sally and Ben were drawing shapes in chalk on the school playground. Can you work out what shapes each of them drew using the clues?

What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.

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

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?

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?

I cut this square into two different shapes. What can you say about the relationship between them?

How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?

Measure problems for primary learners to work on with others.

Measure problems for inquiring primary learners.

Measure problems at primary level that may require determination.

Measure problems at primary level that require careful consideration.

If you move the tiles around, can you make squares with different coloured edges?

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?

Polygons drawn on square dotty paper have dots on their perimeter (p) and often internal (i) ones as well. Find a relationship between p, i and the area of the polygons.

Draw a square. A second square of the same size slides around the first always maintaining contact and keeping the same orientation. How far does the dot travel?

Points A, B and C are the centres of three circles, each one of which touches the other two. Prove that the perimeter of the triangle ABC is equal to the diameter of the largest circle.

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

An AP rectangle is one whose area is numerically equal to its perimeter. If you are given the length of a side can you always find an AP rectangle with one side the given length?

Can you predict, without drawing, what the perimeter of the next shape in this pattern will be if we continue drawing them in the same way?

Create some shapes by combining two or more rectangles. What can you say about the areas and perimeters of the shapes you can make?

Can you find rectangles where the value of the area is the same as the value of the perimeter?

I'm thinking of a rectangle with an area of 24. What could its perimeter be?