Samia Henaine designed the prompt for pupils in grades 2 and 3 (years 3 and 4) to test a statement about the perimeter of a rectangle. Pupils create examples by doubling the length of their own rectangles. They measure the sides, calculate perimeters, and decide if the statement is always, sometimes, or never true.

Pupils learn about the concept of perimeter through the inquiry. The teacher aims to co-construct an understanding by drawing out the knowledge pupils already hold and then drawing upon it to develop lines of inquiry. 

Pupils might require a more structured explanation of the concept but this would emerge from their responses to the prompt. 

Question, notice, and wonder

In the first phase of the inquiry, Samia anticipates pupils making these contributions:

Question

• Is the perimeter really double or has it changed by a different amount?

• What would happen if we doubled the other side instead?

• What if we doubled both sides at the same time?

Notice

• Rectangle B still has four sides, just like Rectangle A.

• Only the long side got longer; the short side stayed the same.

• The new perimeter is not double the old one.

Wonder

• I wonder if doubling one side always changes the perimeter by the same amount.

• I wonder what happens to the perimeter if we make a side three times as long instead of doubling it.

Explaining the prompt

The statement in the prompt is false. When you double the length of one side of a rectangle, the perimeter increases by twice the length of that side. As the other pair of sides remains unchanged, the perimeter does not double (see the diagram below).