Fixed perimetre rectangles and area (PDF, 35 KB)
*Measurement progression, 5th step *

## The purpose of the activity

In this activity, the learners develop an understanding of how to calculate the area and perimeter of rectangles from the measurement of side lengths. They learn that the areas of rectangles with fixed perimeters do not remain the same.

## The teaching points

- The learners understand that the length around an object is its perimeter.
- The learners understand that the perimeter of a rectangle is calculated by adding the lengths of four sides together or by adding the lengths of two adjacent sides together and multiplying the result by two.
- The learners understand that the area of a rectangle is calculated by multiplying together adjacent side lengths.
- The learners understand that the rectangle with the largest area for a fixed perimeter is a square.
- The learners can measure length using metres, centimetres and millimetres, and area using square centimetres (cm2) and square millimeters (mm2).
- Discuss with the learners relevant or authentic situations where measuring the perimeter or area of rectangles is applicable.

## Resources

- Rulers and measuring tapes (marked in metres, centimetres, millimetres).
- Grid paper.
- Scissors.
- A selection of rectangular and square objects.

## The guided teaching and learning sequence

1. Draw a rectangle on the board and ask the learners to identify the perimeter.

“Which is the perimeter?”

“How would you calculate the perimeter?”

2. Ask for a volunteer to measure the length of sides and record their measurements on the board. Use this as an opportunity to check the learners are measuring accurately and giving the measurement unit.

3. Ask the learners to calculate the perimeter from the side length measurements given.

“How did you calculate the perimeter in centimetres?” (Use this as an opportunity to share addition strategies).

4. Give each of the learners some grid paper and ask them to draw rectangles, with whole number sides, that have perimeters of 24 centimetres.

5. Ask: “How many rectangles have you found?” (6)

6. Record the rectangles in a table.

“How do you know that you have found all the possible rectangles?” (Notice if the learners are systematic in their exploration. For example, if they start with the smallest side (1 centimetre) or the largest side (11 centimetres) and increase or decrease in ones from that side length until they get to side lengths of 6, etc) “Is a 10 x 2 rectangle the same as a 2 x 10 rectangle?” “Why?”

7. Ask the learners to explain how to calculate the area of a 10 x 2 rectangle.

If they counted squares, ask if they could do it another way. Encourage them to notice that you multiply the side lengths together, which in this case is 10 x 2 = 20 cm2.

8. Ask:

“Do you think the rectangles with a perimeter of 24 centimetres have the same area?”

“Which do you think will have the largest area?” “Why?”

“Which will have the smallest area?” “Why?”

9. Ask the learners to complete the table to find out which has the smallest and largest area.

## Follow-up activity

Ask the learners to work in pairs to find the area and perimeter of the rectangular faces of a variety of objects (books, shoe box, room, desk top, computer screen).

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