Perimeter and Area

Overview

In lesson 12 of 28, learners distinguish perimeter as the distance around a shape and area as the space covered by equal square units. They use centimetres and square centimetres to model, calculate and explain the perimeter and area of rectangles, applying their understanding to a garden design inspired by places and spaces across Aotearoa.

Learning intentions

• WALT distinguish between perimeter and area.
• WALT measure and calculate the perimeter of rectangles.
• WALT find the area of rectangles using equal square units.
• WALT explain our mathematical thinking and check whether an answer is reasonable.

Success criteria

• I can describe perimeter as the distance around a boundary.
• I can describe area as the space covered by square units.
• I can calculate the perimeter and area of a rectangle and include the correct units.
• I can show and explain how I know my answer is correct.

Curriculum links

• Mathematics and Statistics: measurement and geometry, using standard units to describe length and area.
• Mathematics and Statistics: representing, solving and communicating mathematical ideas and reasoning.
• Mathsteasers: higher-order thinking questions that deepen understanding for advanced learners.
• Mathsteasers / Alignment: connecting challenge questions with familiar mathematical content.

Lesson structure (60 minutes)

1. 0–5 min · Hook and prediction. Open with the garden boundary hook slide showing two rectangular gardens: one with a long boundary and one with many covered squares; ask, “Which garden needs more fencing? Which covers more ground?” Students make a quick prediction, then share what they think “around” and “inside” mean.

2. 5–15 min · Explicit teaching and modelling. Use the perimeter and area modelling slides and draw a 5 cm by 3 cm rectangle. Trace the boundary in one colour and shade the inside in another. Model perimeter as 5 + 3 + 5 + 3 = 16 cm, and area as five rows of three equal squares, or 5 × 3 = 15 cm². Emphasise that perimeter uses length units and area uses square units. Students copy the labelled model and rehearse the two definitions with a partner.

3. 15–22 min · Guided check. Distribute the perimeter and area practice worksheet and complete the “Must Do” example together: a 4 cm by 2 cm rectangle has perimeter 12 cm and area 8 cm². Ask learners to colour the boundary red, the covered squares blue, and write both units. Students explain why the answers are not interchangeable, while the teacher checks counting, addition and multiplication strategies.

4. 22–42 min · Design a Garden investigation. In groups of four or five, students use tiles, string and geoboards to create a rectangular garden, then record its side lengths, perimeter and area on the worksheet. Provide graph paper for drawing and labelling the final design. Groups should make at least two different rectangles and compare which has the greater perimeter or area. Prompt with: “How can you prove the perimeter?” “How many equal squares cover the garden?” and “Can two gardens have the same perimeter but different areas?” Use the Design a Garden instruction and discussion slides to display the step-by-step routine. Circulate and question rather than correct immediately.

5. 42–53 min · Challenge and sharing. Students complete the “Can Do”: find the area of a 3 cm by 6 cm rectangle, explaining why it is 18 cm². Early finishers attempt the “Try”: find as many rectangles as possible with a perimeter of 20 cm, recording side lengths and areas. Groups share one design and one discovery. Invite learners to notice that rectangles can have the same perimeter but different areas.

6. 53–60 min · Plenary and exit check. Return to the final reflection and exit-question slide. Students answer orally: “What is the difference between perimeter and area?” They then complete the final worksheet questions: calculate the perimeter and area of a 4 cm by 2 cm rectangle, label the units, and draw a quick representation. Collect responses to identify learners needing further support.

Resources

• the complete perimeter and area teaching deck
• the perimeter and area practice worksheet
• Centimetre rulers
• 1 cm square tiles
• String
• Geoboards and elastic bands
• Pencils, coloured pencils and erasers
• 1 cm graph paper
• Whiteboard and markers

Assessment

• Observe whether learners trace the full boundary, count square units accurately and select cm or cm² appropriately.
• Listen to group explanations during the garden investigation; ask learners to justify rather than simply state answers.
• Use the Must Do and exit responses to group learners for the next lesson: secure, developing or requiring concrete modelling.

Differentiation

• Support learners with a partially completed rectangle, colour-coded prompts, a perimeter sentence frame (“I add all the sides…”), and an area frame (“There are ___ rows of ___ squares…”).
• Allow learners to build every rectangle with tiles before recording calculations; pair students strategically and provide a ruler with clear centimetre markings.
• For EAL learners, display and rehearse “boundary”, “around”, “inside”, “length”, “width”, “perimeter”, “area”, “cm” and “cm²” with gestures and diagrams.
• Extend confident learners by asking them to prove which rectangle with perimeter 20 cm has the greatest area, or to design a garden with a specified area and compare possible perimeters.