Perimeter Area Detectives

Overview

Students investigate the difference between perimeter and area by building rectangles with square tiles and recording their measurements. The lesson activates prior learning about length, multiplication and arrays, then develops mathematical reasoning through a short challenge suitable for Years 5–6.

Learning intentions

• WALT distinguish between perimeter and area.
• WALT calculate the perimeter and area of rectangles.
• WALT use square units and centimetres correctly.
• WALT explain how different rectangles can have the same area or perimeter.

Success criteria

• I can describe perimeter as the distance around a shape and area as the space inside it.
• I can measure and calculate using appropriate units.
• I can show my thinking with a diagram, number sentence or explanation.
• I can test whether my answer is reasonable.

Curriculum links

• Mathematics and Statistics — Mathsteasers: higher-order thinking questions that challenge advanced learners and deepen understanding.
• Mathematics and Statistics — Mathsteasers: additional resources for advanced learners.
• Mathematics and Statistics — Mathsteasers: topics and challenges aligned with classroom mathematics learning.

Lesson structure (30 minutes)

1. 0–4 min · Hook and activate. Teacher opens with the hook and learning intention slides and displays two rectangles: one long and narrow, one close to a square. Ask, “Which shape has the greater area? Which has the greater perimeter? How could we prove it?” Students make a quick prediction, then share a reason with a partner.

2. 4–9 min · Clarify the ideas. Teacher uses the perimeter and area teaching slides to model perimeter as the total distance around a shape and area as the number of square units covering its surface. Build a 4-by-3 rectangle with square tiles, labelling length, width, perimeter calculation (4 + 3 + 4 + 3 = 14) units and area calculation (4 × 3 = 12) square units. Students identify the units and explain why area is measured in square units.

3. 9–18 min · Hands-on investigation. Teacher places students in groups of three and gives each group 24 square tiles, a ruler and recording paper. Display the instructions from the investigation instruction slide: “Build as many different rectangles as you can using exactly 24 tiles. Record the length, width, area and perimeter of each.” Students build, sketch or photograph rectangles, calculate each perimeter, and look for patterns. Encourage roles of builder, recorder and checker, with roles changing halfway through.

4. 18–24 min · Reasoning challenge. Teacher distributes the rectangle investigation worksheet and poses the challenge shown on the challenge and discussion slides: “Can two rectangles have the same area but different perimeters? Can two rectangles have the same perimeter but different areas?” Students use their tile models and worksheet tables to find examples and explain how they know. Groups compare results with another group.

5. 24–28 min · Share and connect. Teacher selects two contrasting examples, such as 1-by-24 and 4-by-6, and records their area and perimeter. Ask, “What changes when a rectangle becomes longer and narrower? What happens when it becomes more like a square?” Students contribute explanations and correct any confusion between units, perimeter and area.

6. 28–30 min · Exit check. Teacher displays the final prompt from the plenary and exit prompt slide: “A garden is 7 m long and 3 m wide. Find its perimeter and area. Label both answers correctly.” Students complete the final section of the rectangle investigation worksheet independently and hand it in as they leave.

Resources

• the perimeter and area investigation deck
• the rectangle investigation worksheet
• 24 square tiles per group of three
• Rulers or one-centimetre grid tools
• Small whiteboards and pens
• Pencils and erasers
• Large paper or group recording sheets
• Calculators for selected learners who need support with checking

Assessment

• Listen during the hook and teaching discussion for whether students distinguish “around” from “inside” and use correct units.
• Check group models, sketches and calculations during the investigation; ask, “How do you know?” rather than accepting an answer without reasoning.
• Use the independent exit prompt to assess calculation, unit selection and understanding of the difference between perimeter and area.

Differentiation

• Support learners with pre-drawn rectangles, partially completed tables, sentence starters such as “The perimeter is … because …” and physical tiles kept beside them while calculating.
• Use mixed-readiness groups with clearly assigned roles. Pair spoken explanations with diagrams and gestures for English language learners.
• For learners requiring additional support, begin with rectangles whose side lengths are whole numbers within 1–10 and allow multiplication facts charts or a calculator for checking.
• Extend confident learners by asking them to prove whether a rectangle with a fixed area can have the smallest possible perimeter, or to find all whole-number rectangles with an area of 36 square units.