Unit #5: Comparing Measures

Lesson Title: Comparing Perimeter and Area

Lesson 5 of 8 in the "Perimeter and Area Explorers" unit

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📌 NZ Curriculum Links

Learning Area: Mathematics and Statistics
Strand: Geometry and Measurement
Achievement Objective (Level 2):

Measurement: Students will develop an understanding of measurable attributes of objects and the units, systems, and processes of measurement. In this lesson, students will identify and compare the perimeter and area of shapes and discuss the differences between these two concepts using non-standard and standard units.

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🎯 Learning Intentions

• I am learning to compare and contrast perimeter and area.
• I can describe how two shapes may have the same perimeter but different areas, and vice versa.
• I can explain the difference between measuring the outside and the inside of a shape.

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✅ Success Criteria

By the end of this lesson, students will be able to:

• Correctly calculate the perimeter and area of simple rectilinear shapes using blocks, square units, or rulers.
• Show and explain that shapes with the same perimeter can have different areas.
• Show and explain that shapes with the same area can have different perimeters.

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🕒 Lesson Duration: 60 Minutes

Class size: 30 students
Level: Year 3–4

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🧠 Prior Knowledge Needed

Students should already be familiar with:

• Counting units to find perimeter or area.
• The concept of perimeter as the distance around a shape.
• The concept of area as the amount of space inside a shape.
• Using square grids to estimate and compare area.

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🧰 Materials

• 1 cm square grid paper (enough for pairs of students)
• Coloured counters or square tiles
• Rulers
• Large laminated shapes (rectangles and irregular shapes)
• Whiteboards and markers
• “Shape Challenge Cards” – a set of prompt cards for exploration
• A3 poster paper for plenary discussion

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🧩 Lesson Outline

1. Engage & Warm-Up (10 minutes)

Activity: "Fence or Carpet?"
Pose the question:

“If you were building a fence around your garden, what would you measure? What about laying carpet inside a room?”
Allow students to talk in pairs, then gather responses.
Clarify the difference between perimeter (fence) and area (carpet).

Mini Visual:
Draw a simple rectangle on the board. Ask:

• “What is the perimeter?” Count the sides aloud.
• “What is the area?” Count or visualise the squares inside.
  Use coloured tiles to illustrate it physically.

Purpose: Activate prior knowledge and link mathematics to real-world contexts.

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2. Explore Part 1: Hands-On Comparison (15 minutes)

Activity: "Same Perimeter, Different Area"
Students work in pairs using square grid paper and coloured tiles.

Task:

• Make at least 3 different shapes that all have a perimeter of 12 units.
• Shade or tile the shape to calculate the area.

Prompt with questions:

• “What’s the smallest area you can make with a perimeter of 12?”
• “What’s the largest?”

Support: Provide a table for students to record:

Shape #	Perimeter (units)	Area (sq units)

Purpose: Students visualise how perimeter and area are not always proportional.

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3. Explore Part 2: Role Reversal (15 minutes)

Activity: "Same Area, Different Perimeter"
Provide students with counters/tiles and ask them to create shapes that all have an area of 12 square units.

Challenge:

• “Can you make a long, skinny one?”
• “Can you make one that is as square as possible?”
• “What do you notice about the perimeters now?”
  Students measure perimeters using rulers or by counting unit lengths when using tiles.

Stretch: Some students could estimate and then confirm using measurement tools.

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4. Reflect & Consolidate (10 minutes)

Group Discussion:
Students share one shape they created and discuss why it was interesting.

Guiding Questions:

• “Which shape surprised you and why?”
• “Were you expecting the area to stay the same?”
• “How can the same 'outside' measurement result in different 'insides'?”

Use whiteboard real-time drawing or student posters to highlight findings.

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5. Connect to Real Life (5 minutes)

Mini Scenario:
Present two gardens:

• Garden A has a perimeter of 20m and area of 16m².
• Garden B also has a perimeter of 20m but an area of 24m².
  Ask: “Which garden would be better for planting vegetables? Why?”
  Encourage students to justify using what they’ve learned.

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6. Plenary & Exit Slip (5 minutes)

Summary as a Class:
On poster paper, co-construct a Venn Diagram:

• In left circle: What is perimeter?
• In right circle: What is area?
• In the middle: What is the same/connected?

Exit Slip Question:

“Draw a shape. Label its perimeter and area. Tell me one thing you learned today.”

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🔄 Differentiation

For Support:

• Work in mixed-ability groups.
• Use pre-drawn shapes with side lengths included.
• Provide perimeter and area anchors/resources.

For Extension:

• Introduce irregular L-shaped figures.
• Ask “Can you create a rule or pattern?”
• Provide challenges such as: “Make a ‘house’ shape with fixed area but different features.”

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📌 Assessment for Learning

• Observation of group discussion
• Accuracy of measurements and comparisons in tables
• Thoughtfulness in exit slips
• Use of mathematical language (perimeter, measure, length, area, square units)

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📚 Links to Future Learning

In the next lesson (Lesson 6), students will design their own mini park, applying their knowledge of perimeter and area to plan fences, paths, and grass spaces. They’ll use the concepts from this lesson to optimise space and cost effectiveness.

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🎉 Teacher Tip: Make it Memorable

Pair this lesson with a “Perimeter v Area” relay game outdoors, where students run to collect either "perimeter" or "area" tokens in designated zones. It blends kinaesthetic energy with conceptual reinforcement.

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He waka eke noa – We are all in this together.
Let’s support our learners as they navigate the landscapes of measurement, discovering how maths helps them see the world in new ways.