Shapes in Our World

Lesson Overview

Subject: Mathematics
Year Level: Year 10
Duration: 60 minutes
Curriculum Area: New Zealand Curriculum – Mathematics and Statistics
Level: Level 5
Strand: Geometry and Measurement
Achievement Objective:

• Students will calculate the area and perimeter of various 2D shapes, including composite shapes.
• Apply mathematical reasoning in real-world contexts.

---

Lesson Objectives

By the end of this lesson, students will:

1. Understand and apply formulas for area and perimeter of common shapes.
2. Solve real-world problems involving measurement.
3. Work collaboratively to design and justify a floor plan using shape concepts.

---

Materials

• Whiteboard & markers
• Grid paper
• Scissors & glue
• Rulers & pencils
• Printed floor plan templates
• Large sheets of paper for group work
• Calculator (optional)

---

Lesson Breakdown

1. Introduction & Warm-Up (10 mins)

Engagement Question:

Write the following on the board:
"If you were building your dream home, how would you work out how much carpet you need or how much fencing goes around your garden?"

• Encourage student responses (2–3 minutes).
• Briefly recap formulas for:
  • Perimeter of squares, rectangles, triangles, and circles.
  • Area of squares, rectangles, triangles, parallelograms, and circles.
  • Discuss composite shapes (areas combined together).

---

2. Guided Practice (15 mins)

Teacher-Led Example (5 mins):

• Draw a rectangular garden (5m × 8m) on the board.
• Ask students to calculate:
  • The perimeter (walk around the edge).
  • The area (space inside).
• Solve together, reinforcing key concepts.

Pair Work (10 mins):

• Distribute quick fire worksheet with 3 shapes:
  1. A rectangle
  2. A triangle
  3. A composite shape made from 2 rectangles
• In pairs, students solve for area and perimeter.

---

3. Real-World Challenge (20 mins)

Task: Designing a tiny house floor plan!

• Students are given the role of architects designing a tiny home.
• Each group (4 students) receives a blank floor plan grid.
• They must:
  1. Design rooms using rectangles, triangles, and circles.
  2. Calculate the total floor area.
  3. Find the perimeter of the outer walls (for building costs!).

Present & Justify (5 mins):

• 2–3 groups briefly share their layouts.
• Teacher asks guided questions, e.g.,
  • "Why did you choose this layout?"
  • "How does the area impact usability?"

---

4. Wrap-Up & Reflection (10 mins)

• Exit slip question: (written response on sticky note)
  • "Explain in your own words why knowing area and perimeter is useful in real life."
• Share a real-life application—for example, designers using maths to create sports fields or buildings.

---

Differentiation Strategies

• For struggling students: Provide a formula reference sheet. Offer smaller step-by-step problems before moving to composite shapes.
• For advanced learners: Challenge students to estimate materials (e.g., carpet) for their house using real-world values.

---

Teacher Reflection & Next Steps

• Review student exit slips for misconceptions.
• Plan next lesson on surface area and volume.
• Provide students with an online simulation activity (in a future lesson) to design more complex spaces.

---

This interactive lesson keeps students engaged while ensuring real-world relevance. They'll see maths in action—not just on paper. 🚀