Périmètre et Aire

Overview

Grade: 5
Duration: 60 minutes
Class Size: 20 students
Unit: Mesurer avec le Système Métrique (Unit 13 of 15)
Topic: Calculer le périmètre et l’aire : Application pratique
Curriculum Reference:

• Mathematics, Grade 4-6, Ontario Curriculum (2023), Measurement Strand
• Specific Expectations:
  • MA4MD4: Calculate the perimeter and area of rectangles and other polygons by decomposing shapes as required
  • MA4MD3: Estimate, measure, and record perimeter and area, using appropriate metric units
  • MA4MD1: Solve problems involving measurement of perimeter and area

---

Learning Goals

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

• Apply their understanding of perimeter and area calculations to real-world shapes and projects
• Collaborate effectively in groups to solve measurement problems
• Use metric units (cm, m, m²) accurately and convert when necessary
• Demonstrate fluency with formulas for perimeter and area of various polygonal shapes
• Communicate their mathematical reasoning orally and in writing

---

Materials Needed

• Graph paper (20 sheets, one per student)
• Rulers (20 pieces, metric system)
• Large construction paper (A3 size) for group projects
• Scissors and coloured markers
• Calculators (optional, to support computation)
• Whiteboard or chart paper
• Printed worksheet with various polygons (rectangles, composite shapes) for guided practice

---

Lesson Breakdown

1. Introduction & Review (10 minutes)

• Begin by writing “Périmètre et Aire” on the board.
• Briefly review the formulas for perimeter and area of rectangles and polygons (P = sum of all side lengths; A = length × width for rectangles; decomposition strategies for irregular shapes).
• Ask probing questions:
  • “Comment peut-on mesurer le périmètre d’une forme irrégulière?”
  • “Pourquoi est-il important de comprendre l’aire dans des situations réelles?”
• Use a quick visual: draw a rectangle and an irregular shape on the board, model how to calculate both perimeter and area.

2. Group Application Project (35 minutes)

Context: Students will apply their learning by creating a “plan” for a small “jardin” or “terrain de jeu” using graph paper and coloured markers.

Step 1: Group formation (4 groups of 5 students)

• Each group designs a irregular polygon using graph paper sheets taped together on an A3 sheet.
• Encourage creativity: include different shapes such as rectangles, triangles, squares combined.

Step 2: Design challenge (10 minutes)

• Groups sketch their shape to scale, marking all known sides (in cm).
• Assign different metric units to groups (e.g., one group works in cm, another in metres – reinforce unit conversions).

Step 3: Calculate perimeter and area (15 minutes)

• Students calculate the perimeter by adding side lengths.
• For area, groups decompose their shape into rectangles and triangles, then sum areas.
• Students record all calculations, showing their reasoning and units clearly.

Step 4: Prepare presentation (6 minutes)

• Groups prepare a short explanation (2-3 minutes) about how they calculated the perimeter and area, challenges they faced, and real-life applications.

3. Group Presentations & Class Discussion (10 minutes)

• Each group shares their findings.
• Discuss how decomposition helps with irregular shapes.
• Reinforce the importance of accuracy with units.
• Teacher provides formative feedback addressing math language, accuracy, and group collaboration.

4. Conclusion and Exit Ticket (5 minutes)

• Exit ticket: Each student solves one quick perimeter or area problem independently (e.g., “Calcule l’aire d’un rectangle de 6 m sur 4 m”).
• Collect exit tickets to informally assess individual understanding before next lesson.

---

Differentiation Strategies

• For advanced learners: Challenge to include calculation of area for triangles using the formula (base × height ÷ 2).
• For learners needing support: Provide step-by-step worksheets with guided questions and partially completed examples.
• Peer tutors: Use stronger students to support peers in groups during calculations.

---

Assessment and Evaluation

• Formative: Observation during group work, accuracy of calculations, oral explanations during presentations, and exit ticket responses.
• Success Criteria:
  • Correct use of metric units in context
  • Accurate calculation of perimeter and area, including decomposed shapes
  • Clear mathematical communication orally and in writing
• Next steps: Use collected data to plan review or extension activities in Lesson 14.

---

Connections to the Ontario Curriculum (2023)

• Mathematics – Measurement Strand

  • Students solve problems involving perimeter and area (MA4MD1).
  • They use appropriate units of measurement, including conversions (MA4MD3).
  • Apply strategies to calculate area and perimeter of polygons by decomposing shapes (MA4MD4).

• Mathematical Process Expectations

  • Reasoning & Proving: Justify their solution strategies during presentations.
  • Reflecting: Evaluate different approaches to decomposing shapes.
  • Communicating: Use precise mathematical language and symbols.

---

Teacher Reflection Notes (to enhance future delivery)

• Consider incorporating technology, such as digital applets or interactive whiteboard activities, to simulate decomposition of shapes.
• Extend the project by integrating cross-curricular links with Science (e.g., measurement in land use or biology).
• Explore opportunities for experiential learning outdoors with actual perimeter and area measurement of classroom courtyard or playground.

---

This engaging, hands-on lesson promotes critical thinking, collaboration, and real-world math application while rigorously aligning with the Ontario Curriculum and Grade 5 developmental expectations.