Perimeter and Polygons

Grade 5 Mathematics

Duration: 70 minutes
Class Size: 20 students
Ontario Curriculum Reference:

• Measurement and Geometry (MG5.1): Solve problems involving perimeter by selecting and using appropriate strategies.
• Measurement and Geometry (MG5.2): Classify and compare polygons, including squares, rhombuses, rectangles, and triangles, based on their properties.
• Mathematical Processes (MP): Reasoning, Problem Solving, Reflecting

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Learning Objectives

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

• Identify and describe properties of squares, rhombuses, rectangles, and triangles.
• Calculate the perimeter of these shapes using given side lengths.
• Apply perimeter calculation skills to real-world contexts, specifically Nunavut's territorial map or simplified shapes inspired by Nunavut.
• Communicate their understanding clearly using mathematical language and representations.

"I can..." statements:

• I can identify and describe squares, rhombuses, rectangles, and triangles.
• I can calculate the perimeter of these shapes.
• I can use perimeter calculations to solve problems about areas like Nunavut territory.
• I can explain how I found the perimeter and why it makes sense.

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Success Criteria

• Correctly name each 2D shape and list at least two properties (e.g., equal sides, right angles).
• Show clear, accurate calculations of perimeter with correct units.
• Demonstrate thinking by explaining perimeter in context (Nunavut).
• Use mathematical terms appropriately during discussions and written work.

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Materials and Resources

• Large classroom map or printed outline of Nunavut (simplified).
• Shape cut-outs (squares, rhombuses, rectangles, triangles) made from card stock.
• Rulers and measuring tapes.
• Graph paper and pencils.
• Whiteboard and markers or interactive board.
• Perimeter calculation worksheet featuring Nunavut-inspired shapes.

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Lesson Outline

1. Introduction (10 mins)

• Engage: Show students a simplified map of Nunavut – highlight its approximate geometric shape boundaries using polygons.
• Discuss why understanding shapes and measurements might be useful for people living in and governing Nunavut.
• Briefly review definitions and properties of squares, rhombuses, rectangles, and triangles using shape cut-outs as visual aids.

Teacher Talking Points:

• “Today, we’ll learn how to measure the distance around different shapes. This is called the perimeter.”
• “We will also learn about four special shapes and see how they help us understand the real-world shape of Nunavut.”

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2. Exploration Activity (20 mins)

• Shape Properties Review: In pairs, students receive a set of shape cut-outs. Using rulers, they measure side lengths and verify properties (equal sides, right angles).
• Perimeter Calculation: Students calculate the perimeter of each shape:
  • Square (all sides equal)
  • Rhombus (all sides equal but angles not 90°)
  • Rectangle (opposite sides equal, right angles)
  • Triangle (sum of three sides)
• Students record calculations on worksheets with scaffolded templates.

Differentiation:

• Students needing support get printed formulas and step-by-step guidance cards.
• Challenge learners asked to explain differences between rhombus and square in their own words.

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3. Real-World Connection — Nunavut Maps (15 mins)

• Teachers display printed simplified polygonal outlines of Nunavut territory broken into squares, rectangles, and triangles.
• Students estimate or use given side lengths to calculate approximate perimeter sections, then total perimeter.
• Discuss what perimeter means for communities, e.g., how far it might be to travel around part of Nunavut.

"I can" connection:

• “I can use what I know about perimeters to solve real-world problems.”

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4. Group Problem-Solving (15 mins)

• Form small groups (4-5 students). Each group receives a “Nunavut puzzle” with polygons representing regions.
• Task: calculate perimeter of combined shapes and explain their strategy.
• Use whiteboards or chart paper to share their solution visually and verbally.

Differentiation:

• Provide illustrated perimeter formula posters for reference.
• Encourage verbal explanation, drawing, or number sentences depending on student strengths.

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5. Reflection and Assessment (10 mins)

• Whole class shares one thing they learned and one question they still have.
• Exit ticket: each student writes down either a perimeter calculation or identifies the properties of one shape discussed.
• Teacher circulates to assess understanding and provides quick feedback.

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Assessment and Feedback

• Formative assessment through observation during activities, group discussions, and exit tickets.
• Mark perimeter worksheets and check for accuracy and reasoning.
• Provide targeted feedback, noting strengths and instrumental next steps for individuals or groups.

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Additional Differentiation Strategies

• Use of language support visuals and bilingual terminology for ELL students.
• Manipulatives and hands-on measuring for tactile learners.
• Oral formative assessment options for students with writing difficulties.
• Extension challenge: incorporate irregular shapes or introduce basic area calculation for advanced learners.

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Teacher Notes and Tips

• Emphasize the connection between geometry and geography to build engagement and contextual understanding.
• Encourage students to explain reasoning fully—this builds mathematical communication skills required in the Ontario curriculum.
• Use questioning like “How do you know the perimeter will increase/decrease if the side length changes?” to deepen thinking.

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By connecting shape properties, perimeter concepts, and the unique geography of Nunavut, this lesson honours Ontario Curriculum expectations while promoting curiosity and real-world problem solving.