Exploring Compound Polygons

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Grade Level: 5

Duration: 60 minutes

Class Size: 25 students

Subject: Mathematics

Common Core State Standards (CCSS) Alignment:

• CCSS.MATH.CONTENT.5.G.B.3
  Understand that attributes belonging to a category of two-dimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so squares have four right angles.
• CCSS.MATH.CONTENT.5.G.B.4
  Classify two-dimensional figures in a hierarchy based on properties.

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Learning Objectives

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

1. Define compound polygons and identify their components.
2. Classify compound polygons based on their attributes and sub-parts.
3. Create compound polygons by combining basic polygons.
4. Explain their reasoning for classification using geometric vocabulary.

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Materials Needed

• Chart paper with basic polygons drawn (triangles, rectangles, squares, etc.)
• Construction paper or cardstock polygons (various shapes)
• Scissors and glue sticks
• Whiteboards and dry erase markers (1 per student)
• Worksheets with identification, classification, and creation tasks (see activities)
• Rulers and protractors for measurement (optional)

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Lesson Structure

1. Introduction & Hook (10 minutes)

Depth of Knowledge (DOK) Level 1: Recall and Reproduction

• Begin by reviewing basic polygon vocabulary and properties: sides, vertices, angles.
• Show simple polygons drawn on the board (e.g., triangle, rectangle).
• Ask students to name shapes and list key features out loud.
• Introduce the term compound polygon: a polygon made by joining two or more simple polygons along an edge.
• Show a compound polygon visual example (e.g., an L-shape made from squares and rectangles).
• Ask: "What polygons did you see combined?" to activate prior knowledge.

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2. Guided Exploration (15 minutes)

DOK Level 2: Skills and Concepts

• Distribute pre-cut basic polygons to students, grouped in sets of 5 shapes.
• Explain how to combine polygons by matching and gluing edges together to form compound polygons.
• Demonstrate how to create several examples step-by-step:
  • Join two triangles to make a diamond-shaped polygon.
  • Join a rectangle and square to form an L-shaped polygon.
• Students work in pairs to create at least two compound polygons on card stock.
• As they work, circulate and ask:
  • "Which polygons are you combining?"
  • "How more sides/angles does the new shape have?"
  • "What do you notice about the edges where the polygons join?"
• Use questioning to help students articulate properties of their compound polygons.

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3. Classification & Discussion (15 minutes)

DOK Level 3: Strategic Thinking and Reasoning

• Hand out worksheet Part A: Identify compound polygons and underline the component polygons.
• Hand out worksheet Part B: Classify each compound polygon based on attributes (number of sides, angles, symmetry).
• Students complete worksheet individually or in small groups while referring to their constructed shapes.
• Lead group discussion on why specific compound polygons fit into certain classifications. Encourage geometric vocabulary such as "adjacent sides," "vertices," "convex," and "concave."
• Emphasize how sub-parts’ attributes impact overall shape properties.

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4. Creation and Application (12 minutes)

DOK Level 3: Reasoning and Extended Thinking

• Challenge students to create a “new” compound polygon by combining at least three polygons from the set.
• Students must:
  • Name all the polygons they used.
  • Sketch the shape on their whiteboard or worksheet.
  • Write a short explanation (2-3 sentences) about why their new polygon is a compound polygon and what properties it has.
• Volunteers share their polygons and reasoning with the class.

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5. Formative Assessment & Wrap-Up (8 minutes)

• Conduct an exit ticket activity:
  • Provide two compound polygons and ask students to:
    1. Identify the component polygons.
    2. State one property of each component polygon.
    3. Explain why the shape is a compound polygon.
• Collect exit tickets to gauge understanding for next steps in instruction.
• Recap the lesson by asking:
  • "What is a compound polygon?"
  • "How can combining polygons change the overall shape?"
  • Reinforce connections to CCSS related to classification and attribute analysis of polygons.

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Differentiation Notes

• Provide extra guided support and visual aids for students who struggle with spatial concepts, including tactile polygon models.
• Offer extension challenges to advanced students, such as exploring concave vs convex compound polygons or calculating perimeter of their compound shapes.

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Sample Worksheet Extract (for teacher creation)

Part A: Identify the polygons
Look at the compound polygon below. Circle and write the name of each simple polygon that forms the compound shape.

Part B: Classify the compound polygon

• How many sides does the compound polygon have?
• Are the polygons joined along full edges or just points?
• Is the compound shape convex or concave?
• Which properties from the simple polygons have stayed the same or changed when combined?

Part C: Creation challenge
Draw your own compound polygon using at least three basic polygons. Label each part and describe its properties underneath.

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This detailed lesson plan integrates CCSS standards by explicitly linking classification and understanding of polygon properties to compound polygons. The gradual scaffolding from identification to creation and explanation promotes deeper mathematical thinking aligned with Webb’s DOK levels 1-3. The hands-on approach, paired with guided questioning and formative checks, aims to fully engage 5th graders in mastering this geometry topic.