Exploring Polygon Parts

Grade Level

3rd Grade

Duration

45 minutes

Class Size

15 Students

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Common Core Standards

CCSS.MATH.CONTENT.3.G.A.2
Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. Understand and identify polygons by decomposing them into triangles, rectangles, or other polygons.

CCSS.MATH.PRACTICE.MP1
Make sense of problems and persevere in solving them.

CCSS.MATH.PRACTICE.MP4
Model with mathematics.

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Learning Objectives

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

• Decompose a polygon into two or more smaller polygons (such as triangles, rectangles, or other shapes).
• Recognize and name the newly formed polygons from decomposing larger polygons.
• Explain their reasoning process during decomposition using precise mathematical language.
• Visualize and draw decompositions to demonstrate understanding of polygon parts.

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Materials Needed

• Large chart paper with different polygons printed/drawn (e.g., pentagons, hexagons, irregular polygons)
• Scissors
• Rulers
• Small whiteboards and dry-erase markers (one per student)
• Polygon cut-out sets for each student (pre-cut cardboard or heavy paper polygons)
• Glue sticks
• Worksheets with polygons outlined for decomposition

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Lesson Structure

1. Introduction & Engagement (8 minutes)

• Begin with a quick review of polygons: "What is a polygon?"
• Show various polygons on chart paper. Ask: "Can you name these polygons?"
• Introduce the concept: “Today, we will learn how to take apart polygons into smaller polygons.”
• Use a big pentagon cut-out. Model by folding or cutting it into smaller polygons (e.g., triangle + quadrilateral).
• Ask students what shapes they see in the parts after cutting. Emphasize naming the polygons.

2. Guided Practice - Whole Group (12 minutes)

• Distribute polygon cut-outs (each student gets one different polygon).
• Together as a class, guide students step-by-step to decompose their polygon into at least two smaller polygons. Model the process:
  • Draw a line inside the polygon connecting two vertices that do not share a side to create smaller shapes.
  • Identify the new shapes created.
• Ask students to name each polygon part (e.g., "This is a triangle. What is this one?").
• Use questioning strategies to develop reasoning, e.g., “Why do you think this part is a rectangle and not a triangle?”
• Encourage students to replicate the decomposition on their own whiteboards, then discuss their drawings.

3. Independent or Small Group Practice (15 minutes)

• Students work in groups of 3 using scissors, glue, and polygon cut-outs:
  • Each group picks one complex polygon.
  • They cut it into two or more smaller polygons.
  • They will arrange and glue the parts on a piece of paper and label the polygons formed.
• Teachers circulate, observe, and prompt with guiding questions:
  • “Can you find a way to make triangles?”
  • “What new polygons did you create?”
  • “How do the parts fit together to make the original shape?”

4. Sharing and Reflection (7 minutes)

• Each group shares their decomposed polygon, labels, and explains which polygons they found.
• Class discusses the differences and similarities between decompositions.
• Teacher reinforces vocabulary: polygon, triangle, quadrilateral, decomposing, parts.

5. Exit Ticket Assessment (3 minutes)

• Hand out a simple worksheet where students must draw a line to decompose a polygon into two shapes and name each one.
• Collect for quick formative assessment to gauge understanding.

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Differentiation

• For Students Needing Support:
  Use polygons that naturally divide into rectangles and triangles (e.g., rectangles and right triangles). Provide tracing templates to help draw lines neatly.
• For Advanced Students:
  Challenge students to decompose polygons into more than two parts and identify at least three types of polygons.

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Assessment Criteria

• Ability to manually decompose polygons into smaller polygons.
• Correct identification and naming of new polygons formed.
• Clear explanation of how decomposition was done, either verbally or in writing/drawing.

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Reflection for Teachers

• Did students demonstrate flexibility in seeing polygons as composed of smaller shapes?
• Were students able to apply vocabulary correctly?
• How to adjust future lessons to incorporate more modeling or hands-on activities?

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Extension Ideas

• Use a digital geometry app or interactive whiteboard to allow virtual decomposition and manipulation of polygons.
• Create polygon puzzles for students to reconstruct after decomposition.
• Introduce area concepts by comparing areas before and after decomposition in subsequent lessons.

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This lesson plan is designed to actively engage 3rd graders with hands-on, reasoning-rich math aligned with Common Core standards that emphasize spatial reasoning, vocabulary, modeling with mathematics, and problem-solving perseverance.