Classifying Polygons

Classifying polygons benefits greatly from active learning because it requires hands-on manipulation and visual comparison. When students physically sort shapes or construct them, they build a concrete understanding of attributes like sides and angles, moving beyond rote memorization.

• 3rd Grade
• Mathematics
• 3 activities
• 30 min–45 min

Stations Rotation

⏱ 45 min·Small Groups

Shape Sorting Challenge

Provide students with a variety of polygon cutouts. Have them work in small groups to sort the shapes into categories based on attributes they identify themselves, then introduce formal geometric terms. Groups then present their sorting criteria and justifications.

Prepare & details

Differentiate what specific attributes make a quadrilateral a square versus a rectangle.

Facilitation Tip: During the Stations Rotation, ensure each station has clear instructions and all necessary materials readily available so students can transition smoothly and focus on the task.

Setup: Tables/desks arranged in 4-6 distinct stations around room

Materials: Station instruction cards, Different materials per station, Rotation timer

• Remember
• Understand
• Apply
• Analyze
• Self-Management
• Relationship Skills

Stations Rotation

⏱ 30 min·Whole Class

Attribute Bingo

Create bingo cards with polygon names (e.g., square, isosceles triangle) and call out attributes (e.g., 'has four equal sides,' 'has one right angle'). Students mark the corresponding polygon on their card. The first to get bingo wins.

Prepare & details

Explain how to group shapes based on their angles and side lengths.

Facilitation Tip: During Think-Pair-Share, prompt students to use precise mathematical language when discussing polygon attributes with their partner before sharing with the class.

Setup: Tables/desks arranged in 4-6 distinct stations around room

Materials: Station instruction cards, Different materials per station, Rotation timer

• Remember
• Understand
• Apply
• Analyze
• Self-Management
• Relationship Skills

Stations Rotation

⏱ 40 min·Individual

Polygon Construction Lab

Using geoboards and rubber bands, or drawing software, students construct polygons that meet specific attribute criteria. Challenge them to create shapes that fit into multiple categories.

Prepare & details

Justify why a shape can belong to more than one category at the same time.

Facilitation Tip: During the Stations Rotation, circulate to observe groups during the Shape Sorting Challenge, asking probing questions about why they placed certain shapes together or apart.

Setup: Tables/desks arranged in 4-6 distinct stations around room

Materials: Station instruction cards, Different materials per station, Rotation timer

• Remember
• Understand
• Apply
• Analyze
• Self-Management
• Relationship Skills

Teaching This Topic

This topic is best taught by emphasizing attribute identification and hierarchical classification. Instead of just presenting definitions, use active sorting and construction tasks to let students discover relationships between shapes. Avoid teaching shapes in isolation; instead, highlight how a square is a specific type of rectangle and rhombus.

What to Expect

Students will be able to accurately sort polygons based on their attributes and explain the reasoning for their classifications. They will demonstrate understanding that shapes can belong to multiple categories by correctly labeling them with all applicable names.

Watch Out for These Misconceptions

Common Misconception

During the Shape Sorting Challenge, watch for students who separate squares from rectangles, stating that squares cannot be rectangles.

What to Teach Instead

Redirect students by asking them to identify the attributes of a rectangle (four sides, four right angles) and then check if a square possesses those same attributes, guiding them to place the square within the rectangle group.

Common Misconception

During the Polygon Construction Lab, watch for students who label a constructed shape with only one name when it could fit multiple categories.

What to Teach Instead

Prompt students to list all possible classifications for their constructed shapes, encouraging them to think about all the attributes they built into the polygon and how those relate to broader categories.

Assessment Ideas

Quick Check

During the Shape Sorting Challenge, observe groups and ask them to explain the sorting rules they have established for their piles of polygons.

Peer Assessment

After the Polygon Construction Lab, have students swap their constructed polygons and check each other's work, ensuring the polygons meet the specified attributes and are correctly labeled with all possible classifications.

Discussion Prompt

During Think-Pair-Share, pose the question: 'How is an isosceles triangle different from and similar to an equilateral triangle?' and listen for student use of attribute vocabulary.

Extensions & Scaffolding

• Challenge: Ask students to design a polygon with a specific set of attributes and justify their design.
• Scaffolding: Provide pre-filled attribute charts for students to match with shape cutouts during the sorting activity.
• Deeper Exploration: Have students research and present on polygons found in real-world architecture or nature, classifying them by their properties.