Mathematics · Grade 7

Active learning ideas

Angles in Polygons

Active learning is particularly effective for exploring angles in polygons because it moves beyond rote memorization of formulas. Hands-on activities allow students to discover geometric relationships themselves, fostering deeper conceptual understanding and retention. Engaging with polygons physically and visually makes abstract concepts like angle sums more concrete and intuitive.

• Ontario Curriculum Expectations
• 7.G.B.5

• 30–60 min
• Pairs → Whole Class
• 3 activities

Activity 01

• Stations Rotation
• 60 min · Small Groups

Polygon Angle Discovery Stations

Students rotate through stations where they construct polygons from straws and fasteners, measure interior and exterior angles using protractors, and record data. They then analyze their findings to identify patterns and derive formulas for angle sums.

Analyze the relationship between the number of sides of a polygon and the sum of its interior angles.

Facilitation Tip

During the Stations Rotation, ensure students are actively constructing and measuring at each station, prompting them to record their findings before moving on.

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

Activity 02

• Stations Rotation
• 45 min · Small Groups

Tessellation Exploration

Using regular polygons, students attempt to tessellate a flat surface. This activity naturally leads to discussions about the interior angles of regular polygons and why certain shapes work together to fill a space without gaps or overlaps.

Predict the measure of each interior angle in a regular polygon.

Facilitation Tip

When facilitating Concept Mapping, encourage students to draw connections not just between formulas, but also between the visual representations of polygons and their angle properties.

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

Activity 03

• Stations Rotation
• 30 min · Pairs

Exterior Angle Walk

Students imagine walking along the perimeter of various polygons, turning at each vertex. They measure the exterior angle at each turn and sum them up, discovering the constant sum of 360 degrees through kinesthetic learning.

Compare the sum of exterior angles for different types of polygons.

Facilitation Tip

During the Exterior Angle Walk, ask students to verbalize the degree of their 'turn' at each vertex and connect this to the total rotation.

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

A few notes on teaching this unit

When teaching angles in polygons, prioritize conceptual understanding over formula memorization. Start with concrete examples and visual aids, allowing students to derive formulas through exploration, as facilitated by activities like Stations Rotation. Emphasize the 'why' behind the formulas, particularly the division of polygons into triangles to find interior angle sums and the concept of a full rotation for exterior angles.

Students will successfully articulate the relationship between the number of sides and the sum of interior angles, and explain why the sum of exterior angles is always 360 degrees for convex polygons. They will be able to use formulas accurately and demonstrate their understanding through constructed models and visual representations.

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Watch Out for These Misconceptions

• During Polygon Angle Discovery Stations, watch for students who struggle with the formula for the sum of interior angles, simply counting sides without understanding the pattern.

  Redirect students to the straw constructions: ask them to divide their constructed polygons into triangles and count the triangles to visually confirm the formula's origin, reinforcing that the sum is related to the number of triangles, not just an arbitrary increase.

• During the Exterior Angle Walk, students may assume the concept of turning angles is only relevant for triangles.

  Prompt students to extend the 'walk' to a hexagon or octagon, asking them to measure or estimate their turns at each vertex and then sum these turns to observe that the total remains 360 degrees, demonstrating its universality for convex polygons.

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Methods used in this brief

• Stations Rotation