Triangles Interior Angles

Overview

In this second lesson of the unit, students will explore how the interior angles of a triangle relate to each other. Using hands-on models, they will measure and verify that the sum of interior angles is always 180°.

Learning intentions

• Students will investigate triangle angle properties using paper folding, cutting, and measuring.
• Students will determine the sum of the interior angles in multiple triangles.
• Students will explain their results using angle language and simple reasoning.

Success criteria

• I can measure and record the three interior angles of different triangles.
• I can show (with a model or diagram) that the interior angles of a triangle add to 180°.
• I can use my results to predict the missing interior angle in a triangle.
• I can communicate my reasoning clearly to my group.

Curriculum links

• Angle relationships and properties of 2D shapes.
• Measurement of angles using appropriate tools (protractor) and recording accurately.
• Reasoning and communication using mathematical language for angles and shapes.

Lesson structure (60 minutes)

1. 0–5 min | Launch with question

• Display a triangle and ask: “If we know two interior angles, how could we find the third?”
• Tell students today’s goal: discover the constant sum by experimenting with triangles.

2. 5–12 min | Quick model demo (teacher)

• Show one triangle and guide a quick “reveal” using paper: fold or cut so the three angles are placed together at a point or along a straight line.
• Record the idea that the angles combine to form a larger angle (students will confirm with measurement later).

3. 12–18 min | Formation of groups and roles

• Students form groups of 3–5. Assign roles: measurer (protractor), recorder (data table), materials manager (cutting/folding), and reporter (explains findings).
• Provide each group with triangle templates (acute, right, obtuse), plus a data sheet.

4. 18–33 min | Investigation: measure and record

• Students measure each interior angle with a protractor, record in a table, and compute the sum for each triangle.
• They repeat for at least three triangles and note any rounding issues (e.g., to the nearest degree).

5. 33–42 min | Angle “assemble” evidence

• Students use cut-out angles from their triangles and place them together using the provided method (around a point or along a straight line, as in the demo).
• They estimate the resulting angle, then connect it to what they measured for the sum.

6. 42–52 min | Whole-class discussion and pattern finding

• Each group shares one triangle’s measured angles and their total. As a class, confirm the pattern: sums are consistently 180°.
• Teacher prompts: “Why do you think the sum stays the same even when the triangle changes shape?”

7. 52–60 min | Exit task: find a missing angle

• Students complete a short independent task: “In a triangle, one angle is 64°, another is 92°. What is the third interior angle?”
• Collect responses and look for correct subtraction from 180° and clear working.

Resources

• Triangle templates: acute, right, obtuse (at least three per group)
• Protractors and straight edges
• Scissors and glue sticks (or tape) for assembling cut angles
• Angle data recording sheet with a table for three angles and their sum
• A class chart for recording triangle angle sums
• Sample “angle cut-outs” or pre-cut angle pieces for demonstration (optional but helpful)
• Student notebooks for evidence writing
• Exit ticket slips

Assessment

• Observation during group work: accurate measuring, correct recording, and participation in assembling the angles.
• Formative check during discussion: ability to state the angle sum pattern and use angle vocabulary.
• Exit task: correct missing-angle calculation and brief explanation using the 180° interior angle sum.

Differentiation

• Support
• Provide a “measuring checklist” (align baseline, read the correct scale, record clearly).
• Give one pre-labeled example triangle with measured angles to model how to fill the table.
• Extension (advanced learners)
• Add a challenge: create a triangle where one angle is 37° and another is 58°. Predict the third angle without measuring, then check by measurement.
• Ask for a general statement: “For any triangle, the sum of interior angles is always ___.” Include a justification based on evidence from their cut-out assembly.
• EAL/SEN
• Offer sentence starters for reasoning: “The sum is 180° because…”, “I noticed that…”, “When the triangle changes…”
• Allow assistive tools (printed large protractor, pre-cut triangles) and extra time for measuring.