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Math lesson plan · 7th grade (Year 8 in England) · 45 minutes

Missing angles in triangles, including isosceles and algebra

Geometry

CCSS 7.G.A.2CCSS 8.G.A.5England: KS3 Geometry and measuresEngland: GCSE Foundation Geometry and measures

Objective and success criteria

Students will: Missing angles in triangles, including isosceles and algebra.

  • I can answer questions on today's skill on my own, without help.
  • I can explain each step and say why it works.
  • I can check my answer and spot a mistake.

Before and after

Needs first: Classify triangles; angles in a triangle; Two-step equations

Leads to: Use the exterior angle of a triangle

Materials: Rulers and protractors, Squared or dotted paper, Shape cut-outs, Mini whiteboards and pens, Printed student sheet (below).

Warm-up · 5 min

  • Quick retrieval from earlier learning (Classify triangles; angles in a triangle; Two-step equations). Students answer on mini whiteboards.
  • Show answers together and note who needs support in the main task.
  1. A triangle has all three sides equal. What type of triangle is it? (right-angled / equilateral / isosceles / scalene) → equilateralPrompt: Equilateral: all sides equal. Isosceles: two equal. Scalene: none equal.
  2. A triangle has no equal sides. What type of triangle is it? (equilateral / right-angled / scalene / isosceles) → scalenePrompt: Equilateral: all sides equal. Isosceles: two equal. Scalene: none equal.
  3. A triangle has one angle of 90°. What type of triangle is it? (scalene / right-angled / equilateral / isosceles) → right-angledPrompt: Equilateral: all sides equal. Isosceles: two equal. Scalene: none equal.

Hook · 5 min

  • Show a photo of a building, a tile pattern or a road sign and ask what shapes and angles students can spot.
  • Share the objective: Missing angles in triangles, including isosceles and algebra. Read the success criteria together.

I do: model it · 10 min

  • Work through the example out loud, saying why you do each step, not just what you do.
  • Example: The angles of a triangle are x, 3x and 5x. What is the largest angle, in degrees?
  • Step 1: 9x = 180
  • Step 2: x = 20
  • Step 3: 5 × 20 = 100°
  • Answer: 100
  • Pause after each step and ask a student to say what comes next.

We do: guided practice · 10 min

  • Do these together. Students try each step on whiteboards before you reveal it.
  • Use the hints as prompts rather than giving the answer.
  1. The angles of a triangle are 2x, 3x and 4x. What is the largest angle, in degrees? → 80Prompt: They add to 180°: 9x = 180.
  2. In a triangle, two angles are 28° and 78°. One side is extended to make an exterior angle next to the third angle. How big is that exterior angle? → 106Prompt: Find the third angle first, then use the straight line.

You do: independent practice · 10 min

  • Students work on the student sheet. Circulate and check the first two answers of every student early.
  • Students who finish: write a question of their own for a partner, with the answer.

The 8 questions are on the student sheet below, with answers in the key.

Exit ticket · 5 min

  • Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
  1. The angles of a triangle are 3x, 4x and 5x. What is the largest angle, in degrees? → 75Prompt: They add to 180°: 12x = 180.
  2. In a triangle, two angles are 79° and 35°. One side is extended to make an exterior angle next to the third angle. How big is that exterior angle? → 114Prompt: Find the third angle first, then use the straight line.

Watch out for

  • Thinking a square turned on its corner is no longer a square.
  • Reading the wrong scale on a protractor.

Support and stretch

Support

  • Review first: Classify triangles; angles in a triangle.
  • Use concrete materials: rulers and protractors.
  • Give the first step of each question, or a partly worked example to finish.
  • Pair with a confident partner for the guided practice.

Stretch

  • Move on to: Use the exterior angle of a triangle.
  • Explain a common mistake in writing and how to fix it.
  • Write a word problem that uses today's skill, then solve a partner's.

Homework and more practice

Free online practice with hints and printable worksheets for this skill: eurekami.com/math/grade-7.

Free lesson plan from eurekami.com/lesson-plan-builder

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Missing angles in triangles, including isosceles and algebra

Name

Date

Score/ 8

  1. Question 1

    In a triangle, two angles are 59° and 81°. One side is extended to make an exterior angle next to the third angle. How big is that exterior angle?

    Answer

  2. Question 2

    An isosceles triangle has a top angle of 52°. The other two angles are equal. What is each of them?

    ??52°

    Answer

  3. Question 3

    The angles of a triangle are x, x and 2x. What is the largest angle, in degrees?

    Answer

  4. Question 4

    In a triangle, two angles are 45° and 78°. One side is extended to make an exterior angle next to the third angle. How big is that exterior angle?

    Answer

  5. Question 5

    An isosceles triangle has a top angle of 86°. The other two angles are equal. What is each of them?

    ??86°

    Answer

  6. Question 6

    The angles of a triangle are 3x, 4x and 5x. What is the largest angle, in degrees?

    Answer

  7. Question 7

    In a triangle, two angles are 26° and 89°. One side is extended to make an exterior angle next to the third angle. How big is that exterior angle?

    Answer

  8. Question 8

    An isosceles triangle has two equal base angles of 79°. What is the third angle?

    79°79°?

    Answer

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Answer key: Missing angles in triangles, including isosceles and algebra

  1. 1. 140

  2. 2. 64

  3. 3. 90

  4. 4. 123

  5. 5. 47

  6. 6. 75

  7. 7. 115

  8. 8. 22