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Math lesson plan · 10th grade (Year 11 in England) · 30 minutes

Give the reason for each step in an angle argument

Geometry

CCSS HSG.CO.C.9England: GCSE Foundation GeometryEngland: GCSE Higher Geometry

Objective and success criteria

Students will: Give the reason for each step in an angle argument.

  • 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: Angles with parallel lines

Leads to: the next skill in this area.

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

Warm-up · 4 min

  • Quick retrieval from earlier learning (Angles with parallel lines). Students answer on mini whiteboards.
  • Show answers together and note who needs support in the main task.
  1. A line crosses two parallel lines. One angle is 151°. What is the corresponding angle to it, in degrees? → 151Prompt: Alternate angles are equal (Z shape). Corresponding angles are equal (F shape).
  2. Alternate angles on parallel lines are (4x + 23)° and 75°. Find x. → x = 13Prompt: Alternate angles are equal.
  3. A line crosses two parallel lines. One angle is 82°. What is the corresponding angle to it, in degrees? → 82Prompt: Alternate angles are equal (Z shape). Corresponding angles are equal (F shape).

Hook · 3 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: Give the reason for each step in an angle argument. Read the success criteria together.

I do: model it · 7 min

  • Work through the example out loud, saying why you do each step, not just what you do.
  • Example: A line crosses two parallel lines. Angle p and an angle of 139° are between the parallel lines, on opposite sides of the crossing line (a Z shape). Which reason should go with the step that finds p?
  • Step 1: Alternate angles are equal
  • Answer: Alternate angles are equal
  • Pause after each step and ask a student to say what comes next.

We do: guided practice · 6 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. A line crosses two parallel lines. Angle p and an angle of 67° are in the same position at each crossing (an F shape). Which reason should go with the step that finds p? (Angles on a straight line add up to 180° / Angles around a point add up to 360° / Corresponding angles are equal / Alternate angles are equal) → Corresponding angles are equalPrompt: Picture the diagram: is there a crossing, a straight line or parallel lines?
  2. Angle p and an angle of 72° are alternate angles between parallel lines. Find p in degrees. → 72Prompt: Decide whether the angles are equal or add up to 180°.

You do: independent practice · 7 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 6 questions are on the student sheet below, with answers in the key.

Exit ticket · 3 min

  • Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
  1. A line crosses two parallel lines. Angle p and an angle of 66° are between the parallel lines, on opposite sides of the crossing line (a Z shape). Which reason should go with the step that finds p? (Corresponding angles are equal / Vertically opposite angles are equal / Alternate angles are equal / Angles around a point add up to 360°) → Alternate angles are equalPrompt: Picture the diagram: is there a crossing, a straight line or parallel lines?
  2. Angle p and an angle of 127° are co-interior angles between parallel lines. Find p in degrees. → 53Prompt: Decide whether the angles are equal or add up to 180°.

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: Angles with parallel lines.
  • 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

  • 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-10.

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

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Give the reason for each step in an angle argument

Name

Date

Score/ 6

  1. Question 1

    Two straight lines cross. Angle p is directly across the crossing point from an angle of 50°. Which reason should go with the step that finds p?

    • A. Angles on a straight line add up to 180°
    • B. Vertically opposite angles are equal
    • C. Co-interior angles add up to 180°
    • D. Alternate angles are equal

  2. Question 2

    Angle p and an angle of 70° lie on a straight line. Find p in degrees.

    Answer

  3. Question 3

    Angle p and an angle of 129° sit side by side and together make a straight line. Which reason should go with the step that finds p?

    • A. Angles around a point add up to 360°
    • B. Angles on a straight line add up to 180°
    • C. Corresponding angles are equal
    • D. Alternate angles are equal

  4. Question 4

    Angle p and an angle of 82° are co-interior angles between parallel lines. Find p in degrees.

    Answer

  5. Question 5

    A line crosses two parallel lines. Angle p and an angle of 73° are between the parallel lines, on opposite sides of the crossing line (a Z shape). Which reason should go with the step that finds p?

    • A. Corresponding angles are equal
    • B. Vertically opposite angles are equal
    • C. Alternate angles are equal
    • D. Co-interior angles add up to 180°

  6. Question 6

    Angle p and an angle of 107° lie on a straight line. Find p in degrees.

    Answer

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Answer key: Give the reason for each step in an angle argument

  1. 1. B. Vertically opposite angles are equal

  2. 2. 110

  3. 3. B. Angles on a straight line add up to 180°

  4. 4. 98

  5. 5. C. Alternate angles are equal

  6. 6. 73