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Math lesson plan · 10th grade (Year 11 in England) · 60 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 · 6 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 128°. What is the corresponding angle to it, in degrees? → 128Prompt: Alternate angles are equal (Z shape). Corresponding angles are equal (F shape).
  2. Alternate angles on parallel lines are (3x + 29)° and 74°. Find x. → x = 15Prompt: Alternate angles are equal.
  3. A line crosses two parallel lines. One angle is 26°. What is the co-interior (same-side interior) angle to it, in degrees? → 154Prompt: Alternate angles are equal (Z shape). Corresponding angles are equal (F shape).

Hook · 6 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 · 12 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 · 12 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. Angle p and two other angles of 122° and 122° fill the space all the way round a point. Which reason should go with the step that finds p? (Angles around a point add up to 360° / Alternate angles are equal / Corresponding angles are equal / Co-interior angles add up to 180°) → Angles around a point add up to 360°Prompt: Picture the diagram: is there a crossing, a straight line or parallel lines?
  2. Angle p and an angle of 84° are co-interior angles between parallel lines. Find p in degrees. → 96Prompt: Decide whether the angles are equal or add up to 180°.

You do: independent practice · 17 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 · 7 min

  • Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
  1. Angle p and an angle of 88° sit side by side and together make a straight line. Which reason should go with the step that finds p? (Vertically opposite angles are equal / Alternate angles are equal / Co-interior angles add up to 180° / Angles on a straight line add up to 180°) → Angles on a straight line add up to 180°Prompt: Picture the diagram: is there a crossing, a straight line or parallel lines?
  2. Two straight lines cross. Angle p is vertically opposite an angle of 138°. Find p in degrees. → 138Prompt: 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

eurekami

Give the reason for each step in an angle argument

Name

Date

Score/ 8

  1. Question 1

    Angle p and two other angles of 91° and 91° fill the space all the way round a point. Which reason should go with the step that finds p?

    • A. Corresponding angles are equal
    • B. Angles around a point add up to 360°
    • C. Vertically opposite angles are equal
    • D. Co-interior angles add up to 180°

  2. Question 2

    Angle p and an angle of 66° lie on a straight line. Find p in degrees.

    Answer

  3. Question 3

    Two straight lines cross. Angle p is directly across the crossing point from an angle of 114°. Which reason should go with the step that finds p?

    • A. Vertically opposite angles are equal
    • B. Angles on a straight line add up to 180°
    • C. Co-interior angles add up to 180°
    • D. Angles around a point add up to 360°

  4. Question 4

    Two straight lines cross. Angle p is vertically opposite an angle of 67°. Find p in degrees.

    Answer

  5. Question 5

    A line crosses two parallel lines. Angle p and an angle of 59° are in the same position at each crossing (an F shape). Which reason should go with the step that finds p?

    • A. Corresponding angles are equal
    • B. Co-interior angles add up to 180°
    • C. Angles around a point add up to 360°
    • D. Alternate angles are equal

  6. Question 6

    Two straight lines cross. Angle p is vertically opposite an angle of 145°. Find p in degrees.

    Answer

  7. Question 7

    A line crosses two parallel lines. Angle p and an angle of 41° 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. Co-interior angles add up to 180°
    • C. Alternate angles are equal
    • D. Angles on a straight line add up to 180°

  8. Question 8

    Angle p and an angle of 117° are co-interior angles between parallel lines. Find p in degrees.

    Answer

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

  1. 1. B. Angles around a point add up to 360°

  2. 2. 114

  3. 3. A. Vertically opposite angles are equal

  4. 4. 67

  5. 5. A. Corresponding angles are equal

  6. 6. 145

  7. 7. C. Alternate angles are equal

  8. 8. 63