Math lesson plan · 10th grade (Year 11 in England) · 45 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 · 5 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.
- A line crosses two parallel lines. One angle is 113°. What is the alternate angle to it, in degrees? → 113Prompt: Alternate angles are equal (Z shape). Corresponding angles are equal (F shape).
- Alternate angles on parallel lines are (4x + 7)° and 71°. Find x. → x = 16Prompt: Alternate angles are equal.
- A line crosses two parallel lines. One angle is 109°. What is the co-interior (same-side interior) angle to it, in degrees? → 71Prompt: Alternate angles are equal (Z shape). Corresponding angles are equal (F shape).
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: Give the reason for each step in an angle argument. 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: 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 · 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.
- A line crosses two parallel lines. Angle p and an angle of 55° are between the parallel lines, on the same side of the crossing line (a C shape). Which reason should go with the step that finds p? (Alternate angles are equal / Vertically opposite angles are equal / Corresponding angles are equal / Co-interior angles add up to 180°) → Co-interior angles add up to 180°Prompt: Picture the diagram: is there a crossing, a straight line or parallel lines?
- Angle p and an angle of 86° lie on a straight line. Find p in degrees. → 94Prompt: Decide whether the angles are equal or add up to 180°.
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.
- A line crosses two parallel lines. Angle p and an angle of 56° are between the parallel lines, on the same side of the crossing line (a C shape). Which reason should go with the step that finds p? (Co-interior angles add up to 180° / Angles around a point add up to 360° / Vertically opposite angles are equal / Corresponding angles are equal) → Co-interior angles add up to 180°Prompt: Picture the diagram: is there a crossing, a straight line or parallel lines?
- Angle p and an angle of 45° are corresponding angles on parallel lines. Find p in degrees. → 45Prompt: 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