Math lesson plan · 8th grade (Year 9 in England) · 60 minutes
Solve angle equations on parallel lines
Geometry
CCSS 8.G.A.5CCSS 8.EE.C.7England: KS3 Geometry and measuresEngland: GCSE Foundation Geometry and measures
Objective and success criteria
Students will: Solve angle equations on parallel lines.
- 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: Name and use angle pairs on parallel lines; Solve equations with x on both sides
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 (Name and use angle pairs on parallel lines; Solve equations with x on both sides). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- A transversal crosses two parallel lines. Two angles are in the same position at each crossing. What are they called? (alternate exterior / alternate interior / corresponding / co-interior (same-side interior)) → correspondingPrompt: Interior means between the parallel lines; exterior means outside them.
- Two parallel lines are cut by a transversal. One angle is 71°. What is its alternate interior partner? → 71Prompt: Corresponding and alternate angles are equal.
- A transversal crosses two parallel lines. Two angles are between the parallel lines, on the same side of the transversal. What are they called? (alternate exterior / alternate interior / corresponding / co-interior (same-side interior)) → co-interior (same-side interior)Prompt: Interior means between the parallel lines; exterior means outside them.
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: Solve angle equations on parallel lines. 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: Alternate angles on parallel lines are (3x + 21)° and (x + 43)°. Find x.
- Step 1: 3x + 21 = 1x + 43
- Step 2: 2x = 22
- Step 3: x = 11
- Answer: 11
- 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.
- Corresponding angles are (3x + 10)° and (5x − 30)°. Find x. → 20Prompt: Corresponding angles are equal.
- Co-interior angles on parallel lines are (3x + 7)° and (3x + 17)°. Find x. → 26Prompt: Co-interior angles 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.
- Co-interior angles on parallel lines are (3x + 1)° and (2x + 129)°. Find x. → 10Prompt: Co-interior angles add up to 180°.
- Alternate angles on parallel lines are (4x + 20)° and (2x + 62)°. Find x. → 21Prompt: Alternate angles are equal, so set the expressions equal.
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: Name and use angle pairs on 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-8.
Free lesson plan from eurekami.com/lesson-plan-builder