Math lesson plan · 9th grade (Year 10 in England) · 45 minutes
Classify pairs of lines as parallel, perpendicular or neither
Algebra
CCSS HSG.GPE.B.5England: GCSE Higher Algebra
Objective and success criteria
Students will: Classify pairs of lines as parallel, perpendicular or neither.
- 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: Read the slope and intercept from Ax + By = C
Leads to: Tell how many solutions a linear system has
Materials: Balance scales or a balance drawing, Algebra tiles, Function machine cards, Mini whiteboards and pens, Printed student sheet (below).
Warm-up · 5 min
- Quick retrieval from earlier learning (Read the slope and intercept from Ax + By = C). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- What is the slope (gradient) of the line −2x − 2y = −10? → -1Prompt: Rearrange into y = mx + b.
- Find the slope of 2x − 5y = 5. Give a fraction in its simplest form. → 2/5Prompt: Get y on its own.
- At what y-value does −2x − 4y = −16 cross the y-axis? → 4Prompt: On the y-axis, x = 0.
Hook · 5 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Classify pairs of lines as parallel, perpendicular or neither. 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: Line 1: y = (1/3)x + 5 Line 2: y = (1/3)x + 6 Are the lines parallel, perpendicular or neither?
- Step 1: 1/3 and 1/3
- Step 2: Parallel
- Answer: Parallel
- 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.
- Line 1: y = −x + 1 Line 2: y = x + 4 Are the lines parallel, perpendicular or neither? (Parallel / Perpendicular / Neither) → PerpendicularPrompt: Compare the two slopes.
- Line 1: 2x + 2y = −3 Line 2: −y = 3 Are the lines parallel, perpendicular or neither? (Parallel / Perpendicular / Neither) → NeitherPrompt: Find each slope: m = −A/B for Ax + By = C.
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.
- Line 1: y = (1/2)x + 4 Line 2: y = −2x + 2 Are the lines parallel, perpendicular or neither? (Parallel / Perpendicular / Neither) → PerpendicularPrompt: Compare the two slopes.
- Line 1: −4x + 2y = −1 Line 2: −8x + 4y = 24 Are the lines parallel, perpendicular or neither? (Parallel / Perpendicular / Neither) → ParallelPrompt: Find each slope: m = −A/B for Ax + By = C.
Watch out for
- Doing an operation to one side of an equation but not the other.
- Reading 3x as 3 + x, or thinking x always stands for one particular number.
Support and stretch
Support
- Review first: Read the slope and intercept from Ax + By = C.
- Use concrete materials: balance scales or a balance drawing.
- 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: Tell how many solutions a linear system has.
- 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-9.
Free lesson plan from eurekami.com/lesson-plan-builder