Math lesson plan · 9th grade (Year 10 in England) · 45 minutes
Write the equation of a perpendicular line through a point
Algebra
CCSS HSG.GPE.B.5England: GCSE Higher Algebra
Objective and success criteria
Students will: Write the equation of a perpendicular line through a point.
- 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: Write the equation of a parallel line through a point
Leads to: Find equations of tangents and normals
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 (Write the equation of a parallel line through a point). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Find the line parallel to 4x + 4y = 4 through (2, 5). Type the right-hand side of y = … . → -x+7Prompt: Rearrange the given line into y = mx + b to read its slope.
- Find the line parallel to 12x + 4y = 0 through (−4, −6). Type the right-hand side of y = … . → -3x-18Prompt: Rearrange the given line into y = mx + b to read its slope.
- Find the line parallel to −3x + 3y = −6 through (2, 6). Type the right-hand side of y = … . → x+4Prompt: Rearrange the given line into y = mx + b to read its slope.
Hook · 5 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Write the equation of a perpendicular line through a point. 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 has slope 1/2. What is the slope of a line perpendicular to it? Give a fraction or whole number.
- Step 1: 1/2 × m = −1
- Step 2: m = −2
- Answer: -2
- 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 has slope 4. What is the slope of a line perpendicular to it? Give a fraction or whole number. → -1/4Prompt: Perpendicular slopes multiply to −1.
- Find the line perpendicular to y = −x − 5 that passes through (0, 2). Type the right-hand side of y = … . → x+2Prompt: Find the negative reciprocal of the slope.
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 has slope −4/3. What is the slope of a line perpendicular to it? Give a fraction or whole number. → 3/4Prompt: Perpendicular slopes multiply to −1.
- Find the line perpendicular to y = −(1/3)x − 3 through (2, 6). Type the right-hand side of y = … . → 3xPrompt: The new slope is −1 divided by the old slope.
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: Write the equation of a parallel line through a point.
- 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: Find equations of tangents and normals.
- 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