Math lesson plan · 8th grade (Year 9 in England) · 30 minutes
Rearrange ax + by = c to find slope and intercept
Algebra
CCSS 8.EE.B.6CCSS 8.F.B.4England: KS3 AlgebraEngland: GCSE Foundation Algebra
Objective and success criteria
Students will: Rearrange ax + by = c to find slope and intercept.
- 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 y = mx + b from a slope and intercept, or from a graph; Equations with the unknown on both sides
Leads to: the next skill in this area.
Materials: Balance scales or a balance drawing, Algebra tiles, Function machine cards, Mini whiteboards and pens, Printed student sheet (below).
Warm-up · 4 min
- Quick retrieval from earlier learning (Write y = mx + b from a slope and intercept, or from a graph; Equations with the unknown on both sides). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Write the equation of the line with slope 6 and y-intercept 8. Type the right-hand side (y = …). → 6x+8Prompt: Use y = mx + b.
- Solve: 7x − 9 = 6x − 10 → x = -1Prompt: Collect the x terms on one side.
- Write the equation of the line with slope 5 and y-intercept −6. Type the right-hand side (y = …). → 5x-6Prompt: Use y = mx + b.
Hook · 3 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Rearrange ax + by = c to find slope and intercept. Read the success criteria together.
I do: model it · 7 min
- Work through the example out loud, saying why you do each step, not just what you do.
- Example: Find the slope of 3x + 6y = 18. Give a whole number or fraction.
- Step 1: 6y = −3x + 18
- Step 2: y = −(1/2)x + 3
- Step 3: m = −1/2
- Answer: -1/2
- Pause after each step and ask a student to say what comes next.
We do: guided practice · 6 min
- Do these together. Students try each step on whiteboards before you reveal it.
- Use the hints as prompts rather than giving the answer.
- Find the slope of −5x + 3y = 6. Give a whole number or fraction. → 5/3 (1 2/3)Prompt: Get y on its own: move the x-term to the other side.
- What is the y-intercept of −5x + 5y = −20? → -4Prompt: Put x = 0.
You do: independent practice · 7 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 6 questions are on the student sheet below, with answers in the key.
Exit ticket · 3 min
- Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
- What is the y-intercept of −4x + 4y = 8? → 2Prompt: Put x = 0.
- Find the slope of x + 3y = 9. Give a whole number or fraction. → -1/3Prompt: Get y on its own: move the x-term to the other side.
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 y = mx + b from a slope and intercept, or from a graph.
- 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
- 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