Math lesson plan · 9th grade (Year 10 in England) · 45 minutes
Read the slope and intercept from Ax + By = C
Algebra
CCSS HSA.CED.A.4CCSS HSF.IF.C.9England: GCSE Foundation AlgebraEngland: GCSE Higher Algebra
Objective and success criteria
Students will: Read the slope and intercept from Ax + By = C.
- 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: Graphs of linear equations y = mx + b; Rearrange formulas (change the subject)
Leads to: Find both axis intercepts of Ax + By = C (cover-up method); Classify pairs of lines as parallel, perpendicular or neither
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 (Graphs of linear equations y = mx + b; Rearrange formulas (change the subject)). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Make x the subject of y = 4x + 1. Type the expression for x. → (y-1)/4Prompt: Undo the operations on x in reverse order.
- Does the point (1, −4) lie on the line y = x − 5? (Yes / No) → YesPrompt: Substitute the x-value into the equation.
- Make x the subject of y = 5x + 3. Type the expression for x. → (y-3)/5Prompt: Undo the operations on x in reverse order.
Hook · 5 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Read the slope and intercept from Ax + By = C. 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: What is the slope (gradient) of the line 3x + y = 0?
- Step 1: y = −3x
- Step 2: y = −3x
- Step 3: m = −3
- Answer: -3
- 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.
- What is the slope (gradient) of the line 8x − 4y = 16? → 2Prompt: Rearrange into y = mx + b.
- Find the slope of 4x + 5y = 15. Give a fraction in its simplest form. → -4/5Prompt: Get y on its own.
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.
- At what y-value does 4x + 5y = −30 cross the y-axis? → -6Prompt: On the y-axis, x = 0.
- Find the slope of −3x + 5y = −15. Give a fraction in its simplest form. → 3/5Prompt: Get y on its own.
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: Graphs of linear equations y = mx + b.
- 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 both axis intercepts of Ax + By = C (cover-up method); Classify pairs of lines as parallel, perpendicular or neither.
- 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