Math lesson plan · 8th grade (Year 9 in England) · 30 minutes
Solve systems by elimination
Algebra
CCSS 8.EE.C.8.BEngland: KS3 AlgebraEngland: GCSE Foundation Algebra
Objective and success criteria
Students will: Solve systems by elimination.
- 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: Check whether a point solves a system
Leads to: Solve real problems with two equations
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 (Check whether a point solves a system). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Is (−3, −4) a solution of the system −3x + y = 5 and 3x + 4y = −25? (Yes / No) → YesPrompt: Substitute x and y into BOTH equations.
- Which point solves both x + y = −4 and x − y = 0? ((−2, −2) / (−4, 0) / (−1, −3)) → (−2, −2)Prompt: Test each point in both equations.
- Is (4, −1) a solution of the system −4x + 2y = −18 and −3x − y = −11? (Yes / No) → YesPrompt: Substitute x and y into BOTH equations.
Hook · 3 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Solve systems by elimination. 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: Solve: 4x + 3y = 9 and x − 3y = 6. Type the solution like (2, −3).
- Step 1: 5x = 15 → x = 3
- Step 2: 3y = 9 − 12 → y = −1
- Step 3: (3, −1)
- Answer: (3, −1)
- 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.
- Solve: 4x + 5y = −25 and 2x − 5y = 25. Type the solution like (2, −3). → (0, −5)Prompt: The y-terms are opposites. Add the equations to eliminate y.
- Solve: x + 3y = 3 and 3x + 4y = −1. Type the solution like (2, −3). → (−3, 2)Prompt: Multiply the first equation by 3 so the x-terms match.
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.
- Solve: 3x + 4y = −18 and 6x − 3y = −3. Type the solution like (2, −3). → (−2, −3)Prompt: Multiply the first equation by 2 so the x-terms match.
- Solve: 3x + 5y = −37 and 5x − 5y = 5. Type the solution like (2, −3). → (−4, −5)Prompt: The y-terms are opposites. Add the equations to eliminate y.
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: Check whether a point solves a system.
- 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: Solve real problems with two equations.
- 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