Math lesson plan · 8th grade (Year 9 in England) · 30 minutes
Solve systems by substitution
Algebra
CCSS 8.EE.C.8.BEngland: KS3 AlgebraEngland: GCSE Foundation Algebra
Objective and success criteria
Students will: Solve systems by substitution.
- 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; Solve equations with x on both sides
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; Solve equations with x on both sides). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Is (4, 4) a solution of the system −3x − 3y = −24 and −x + 3y = 7? (Yes / No) → NoPrompt: Substitute x and y into BOTH equations.
- Which point solves both x + y = 4 and x − y = −2? ((4, −2) / (2, 2) / (1, 3) / (3, 1)) → (1, 3)Prompt: Test each point in both equations.
- Is (−3, −2) a solution of the system 2x − y = −4 and −4x − 3y = 18? (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 substitution. 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 the system: y = x + 1 and 5x + 3y = 3. Type the solution like (2, −3).
- Step 1: 5x + 3(x + 1) = 3
- Step 2: 8x = 0 → x = 0
- Step 3: y = 1
- Step 4: (0, 1)
- Answer: (0, 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 the system: y = −x + 1 and 2x − y = 2. Type the solution like (2, −3). → (1, 0)Prompt: Substitute −x + 1 for y in the second equation.
- Solve: x = 3y − 2 and x + y = 10. Type the solution like (2, 3). → (7, 3)Prompt: Replace x in the second equation.
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: x = 4y − 29 and x + y = 16. Type the solution like (2, 3). → (7, 9)Prompt: Replace x in the second equation.
- Solve the system: y = x − 3 and x + 3y = −13. Type the solution like (2, −3). → (−1, −4)Prompt: Substitute x − 3 for y in the second equation.
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