Math lesson plan · 8th grade (Year 9 in England) · 60 minutes
Systems of linear equations (simultaneous equations)
Algebra
CCSS 8.EE.C.8England: GCSE Foundation AlgebraEngland: GCSE Higher Algebra
Objective and success criteria
Students will: Systems of linear equations (simultaneous equations).
- 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: Equations with the unknown on both sides; Graphs of linear equations y = mx + b
Leads to: Systems of equations: word problems; Linear and quadratic systems; Matrices: operations and determinants
Materials: Balance scales or a balance drawing, Algebra tiles, Function machine cards, Mini whiteboards and pens, Printed student sheet (below).
Warm-up · 6 min
- Quick retrieval from earlier learning (Equations with the unknown on both sides; Graphs of linear equations y = mx + b). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Solve: 3x − 7 = 4x − 16 → x = 9Prompt: Collect the x terms on one side.
- Solve: 3(x + 6) = 5(x − 1) + 31 → x = -4Prompt: Expand the brackets on both sides first.
- Solve: 9x − 11 = x − 27 → x = -2Prompt: Collect the x terms on one side.
Hook · 6 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Systems of linear equations (simultaneous equations). Read the success criteria together.
I do: model it · 12 min
- Work through the example out loud, saying why you do each step, not just what you do.
- Example: Solve the system: y = −2x + 1 and 3x + 2y = 4. Find x.
- Step 1: 3x + 2(−2x + 1) = 4
- Step 2: −x + 2 = 4
- Step 3: x = −2
- Answer: x = -2
- Pause after each step and ask a student to say what comes next.
We do: guided practice · 12 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 = 2x − 3 and x + 3y = 33. Find x. → x = 6Prompt: Substitute the first equation into the second.
- Solve: 5x + 3y = 39 and 4x − 3y = −12. Find y. → 8Prompt: The y terms have opposite coefficients: add the equations to eliminate y.
You do: independent practice · 17 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 · 7 min
- Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
- Solve: 5x + 4y = −6 and 5x − 4y = 26. Find y. → -4Prompt: The y terms have opposite coefficients: add the equations to eliminate y.
- Solve the system: y = 4x + 5 and x + y = −20. Find x. → x = -5Prompt: Substitute the first equation into the second.
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: Equations with the unknown on both sides.
- 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: Systems of equations: word problems; Linear and quadratic systems; Matrices: operations and determinants.
- 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