Math lesson plan · 8th grade (Year 9 in England) · 30 minutes
Check whether a point solves a system
Algebra
CCSS 8.EE.C.8.AEngland: KS3 AlgebraEngland: GCSE Foundation Algebra
Objective and success criteria
Students will: Check whether a point solves a system.
- 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: Systems of linear equations (simultaneous equations)
Leads to: Solve a system by reading the intersection of two lines; Solve systems by substitution; Solve systems by elimination
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 (Systems of linear equations (simultaneous equations)). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Solve the system: y = −2x − 3 and x + 2y = 9. Find x. → x = -5Prompt: Substitute the first equation into the second.
- Solve: 4x + 4y = 8 and 2x − 4y = 10. Find y. → -1Prompt: The y terms have opposite coefficients: add the equations to eliminate y.
- Solve the system: y = −3x − 3 and 3x + 3y = −9. Find x. → x = 0Prompt: Substitute the first equation into the second.
Hook · 3 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Check whether a point solves a system. 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: Is (−5, 3) a solution of the system −2x + y = 13 and 2x + 4y = 2?
- Step 1: First: 13 ✓
- Step 2: Second: 2 ✓
- Step 3: Yes.
- Answer: Yes
- 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.
- Is (5, 4) a solution of the system 3x − 3y = 3 and −x + 4y = 13? (Yes / No) → NoPrompt: Substitute x and y into BOTH equations.
- Which point solves both x + y = 3 and x − y = −9? ((−3, 6) / (3, −9) / (6, −3) / (−2, 5)) → (−3, 6)Prompt: Test each point in both equations.
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.
- Is (3, 3) a solution of the system −4x + y = −9 and −x − y = −6? (Yes / No) → YesPrompt: Substitute x and y into BOTH equations.
- Which point solves both x + y = −4 and x − y = −2? ((−2, −2) / (−1, −3) / (−4, −2) / (−3, −1)) → (−3, −1)Prompt: Test each point in both equations.
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: Systems of linear equations (simultaneous equations).
- 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 a system by reading the intersection of two lines; Solve systems by substitution; Solve systems by elimination.
- 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