Math lesson plan · 8th grade (Year 9 in England) · 30 minutes
Predict the number of solutions of a system
Algebra
CCSS 8.EE.C.8.BEngland: KS3 Algebra
Objective and success criteria
Students will: Predict the number of solutions of 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: Solve a system by reading the intersection of two lines
Leads to: the next skill in this area.
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 (Solve a system by reading the intersection of two lines). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
Hook · 3 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Predict the number of solutions of 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: How many solutions does the system y = −x + 1 and 2y = −2x + 2 have?
- Step 1: Infinitely many
- Answer: Infinitely many
- 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.
- How many solutions does the system y = −x + 1 and y = −x − 3 have? (0 / Infinitely many / 1) → 0Prompt: Write both in y = mx + b form and compare slopes and intercepts.
- For which value of k does the system y = −3x − 8 and y = kx − 3 have NO solution? → -3Prompt: No solution means the lines never meet.
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.
- How many solutions does the system y = 5x − 3 and y = 5x have? (0 / Infinitely many / 1) → 0Prompt: Write both in y = mx + b form and compare slopes and intercepts.
- For which value of k does the system y = −6x + 1 and y = kx + 6 have NO solution? → -6Prompt: No solution means the lines never meet.
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: Solve a system by reading the intersection of two lines.
- 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
- 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