Math lesson plan · 8th grade (Year 9 in England) · 45 minutes
Equations with one solution, no solution or infinitely many
Algebra
CCSS 8.EE.C.7.AEngland: KS3 Algebra
Objective and success criteria
Students will: Equations with one solution, no solution or infinitely many.
- 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 equations with brackets and x on both sides
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 · 5 min
- Quick retrieval from earlier learning (Solve equations with brackets and x on both sides). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Solve: 5(x + 5) = x − 3 → x = -7Prompt: Expand the brackets first.
- Solve: 3(x + 5) = 4(x − 4) + 28 → x = 3Prompt: Expand both brackets.
- A rectangle is (x + 1) cm long and 3 cm wide. A square has sides of (x − 2) cm. Their perimeters are equal, so 2(x + 1 + 3) = 4(x − 2). Find x. → x = 8Prompt: Expand both sides.
Hook · 5 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Equations with one solution, no solution or infinitely many. Read the success criteria together.
I do: model it · 10 min
- Work through the example out loud, saying why you do each step, not just what you do.
- Example: How many solutions does 2(x + 8) = 2x + 16 have?
- Step 1: 2x + 16 = 2x + 16
- Step 2: Infinitely many solutions
- Answer: Infinitely many solutions
- Pause after each step and ask a student to say what comes next.
We do: guided practice · 10 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 3(x + 2) = 3x + 6 have? (No solution / Infinitely many solutions / Exactly one solution) → Infinitely many solutionsPrompt: Expand the left side and compare it with the right side.
- 3x − 9 = □x + (−1). For which value of □ does the equation have NO solution? → 3Prompt: No solution happens when the x-terms match but the numbers don't.
You do: independent practice · 10 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 · 5 min
- Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
- 4x + 4 = □x + 9. For which value of □ does the equation have NO solution? → 4Prompt: No solution happens when the x-terms match but the numbers don't.
- How many solutions does 2(x + 3) = 2x + 6 have? (No solution / Infinitely many solutions / Exactly one solution) → Infinitely many solutionsPrompt: Expand the left side and compare it with the right side.
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 equations with brackets and x 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
- 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