Math lesson plan · 9th grade (Year 10 in England) · 30 minutes
Decide if a linear equation has one, none or infinitely many solutions
Algebra
CCSS 8.EE.C.7.ACCSS HSA.REI.B.3England: GCSE Foundation Algebra
Objective and success criteria
Students will: Decide if a linear equation has one, none or infinitely many solutions.
- 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
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 (Equations with the unknown on both sides). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Solve: 4x + 3 = 6x + 13 → x = -5Prompt: Collect the x terms on one side.
- Solve: 2(x − 3) = 1(x + 6) − 2 → x = 10Prompt: Expand the brackets on both sides first.
- How many solutions does 3x + 8 = 3x + 8 have? (No solution / Infinitely many solutions / Exactly one solution) → Infinitely many solutionsPrompt: Subtract the x terms from both sides. What is left?
Hook · 3 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Decide if a linear equation has one, none or infinitely many solutions. 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 6(x + 5) + 8 = 6x + 38 have?
- Step 1: 6x + 38 = 6x + 38
- Step 2: Both sides are identical: infinitely many solutions.
- Step 3: Infinitely many solutions
- Answer: Infinitely many solutions
- 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 5(x − 5) − 3 = 5x − 28 have? (Exactly one solution / No solution / Infinitely many solutions) → Infinitely many solutionsPrompt: Expand the brackets and collect like terms on each side.
- For what value of k does −5x − 4 = kx + 2 have no solution? → -5Prompt: An equation has no solution when the x terms cancel but the numbers don't.
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.
- Find the value of c that makes 2(3x + 3) = 6x + c true for every value of x. → 6Prompt: True for every x means both sides are the same expression.
- For what value of k does −4x + 3 = kx + 9 have no solution? → -4Prompt: An equation has no solution when the x terms cancel but the numbers don't.
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
- 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-9.
Free lesson plan from eurekami.com/lesson-plan-builder