Math lesson plan · 9th grade (Year 10 in England) · 45 minutes
Solve factorised equations with the zero product property
Algebra
CCSS HSA.REI.B.4.BCCSS HSA.SSE.B.3.AEngland: GCSE Foundation Algebra
Objective and success criteria
Students will: Solve factorised equations with the zero product property.
- 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: One-step equations
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 (One-step equations). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Solve: x/3 = 0 → x = 0Prompt: x is divided by 3. What undoes dividing?
- Solve: x/6 = 4 → x = 24Prompt: x is divided by 6. What undoes dividing?
- Solve: x/8 = −2 → x = -16Prompt: x is divided by 8. What undoes dividing?
Hook · 5 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Solve factorised equations with the zero product property. 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: Solve: (x − 8)(x − 7) = 0. Give both solutions, separated by a comma.
- Step 1: x − 8 = 0 or x − 7 = 0
- Step 2: x = 8 or x = 7
- Answer: x = 7 or x = 8
- 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.
- Solve: (x + 1)(x + 8) = 0. Give both solutions, separated by a comma. → x = -8 or x = -1Prompt: If a product equals zero, at least one factor equals zero.
- Solve: (5x + 8)(x + 3) = 0. Give both solutions (fractions are fine), separated by a comma. → x = -3 or x = -1.6Prompt: Set each factor equal to zero.
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.
- Solve: (x + 3)(x + 7) = 0. Give both solutions, separated by a comma. → x = -7 or x = -3Prompt: If a product equals zero, at least one factor equals zero.
- Solve: x(x + 1)(x − 6) = 0. Give all three solutions, separated by commas. → x = -1 or x = 0 or x = 6Prompt: There are three factors, so there can be three solutions.
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: One-step 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
- 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