Math lesson plan · 9th grade (Year 10 in England) · 45 minutes
Solve multi-step inequalities, including reversing the sign
Algebra
CCSS HSA.REI.B.3England: GCSE Foundation AlgebraEngland: GCSE Higher Algebra
Objective and success criteria
Students will: Solve multi-step inequalities, including reversing the sign.
- 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 linear inequalities
Leads to: Find the error in a worked inequality; Solve double inequalities like a < bx + c < d; Solve 'or' compound inequalities
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 linear inequalities). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Solve: 8x + 1 ≥ −7 (x ≥ 0 / x ≥ −1 / x ≤ −1 / x ≥ −8) → x ≥ −1Prompt: Solve it like an equation, keeping the inequality sign.
- Solve: −2x − 1 > −7 (x < 3 / x > 3 / x > −3 / x < −3) → x < 3Prompt: Isolate the x term first.
- What is the smallest whole number x that satisfies 7x + 15 ≥ 24? → 2Prompt: Solve the inequality first.
Hook · 5 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Solve multi-step inequalities, including reversing the sign. 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 ≥ 15
- Step 1: x ≥ 7
- Step 2: x ≥ 7
- Answer: x ≥ 7
- 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: 2x − 2 ≤ 0 (x ≤ −1 / x ≤ 2 / x ≤ 1 / x ≥ 1) → x ≤ 1Prompt: Solve it like an equation, step by step.
- Solve: 4(x + 6) ≤ 5x + 19 (x ≥ 7 / x ≥ −5 / x ≥ 5 / x ≤ 5) → x ≥ 5Prompt: Expand the bracket, then collect x terms on one side.
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.
- What is the smallest integer that satisfies 4x − 5 > 3? → 3Prompt: Solve the inequality first.
- Solve: −5x − 9 ≥ −24 (x ≥ 3 / x ≤ −3 / x ≤ 3 / x ≤ 4) → x ≤ 3Prompt: Solve it like an equation, step by step.
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 linear inequalities.
- 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: Find the error in a worked inequality; Solve double inequalities like a < bx + c < d; Solve 'or' compound inequalities.
- 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