Math lesson plan · 9th grade (Year 10 in England) · 60 minutes
Solve 'or' compound inequalities
Algebra
CCSS HSA.REI.B.3
Objective and success criteria
Students will: Solve 'or' compound inequalities.
- 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 multi-step inequalities, including reversing the sign
Leads to: Solve absolute value inequalities
Materials: Balance scales or a balance drawing, Algebra tiles, Function machine cards, Mini whiteboards and pens, Printed student sheet (below).
Warm-up · 6 min
- Quick retrieval from earlier learning (Solve multi-step inequalities, including reversing the sign). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Solve: −3x − 8 ≥ −23 (x ≤ 5 / x ≥ 5 / x ≤ −5 / x ≤ 4) → x ≤ 5Prompt: Solve it like an equation, step by step.
- Solve: (x + 6) ≤ −4x − 4 (x ≥ −2 / x ≤ −2 / x ≤ 2 / x ≤ 0) → x ≤ −2Prompt: Expand the bracket, then collect x terms on one side.
- What is the smallest integer that satisfies 6x + 5 ≥ 35? → 5Prompt: Solve the inequality first.
Hook · 6 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Solve 'or' compound inequalities. Read the success criteria together.
I do: model it · 12 min
- Work through the example out loud, saying why you do each step, not just what you do.
- Example: Solve: x − 1 < −1 or 5x − 2 > 18
- Step 1: x < 0
- Step 2: 5x > 20 → x > 4
- Step 3: x < 0 or x > 4
- Answer: x < 0 or x > 4
- Pause after each step and ask a student to say what comes next.
We do: guided practice · 12 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 − 2 < −3 or 4x + 5 > 25 (x > −1 or x < 5 / x < −1 or x > 5 / x < −3 or x > 20 / −1 < x < 5) → x < −1 or x > 5Prompt: Solve each part on its own.
- Solve: x + 5 < 2 or 5x − 2 > 18 (x > −3 or x < 4 / x < 2 or x > 20 / −3 < x < 4 / x < −3 or x > 4) → x < −3 or x > 4Prompt: Solve each part on its own.
You do: independent practice · 17 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 · 7 min
- Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
- Solve: x − 2 < −3 or 2x + 6 > 16 (−1 < x < 5 / x < −1 or x > 5 / x < −3 or x > 10 / x > −1 or x < 5) → x < −1 or x > 5Prompt: Solve each part on its own.
- Solve: x + 1 < −4 or 3x − 5 > −5 (x < −4 or x > 0 / −5 < x < 0 / x > −5 or x < 0 / x < −5 or x > 0) → x < −5 or x > 0Prompt: Solve each part on its own.
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 multi-step inequalities, including reversing the sign.
- 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: Solve absolute value 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