Math lesson plan · 9th grade (Year 10 in England) · 45 minutes
Solve double inequalities like a < bx + c < d
Algebra
CCSS HSA.REI.B.3England: GCSE Higher Algebra
Objective and success criteria
Students will: Solve double inequalities like a < bx + c < d.
- 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: Compound inequalities and integer solutions; Solve multi-step inequalities, including reversing the sign
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 (Compound inequalities and integer solutions; 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: 4x − 7 > 21 (x > −7 / x > 6 / x > 7 / x > 8) → x > 7Prompt: Solve it like an equation, step by step.
- Solve: 2(x + 2) < −x − 8 (x > −4 / x < 4 / x < −2 / x < −4) → x < −4Prompt: Expand the bracket, then collect x terms on one side.
- Solve: 5x − 7 ≥ −22 (x ≤ −3 / x ≥ −4 / x ≥ −3 / x ≥ −2) → x ≥ −3Prompt: Solve it like an equation, step by step.
Hook · 5 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Solve double inequalities like a < bx + c < d. 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: −13 < 4x − 1 < 7
- Step 1: −12 < 4x < 8
- Step 2: −3 < x < 2
- Answer: −3 < x < 2
- 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: 2 < 5x + 2 < 17 (2 < x < 5 / 0 < x < 15 / 0 < x < 3 / −1 < x < 4) → 0 < x < 3Prompt: Whatever you do, do it to all three parts.
- Solve: −10 < −3x + 5 < −1 (−15 < x < −6 / 2 < x < 5 / 5 < x < 2 / −5 < x < −2) → 2 < x < 5Prompt: Subtract the constant from all three parts.
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: 2x + 2 ≥ 4 and 2x + 2 < 14. Write the answer as one double inequality. (1 ≤ x < 6 / x ≤ 1 or x ≥ 6 / 1 ≤ x ≤ 6 / 1 < x ≤ 6) → 1 ≤ x < 6Prompt: Solve each inequality separately.
- Solve: −9 < 2x + 3 < −5 (−12 < x < −8 / −3 < x < −1 / −6 < x < −4 / −7 < x < −3) → −6 < x < −4Prompt: Whatever you do, do it to all three parts.
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: Compound inequalities and integer solutions.
- 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