Math lesson plan · 7th grade (Year 8 in England) · 60 minutes
Solve linear inequalities
Algebra
CCSS 7.EE.B.4.BEngland: GCSE Foundation AlgebraEngland: GCSE Higher Algebra
Objective and success criteria
Students will: Solve linear 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: Two-step equations; Inequalities: meaning and solutions
Leads to: Compound inequalities and integer solutions; Quadratic inequalities; Solve multi-step inequalities, including reversing the sign
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 (Two-step equations; Inequalities: meaning and solutions). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Solve: −8x + 10 = −6 → x = 2Prompt: Subtract 10 from both sides.
- Solve: 8x + 3 = 51 → x = 6Prompt: Subtract 3 from both sides.
- Solve: −4x + 5 = −31 → x = 9Prompt: Subtract 5 from both sides.
Hook · 6 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Solve linear 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: 7x + 10 < 80
- Step 1: 7x < 70
- Step 2: x < 10
- Answer: x < 10
- 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: 8x − 10 ≥ 54 (x ≥ 8 / x ≤ 8 / x ≥ 9 / x ≥ 64) → x ≥ 8Prompt: Solve it like an equation, keeping the inequality sign.
- Solve: −4x + 9 > 13 (x > 1 / x < 1 / x < −1 / x > −1) → x < −1Prompt: Isolate the x term first.
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.
- What is the smallest whole number x that satisfies 4x + 7 > 15? → 3Prompt: Solve the inequality first.
- Solve: −6x − 3 ≤ 33 (x ≤ 6 / x ≤ −6 / x ≥ 6 / x ≥ −6) → x ≥ −6Prompt: Isolate the x term first.
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: Two-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
- Move on to: Compound inequalities and integer solutions; Quadratic inequalities; Solve multi-step inequalities, including reversing the sign.
- 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-7.
Free lesson plan from eurekami.com/lesson-plan-builder