Math lesson plan · 7th grade (Year 8 in England) · 30 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 · 4 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: −5x + 9 = −36 → x = 9Prompt: Subtract 9 from both sides.
- Solve: 9x − 9 = −63 → x = -6Prompt: Add 9 to both sides.
- Solve: −7x − 15 = 55 → x = -10Prompt: Add 15 to both sides.
Hook · 3 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 · 7 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 · 6 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 − 8 < 4 (x < 7 / x < 12 / x > 6 / x < 6) → x < 6Prompt: Solve it like an equation, keeping the inequality sign.
- Solve: −4x − 1 ≥ 3 (x ≤ 1 / x ≤ −1 / x ≥ 1 / x ≥ −1) → x ≤ −1Prompt: Isolate the x term first.
You do: independent practice · 7 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 6 questions are on the student sheet below, with answers in the key.
Exit ticket · 3 min
- Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
- Solve: 3x − 5 ≤ 7 (x ≤ 5 / x ≤ 12 / x ≤ 4 / x ≥ 4) → x ≤ 4Prompt: Solve it like an equation, keeping the inequality sign.
- What is the smallest whole number x that satisfies 7x + 7 ≥ 44? → 6Prompt: Solve the inequality 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