Math lesson plan · 7th grade (Year 8 in England) · 45 minutes
Solve inequality problems about budgets and limits
Algebra
CCSS 7.EE.B.4.BEngland: KS3 Algebra
Objective and success criteria
Students will: Solve inequality problems about budgets and limits.
- 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 two-step inequalities
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 (Solve two-step inequalities). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Solve: 3x + 7 ≤ 28 → x ≤ 7Prompt: Subtract 7 on both sides.
- Solve: −4x − 9 > −9 → x < 0Prompt: Add 9 on both sides.
- Which value of x satisfies 4(x + 4) ≥ 24? (1 / 0 / 4 / −2) → 4Prompt: 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 inequality problems about budgets and limits. 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: Mei has $59 at a fair. Entry costs $6 and each ride costs $4. What is the greatest number of rides Mei can go on?
- Step 1: 4r ≤ 53
- Step 2: r ≤ 13.25
- Step 3: At most 13 rides
- Answer: 13
- 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.
- Daniel has $66 at a fair. Entry costs $12 and each ride costs $3.50. What is the greatest number of rides Daniel can go on? → 15Prompt: Inequality: 12 + 3.5r ≤ 66.
- A lift can carry at most 1000 kg. A 74 kg delivery worker is loading boxes of 32 kg each. What is the greatest number of boxes the worker can take in the lift with them? → 28Prompt: 74 + 32b ≤ 1000
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.
- A lift can carry at most 750 kg. A 81 kg delivery worker is loading boxes of 31 kg each. What is the greatest number of boxes the worker can take in the lift with them? → 21Prompt: 81 + 31b ≤ 750
- Priya has $63 at a fair. Entry costs $6 and each ride costs $1.50. What is the greatest number of rides Priya can go on? → 38Prompt: Inequality: 6 + 1.5r ≤ 63.
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 two-step 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
- 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