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 − 2 ≥ 4 → x ≥ 2Prompt: Add 2 on both sides.
- Solve: −5x − 12 < 13 → x > −5Prompt: Add 12 on both sides.
- Which value of x satisfies 2(x − 5) < −14? (−2 / −4 / 1 / −1) → −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.
- Luis has $76 at a fair. Entry costs $9 and each ride costs $1.50. What is the greatest number of rides Luis can go on? → 44Prompt: Inequality: 9 + 1.5r ≤ 76.
- A lift can carry at most 500 kg. A 65 kg delivery worker is loading boxes of 37 kg each. What is the greatest number of boxes the worker can take in the lift with them? → 11Prompt: 65 + 37b ≤ 500
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 1000 kg. A 81 kg delivery worker is loading boxes of 18 kg each. What is the greatest number of boxes the worker can take in the lift with them? → 51Prompt: 81 + 18b ≤ 1000
- Kai's first three test scores are 85, 74, 80. What is the lowest score Kai needs on the fourth test to have a mean of at least 89? (It may be more than 100; give the number anyway.) → 117Prompt: Mean ≥ 89 means the total must be at least 89 × 4.
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