Math lesson plan · 6th grade (Year 7 in England) · 45 minutes
Inequalities: meaning and solutions
Algebra
CCSS 6.EE.B.5CCSS 6.EE.B.8England: KS3 AlgebraEngland: GCSE Foundation Algebra
Objective and success criteria
Students will: Inequalities: meaning and solutions.
- 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: Negative numbers and absolute value; Write algebraic expressions
Leads to: Solve linear inequalities; Write inequalities for real-life limits; Solve one-step inequalities, including dividing by a negative
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 (Negative numbers and absolute value; Write algebraic expressions). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Which expression means "5 less than n"? (n + 5 / n − 5 / 5 − n / n/5) → n − 5Prompt: Translate the words in order, carefully.
- Which expression means "n divided by 3"? (3 − n / n + 3 / 3n / n/3) → n/3Prompt: Translate the words in order, carefully.
- Which expression means "n divided by 5"? (n + 5 / 5 − n / n/5 / n − 5) → n/5Prompt: Translate the words in order, carefully.
Hook · 5 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Inequalities: meaning and solutions. 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: Which inequality matches? "You must be at least 12 years old to ride." (x is the amount)
- Step 1: x ≥ 12
- Answer: x ≥ 12
- 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.
- Which inequality matches? "The lift holds at most 15 people." (x is the amount) (x > 15 / x < 15 / x ≥ 15 / x ≤ 15) → x ≤ 15Prompt: 'At least' means that number or more.
- Which inequality matches? "More than 5 people came to the concert." (x is the amount) (x > 5 / x < 5 / x ≥ 5 / x ≤ 5) → x > 5Prompt: 'At least' means that number or more.
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.
- Which inequality matches? "The lift holds at most 17 people." (x is the amount) (x > 17 / x < 17 / x ≥ 17 / x ≤ 17) → x ≤ 17Prompt: 'At least' means that number or more.
- Which inequality matches? "The lift holds at most 20 people." (x is the amount) (x > 20 / x < 20 / x ≥ 20 / x ≤ 20) → x ≤ 20Prompt: 'At least' means that number or more.
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: Negative numbers and absolute value.
- 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: Solve linear inequalities; Write inequalities for real-life limits; Solve one-step inequalities, including dividing by a negative.
- 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-6.
Free lesson plan from eurekami.com/lesson-plan-builder