Math lesson plan · 6th grade (Year 7 in England) · 45 minutes
Match inequalities and number-line graphs
Algebra
CCSS 6.EE.B.8England: KS3 Algebra
Objective and success criteria
Students will: Match inequalities and number-line graphs.
- 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: Write inequalities for real-life limits
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 (Write inequalities for real-life limits). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Write an inequality: The speed limit is 8 km/h (s = speed). (Type ≤ as <= and ≥ as >= if you need to.) → s ≤ 8Prompt: “At least” means ≥; “at most” means ≤.
- Write as an inequality: x is less than −5. → x < −5Prompt: Start with x, then the sign, then the number.
- Which inequality matches: A carry-on bag can weigh at most 28 kg (w = mass). (w ≤ 28 / w ≥ 28 / w < 28 / w > 28) → w ≤ 28Prompt: Is 28 itself allowed?
Hook · 5 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Match inequalities and number-line graphs. 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 graph shows x ≥ −5?
- Step 1: Closed circle at −5, arrow right
- Answer: Closed circle at −5, arrow right
- 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 graph shows x < 4? (Closed circle at 4, arrow right / Open circle at 4, arrow right / Open circle at 4, arrow left / Closed circle at 4, arrow left) → Open circle at 4, arrow leftPrompt: Is the number itself included? Then the circle is closed.
- How many of these numbers are solutions of x > −3? −6, −4, −3, −2, 0 → 2Prompt: Test each number in the inequality.
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 graph shows x < −4? (Closed circle at −4, arrow right / Closed circle at −4, arrow left / Open circle at −4, arrow left / Open circle at −4, arrow right) → Open circle at −4, arrow leftPrompt: Is the number itself included? Then the circle is closed.
- How many of these numbers are solutions of x ≥ −4? −7, −5, −4, −3, −1 → 3Prompt: Test each number in the inequality.
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: Write inequalities for real-life limits.
- 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-6.
Free lesson plan from eurekami.com/lesson-plan-builder