Math lesson plan · 9th grade (Year 10 in England) · 45 minutes
Find the error in a worked inequality
Algebra
CCSS HSA.REI.B.3CCSS HSA.REI.A.1England: GCSE Higher Algebra
Objective and success criteria
Students will: Find the error in a worked inequality.
- 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 multi-step inequalities, including reversing the sign
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 multi-step inequalities, including reversing the sign). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Solve: 4x − 1 > 27 (x > 6 / x > 8 / x > −7 / x > 7) → x > 7Prompt: Solve it like an equation, step by step.
- Solve: -3(x − 3) > 4x − 26 (x > 5 / x < −5 / x < 7 / x < 5) → x < 5Prompt: Expand the bracket, then collect x terms on one side.
- What is the smallest integer that satisfies −6x + 7 ≤ −23? → 5Prompt: 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: Find the error in a worked inequality. 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: Ethan solved an inequality: 1) −4x − 3 ≤ 1 2) −4x ≤ 4 3) x ≤ −1 Which line has the first mistake?
- Step 1: Dividing by −4 must reverse the sign: x ≥ −1.
- Step 2: Line 3
- Answer: Line 3
- 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 solved an inequality: 1) −2x + 6 > −6 2) −2x > −12 3) x < 6 Which line has the first mistake? (Line 2 / Line 3 / There is no mistake) → There is no mistakePrompt: Check each step: what was done to both sides?
- Does x = −2 satisfy 5x − 5 > −5? (Yes / No) → NoPrompt: Substitute the value into the left-hand side.
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.
- Does x = −5 satisfy −3x + 4 < 22? (Yes / No) → YesPrompt: Substitute the value into the left-hand side.
- Lucia solved an inequality: 1) −5x + 7 > 12 2) −5x > 5 3) x < −1 Which line has the first mistake? (Line 2 / Line 3 / There is no mistake) → There is no mistakePrompt: Check each step: what was done to both sides?
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 multi-step inequalities, including reversing the sign.
- 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-9.
Free lesson plan from eurekami.com/lesson-plan-builder