Math lesson plan · 11th grade (Year 12 in England) · 45 minutes
Solve absolute value inequalities
Algebra
CCSS HSA.REI.B.3
Objective and success criteria
Students will: Solve absolute value inequalities.
- 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 absolute value equations |ax + b| = c; Solve 'or' compound 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 absolute value equations |ax + b| = c; Solve 'or' compound inequalities). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Solve: |x − 4| = 11. Give both solutions, separated by a comma. → x = -7 or x = 15Prompt: The expression inside can be 11 or −11.
- Solve: |3x| = 12. Give both solutions, separated by a comma. → x = -4 or x = 4Prompt: Split into 3x = 12 and 3x = −12.
- Solve: 3|x − 7| − 9 = 12. Give both solutions, separated by a comma. → x = 0 or x = 14Prompt: Isolate the absolute value first, as if it were a single unknown.
Hook · 5 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Solve absolute value inequalities. 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: Solve: |x + 5| ≥ 3
- Step 1: x ≤ −8 or x ≥ −2
- Answer: x ≤ −8 or x ≥ −2
- 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.
- Solve: |x + 4| ≥ 8 (x ≤ −4 or x ≥ 12 / −12 < x < 4 / x ≤ −12 or x ≥ 4 / x ≥ 4) → x ≤ −12 or x ≥ 4Prompt: |x − a| is the distance from x to a.
- Solve: |4x + 8| ≤ 12 (x ≤ −5 or x ≥ 1 / −20 ≤ x ≤ 4 / −1 ≤ x ≤ 5 / −5 ≤ x ≤ 1) → −5 ≤ x ≤ 1Prompt: Rewrite as −12 ≤ 4x + 8 ≤ 12.
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.
- Solve: |4x| ≤ 12 (x ≤ −3 or x ≥ 3 / −12 ≤ x ≤ 12 / −3 ≤ x ≤ 3) → −3 ≤ x ≤ 3Prompt: Rewrite as −12 ≤ 4x ≤ 12.
- Solve: |x + 4| ≥ 4 (x ≤ −8 or x ≥ 0 / x ≤ 0 or x ≥ 8 / x ≥ 0 / −8 < x < 0) → x ≤ −8 or x ≥ 0Prompt: |x − a| is the distance from x to a.
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 absolute value equations |ax + b| = c.
- 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-11.
Free lesson plan from eurekami.com/lesson-plan-builder