Math lesson plan · 11th grade (Year 12 in England) · 60 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 · 6 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 − 7| = 4. Give both solutions, separated by a comma. → x = 3 or x = 11Prompt: The expression inside can be 4 or −4.
- Solve: |5x + 55| = 25. Give both solutions, separated by a comma. → x = -16 or x = -6Prompt: Split into 5x + 55 = 25 and 5x + 55 = −25.
- Solve: 4|x + 2| − 5 = 3. Give both solutions, separated by a comma. → x = -4 or x = 0Prompt: Isolate the absolute value first, as if it were a single unknown.
Hook · 6 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 · 12 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 · 12 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 + 1| < 6 (x < 5 / −5 < x < 7 / −7 < x < 5 / x ≤ −7 or x ≥ 5) → −7 < x < 5Prompt: |x − a| is the distance from x to a.
- Solve: |4x + 4| ≤ 12 (x ≤ −4 or x ≥ 2 / −2 ≤ x ≤ 4 / −4 ≤ x ≤ 2 / −16 ≤ x ≤ 8) → −4 ≤ x ≤ 2Prompt: Rewrite as −12 ≤ 4x + 4 ≤ 12.
You do: independent practice · 17 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 · 7 min
- Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
- Solve: |x + 1| ≥ 8 (x ≥ 7 / x ≤ −9 or x ≥ 7 / x ≤ −7 or x ≥ 9 / −9 < x < 7) → x ≤ −9 or x ≥ 7Prompt: |x − a| is the distance from x to a.
- Solve: |4x − 8| ≤ 12 (−4 ≤ x ≤ 20 / −1 ≤ x ≤ 5 / −5 ≤ x ≤ 1 / x ≤ −1 or x ≥ 5) → −1 ≤ x ≤ 5Prompt: Rewrite as −12 ≤ 4x − 8 ≤ 12.
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