Math lesson plan · 12th grade (Year 13 in England) · 45 minutes
Absolute value equations and inequalities
Algebra
CCSS HSA.REI.B.3CCSS HSA.CED.A.1
Objective and success criteria
Students will: Absolute value equations and 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: Negative numbers and absolute value; Compound inequalities and integer solutions
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 (Negative numbers and absolute value; Compound inequalities and integer solutions). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- The temperature is 5 °C at noon and −4 °C at night. By how many degrees did it fall? → 9Prompt: Find the distance between the two numbers on the number line.
- The temperature is 10 °C at noon and −3 °C at night. By how many degrees did it fall? → 13Prompt: Find the distance between the two numbers on the number line.
- The temperature is 10 °C at noon and −2 °C at night. By how many degrees did it fall? → 12Prompt: Find the distance between the two numbers on the number line.
Hook · 5 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Absolute value equations and 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: |2x + 20| = 8. Give both solutions, separated by a comma.
- Step 1: 2x + 20 = 8 → x = −6
- Step 2: 2x + 20 = −8 → x = −14
- Answer: x = -14 or x = -6
- 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: |3x + 6| = 9. Give both solutions, separated by a comma. → x = -5 or x = 1Prompt: The inside is either 9 or −9.
- Solve: |x − 6| > 2 (x < 4 or x > 8 / −8 < x < −4 / 4 < x < 8 / x < 8) → x < 4 or x > 8Prompt: |x − a| < k means x is within k of a.
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: |x − 2| > 7 (x < 9 / −5 < x < 9 / −9 < x < 5 / x < −5 or x > 9) → x < −5 or x > 9Prompt: |x − a| < k means x is within k of a.
- Solve: |3x + 12| = 9. Give both solutions, separated by a comma. → x = -7 or x = -1Prompt: The inside is either 9 or −9.
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
- 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-12.
Free lesson plan from eurekami.com/lesson-plan-builder