Math lesson plan · 9th grade (Year 10 in England) · 45 minutes
Solve absolute value equations |ax + b| = c
Algebra
CCSS HSA.CED.A.1CCSS HSA.REI.B.3
Objective and success criteria
Students will: Solve absolute value equations |ax + b| = c.
- 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; Two-step equations
Leads to: Count the solutions of an absolute value equation; Solve absolute value inequalities
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; Two-step equations). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- The temperature is −11 °C at noon and −15 °C at night. By how many degrees did it fall? → 4Prompt: Find the distance between the two numbers on the number line.
- The temperature is 3 °C at noon and −14 °C at night. By how many degrees did it fall? → 17Prompt: Find the distance between the two numbers on the number line.
- The temperature is 5 °C at noon and −12 °C at night. By how many degrees did it fall? → 17Prompt: 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: Solve absolute value equations |ax + b| = c. 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 − 7| = 9. Give both solutions, separated by a comma.
- Step 1: x − 7 = 9 → x = 16
- Step 2: x − 7 = −9 → x = −2
- Step 3: x = −2, x = 16
- Answer: x = -2 or x = 16
- 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 + 1| = 7. Give both solutions, separated by a comma. → x = -8 or x = 6Prompt: The expression inside can be 7 or −7.
- Solve: |2x − 2| = 4. Give both solutions, separated by a comma. → x = -1 or x = 3Prompt: Split into 2x − 2 = 4 and 2x − 2 = −4.
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: |5x − 15| = 15. Give both solutions, separated by a comma. → x = 0 or x = 6Prompt: Split into 5x − 15 = 15 and 5x − 15 = −15.
- Solve: 3|x + 7| + 9 = 24. Give both solutions, separated by a comma. → x = -12 or x = -2Prompt: Isolate the absolute value first, as if it were a single unknown.
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
- Move on to: Count the solutions of an absolute value equation; Solve absolute value inequalities.
- 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