Math lesson plan · 9th grade (Year 10 in England) · 45 minutes
Count the solutions of an absolute value equation
Algebra
CCSS HSA.REI.B.3
Objective and success criteria
Students will: Count the solutions of an absolute value equation.
- 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
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). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Solve: |x + 8| = 9. Give both solutions, separated by a comma. → x = -17 or x = 1Prompt: The expression inside can be 9 or −9.
- Solve: |5x + 45| = 20. Give both solutions, separated by a comma. → x = -13 or x = -5Prompt: Split into 5x + 45 = 20 and 5x + 45 = −20.
- Solve: 3|x − 5| + 4 = 10. Give both solutions, separated by a comma. → x = 3 or x = 7Prompt: 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: Count the solutions of an absolute value equation. 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: How many solutions does |x + 1| = 8 have?
- Step 1: Positive: two solutions.
- Step 2: 2
- Answer: 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.
- How many solutions does |x − 6| = 0 have? → 1Prompt: An absolute value is a distance, so it is never negative.
- How many solutions does 2|x + 3| + 2 = 4 have? → 2Prompt: Isolate the absolute value before deciding.
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.
- How many solutions does 4|x + 5| + 8 = −8 have? → 0Prompt: Isolate the absolute value before deciding.
- How many solutions does |x − 5| = 1 have? → 2Prompt: An absolute value is a distance, so it is never negative.
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-9.
Free lesson plan from eurekami.com/lesson-plan-builder