Math lesson plan · 8th grade (Year 9 in England) · 60 minutes
Combine the laws of exponents
Algebra
CCSS 8.EE.A.1England: KS3 NumberEngland: GCSE Foundation Number
Objective and success criteria
Students will: Combine the laws of exponents.
- 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: Raise a power to a power; Zero and negative exponents
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 (Raise a power to a power; Zero and negative exponents). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- (3⁶)² = 3ᵏ. What is k? → 12Prompt: This means 3⁶ multiplied by itself 2 times.
- Write 5⁻² as a fraction. → 1/25Prompt: A negative exponent means “one over” the positive power.
- Simplify (5x⁵)². (25x⁷ / 25x¹⁰ / 5x¹⁰ / 10x¹⁰) → 25x¹⁰Prompt: Everything inside the brackets is raised to the power.
Hook · 6 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Combine the laws of exponents. 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: (x⁵ × x⁶) ÷ x⁴ = xᵏ. What is k?
- Step 1: 5 + 6 − 4 = 7
- Answer: 7
- 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.
- (x² × x⁶) ÷ x² = xᵏ. What is k? → 6Prompt: Multiply first: add exponents.
- Work out (2²)² ÷ 2⁵. Give a whole number or fraction. → 1/2Prompt: Power of a power: multiply exponents.
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.
- (x³ × x³) ÷ x³ = xᵏ. What is k? → 3Prompt: Multiply first: add exponents.
- Which statement is correct? ((x⁵)³ = x⁸ / x⁴ × x³ = x¹² / x⁴ ÷ x³ = x⁷ / x⁴ × x³ = x⁷) → x⁴ × x³ = x⁷Prompt: Multiplying powers: add exponents. Dividing: subtract.
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: Raise a power to a power.
- 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-8.
Free lesson plan from eurekami.com/lesson-plan-builder