Math lesson plan · 8th grade (Year 9 in England) · 45 minutes
Raise a power to a power
Algebra
CCSS 8.EE.A.1England: KS3 NumberEngland: GCSE Foundation Number
Objective and success criteria
Students will: Raise a power to a power.
- 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: Multiply powers with the same base
Leads to: Combine the laws of exponents
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 (Multiply powers with the same base). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- 7⁷ × 7⁸ = 7ⁿ. What is n? → 15Prompt: Write it out: 7 lots of 7, then 8 more lots of 7.
- Simplify 5a⁵ × 4a⁴. (20a⁹ / 20a²⁰ / 9a²⁰ / 9a⁹) → 20a⁹Prompt: Multiply the numbers.
- Daniel says 2⁵ × 2⁴ = 4⁹. Work out the correct value of 2⁵ × 2⁴ as a number. → 512Prompt: The base stays the same when you multiply powers.
Hook · 5 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Raise a power to a power. 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: (9⁵)⁵ = 9ᵏ. What is k?
- Step 1: 5 × 5 = 25
- Step 2: 9²⁵
- Answer: 25
- 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.
- (9³)³ = 9ᵏ. What is k? → 9Prompt: This means 9³ multiplied by itself 3 times.
- Simplify (3x⁵)³. (27x⁸ / 27x¹⁵ / 3x¹⁵ / 9x¹⁵) → 27x¹⁵Prompt: Everything inside the brackets is raised to the power.
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.
- Simplify (3x²)². (6x⁴ / 3x⁴ / 9x⁴) → 9x⁴Prompt: Everything inside the brackets is raised to the power.
- Write 4⁶ as a power of 2. What is the exponent? → 12Prompt: 4 = 2².
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: Multiply powers with the same base.
- 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: Combine the laws of exponents.
- 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