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.
- 7³ × 7⁵ = 7ⁿ. What is n? → 8Prompt: Write it out: 3 lots of 7, then 5 more lots of 7.
- Simplify 3a⁴ × 6a⁷. (9a²⁸ / 9a¹¹ / 18a²⁸ / 18a¹¹) → 18a¹¹Prompt: Multiply the numbers.
- Noah says 2⁴ × 2⁵ = 4⁹. Work out the correct value of 2⁴ × 2⁵ 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.
- (4²)³ = 4ᵏ. What is k? → 6Prompt: This means 4² multiplied by itself 3 times.
- Simplify (4x³)³. (64x⁹ / 12x⁹ / 4x⁹ / 64x⁶) → 64x⁹Prompt: 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 (5x³)². (10x⁶ / 25x⁶ / 5x⁶ / 25x⁵) → 25x⁶Prompt: Everything inside the brackets is raised to the power.
- Write 4³ as a power of 2. What is the exponent? → 6Prompt: 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