Math lesson plan · 8th grade (Year 9 in England) · 60 minutes
Divide powers with the same base
Algebra
CCSS 8.EE.A.1England: KS3 NumberEngland: GCSE Foundation Number
Objective and success criteria
Students will: Divide powers with the same base.
- 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: Zero and negative exponents
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 (Multiply powers with the same base). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- 5³ × 5⁹ = 5ⁿ. What is n? → 12Prompt: Write it out: 3 lots of 5, then 9 more lots of 5.
- Simplify 3x⁷ × 2x⁶. (5x¹³ / 6x⁴² / 6x¹³ / 5x⁴²) → 6x¹³Prompt: Multiply the numbers.
- Zoe says 2³ × 2⁵ = 4⁸. Work out the correct value of 2³ × 2⁵ as a number. → 256Prompt: The base stays the same when you multiply powers.
Hook · 6 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Divide powers with the same base. 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: 6⁹ ÷ 6⁸ = 6ᵏ. What is k?
- Step 1: 9 − 8 = 1
- Step 2: 6¹
- Answer: 1
- 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.
- 5⁹ ÷ 5⁶ = 5ᵏ. What is k? → 3Prompt: Dividing cancels factors of the base.
- Simplify 10x⁹ ÷ 2x⁶. (5x³ / 5x¹⁵ / 8x³ / 5x²) → 5x³Prompt: Divide the numbers.
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.
- Work out 4¹⁰ ÷ 4⁷ as a number. → 64Prompt: Use the rule first: subtract the exponents.
- 3¹² ÷ 3⁸ = 3ᵏ. What is k? → 4Prompt: Dividing cancels factors of the base.
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: Zero and negative 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