Math lesson plan · 8th grade (Year 9 in England) · 45 minutes
Zero and negative exponents
Algebra
CCSS 8.EE.A.1England: KS3 NumberEngland: GCSE Foundation Number
Objective and success criteria
Students will: Zero and negative 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: Divide 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 (Divide powers with the same base). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- 6⁷ ÷ 6² = 6ᵏ. What is k? → 5Prompt: Dividing cancels factors of the base.
- Simplify 24x⁸ ÷ 6x⁴. (18x⁴ / 4x¹² / 4x² / 4x⁴) → 4x⁴Prompt: Divide the numbers.
- Work out 4⁸ ÷ 4⁵ as a number. → 64Prompt: Use the rule first: subtract the exponents.
Hook · 5 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Zero and negative exponents. 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: Write 8⁻³ as a fraction.
- Step 1: 8⁻³ = 1/8³ = 1/512
- Answer: 1/512
- 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.
- Write 6⁻² as a fraction. → 1/36Prompt: A negative exponent means “one over” the positive power.
- Work out 10³ ÷ 10³. → 1Prompt: Any non-zero number to the power 0 is 1.
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.
- 2¹ ÷ 2³ = 2ᵏ. What is k? (It can be negative.) → -2Prompt: Subtract the exponents: first − second.
- Write 5⁻³ as a fraction. → 1/125Prompt: A negative exponent means “one over” the positive power.
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: Divide 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