Math lesson plan · 8th grade (Year 9 in England) · 45 minutes
Laws of exponents (indices)
Algebra
CCSS 8.EE.A.1England: KS3 NumberEngland: GCSE Foundation NumberEngland: GCSE Higher Number
Objective and success criteria
Students will: Laws of exponents (indices).
- 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: Whole-number exponents; Multiply and divide integers
Leads to: Exponential growth and decay; Fractional and negative indices; Evaluate powers with 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 · 5 min
- Quick retrieval from earlier learning (Whole-number exponents; Multiply and divide integers). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Evaluate 4⁴. → 256Prompt: Write it out: 4 × 4 × 4 × 4
- 1 × (−10) = ? → -10Prompt: First multiply the sizes, ignoring the signs.
- Evaluate 4 × 2³. → 32Prompt: Powers come before multiplication and addition.
Hook · 5 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Laws of exponents (indices). 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: Simplify a³ × a⁹ and write it as a to a single power. What is the power?
- Step 1: a³ × a⁹ = a¹²
- Answer: 12
- 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.
- Simplify y⁸ × y³ and write it as y to a single power. What is the power? → 11Prompt: Multiplying powers of the same base: add the exponents.
- Evaluate 5⁻² as a fraction. → 1/25Prompt: A negative exponent means 'one over' the positive 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 y² × y⁹ and write it as y to a single power. What is the power? → 11Prompt: Multiplying powers of the same base: add the exponents.
- Simplify 2³ × 2⁴ ÷ 2³, then evaluate. Give your answer as a number (a fraction is fine). → 16Prompt: Add exponents when multiplying, subtract when dividing.
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: Whole-number exponents.
- 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: Exponential growth and decay; Fractional and negative indices; Evaluate powers with 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