Math lesson plan · 10th grade (Year 11 in England) · 45 minutes
Fractional and negative indices
Algebra
CCSS HSN.RN.A.1CCSS HSN.RN.A.2England: GCSE Higher Number
Objective and success criteria
Students will: Fractional and negative 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: Laws of exponents (indices); Square roots and cube roots
Leads to: Logarithms; Evaluate fractional and negative fractional powers; Rewrite roots as fractional powers and back
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 (Laws of exponents (indices); Square roots and cube roots). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Simplify x¹² ÷ x⁵ and write it as x to a single power. What is the power? → 7Prompt: Dividing powers of the same base: subtract the exponents.
- What is √36? → 6Prompt: Which number multiplied by itself gives this?
- Evaluate 3⁻² as a fraction. → 1/9Prompt: A negative exponent means 'one over' the positive power.
Hook · 5 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Fractional and negative 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: Evaluate 81^(1/4).
- Step 1: 4√81 = 3
- Step 2: 3¹ = 3
- Answer: 3
- 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.
- Evaluate 64^(2/3). → 16Prompt: The denominator 3 means take the cube root.
- Evaluate 125^(1/3). → 5Prompt: The denominator 3 means take the cube root.
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.
- Evaluate 81^(3/4). → 27Prompt: The denominator 4 means take the 4th root.
- Evaluate 16^(1/2). → 4Prompt: The denominator 2 means take the square root.
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: Laws of exponents (indices).
- 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: Logarithms; Evaluate fractional and negative fractional powers; Rewrite roots as fractional powers and back.
- 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-10.
Free lesson plan from eurekami.com/lesson-plan-builder