Math lesson plan · 10th grade (Year 11 in England) · 45 minutes
Evaluate fractional and negative fractional powers
Algebra
CCSS HSN.RN.A.1CCSS HSN.RN.A.2England: GCSE Higher Number
Objective and success criteria
Students will: Evaluate fractional and negative fractional powers.
- 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: Fractional and negative indices; Evaluate powers with zero and negative exponents
Leads to: the next skill in this area.
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 (Fractional and negative indices; Evaluate powers with zero and negative exponents). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Evaluate 81^(−1/4). → 1/3Prompt: The denominator 4 means take the 4th root.
- Write 4⁻² as a fraction. → 1/16Prompt: A negative exponent means 'one over' the positive power.
- Evaluate (4/3)⁻³. Give a fraction. → 27/64Prompt: A negative exponent flips the fraction.
Hook · 5 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Evaluate fractional and negative fractional powers. 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 16^(1/4).
- Step 1: 4√16 = 2
- Answer: 2
- 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 32^(1/5). → 2Prompt: A power of 1/5 means the 5th root.
- Evaluate 8^(2/3). → 4Prompt: The denominator is the root; the numerator is 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.
- Evaluate 100^(−3/2). Give a fraction. → 1/1000Prompt: The negative sign means take the reciprocal.
- Evaluate 81^(3/4). → 27Prompt: The denominator is the root; the numerator is the 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: Fractional and negative 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
- 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