Math lesson plan · 10th grade (Year 11 in England) · 30 minutes
Rewrite roots as fractional powers and back
Algebra
CCSS HSN.RN.A.2England: GCSE Higher Algebra
Objective and success criteria
Students will: Rewrite roots as fractional powers and back.
- 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
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 · 4 min
- Quick retrieval from earlier learning (Fractional and negative indices). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Evaluate 16^(3/2). → 64Prompt: The denominator 2 means take the square root.
- Evaluate 16^(−1/2). → 1/4Prompt: The denominator 2 means take the square root.
- Evaluate 125^(−3/3). → 1/125Prompt: The denominator 3 means take the cube root.
Hook · 3 min
- Show a "think of a number" puzzle and ask the class to work out the starting number.
- Share the objective: Rewrite roots as fractional powers and back. Read the success criteria together.
I do: model it · 7 min
- Work through the example out loud, saying why you do each step, not just what you do.
- Example: Write ∛(x²) as a power of x.
- Step 1: x^(2/3)
- Answer: x^(2/3)
- Pause after each step and ask a student to say what comes next.
We do: guided practice · 6 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 ∛(x⁵) as a power of x. (x^(3/5) / x^(15) / x^(−5/3) / x^(5/3)) → x^(5/3)Prompt: The root becomes the denominator of the exponent.
- Write x⁴ × √x as a single power of x. Give the exponent as a fraction. → 9/2 (4 1/2)Prompt: √x = x^(1/2).
You do: independent practice · 7 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 6 questions are on the student sheet below, with answers in the key.
Exit ticket · 3 min
- Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
- Write ∜(x⁷) as a power of x. (x^(4/7) / x^(7/4) / x^(3) / x^(28)) → x^(7/4)Prompt: The root becomes the denominator of the exponent.
- Which is equal to 1/∛(x⁵)? (x^(5/3) / x^(3/5) / x^(−5/3) / x^(−3/5)) → x^(−5/3)Prompt: ∛(x⁵) = x^(5/3).
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