Math lesson plan · 8th grade (Year 9 in England) · 45 minutes
Solve x² = p and x³ = p
Number sense
CCSS 8.EE.A.2England: KS3 AlgebraEngland: GCSE Foundation Algebra
Objective and success criteria
Students will: Solve x² = p and x³ = p.
- 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: Cube roots, including negatives; Square roots of fractions and decimals
Leads to: Find a missing radius or height from a volume
Materials: Place value chart, Base-ten blocks or a number line, Mini whiteboards and pens, Printed student sheet (below).
Warm-up · 5 min
- Quick retrieval from earlier learning (Cube roots, including negatives; Square roots of fractions and decimals). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Find ∛(−216). → -6Prompt: What number times itself times itself gives this?
- Find √(64/121). → 8/11Prompt: Take the square root of the top and of the bottom.
- A cube-shaped box has a volume of 1000 cm³. How long is each edge, in cm? → 10Prompt: Volume of a cube = edge³.
Hook · 5 min
- Show a number in the news or a price tag and ask what each digit is worth.
- Share the objective: Solve x² = p and x³ = p. 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: Solve x² = 121. Give both solutions, separated by a comma.
- Step 1: x = ±√121
- Step 2: x = 11 or x = −11
- Answer: x = -11 or x = 11
- 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.
- Solve x² = 49. Give both solutions, separated by a comma. → x = -7 or x = 7Prompt: Which numbers square to give this?
- Solve x³ = 27. → x = 3Prompt: Take the cube root of both sides.
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.
- Solve x³ = 1. → x = 1Prompt: Take the cube root of both sides.
- Solve 2x² = 98 for the positive value of x. → 7Prompt: Divide both sides by 2 first.
Watch out for
- Reading 1,045 as one thousand four hundred five: point to each place and say its value.
- Thinking a longer number is always bigger, even with decimals (0.45 vs 0.5).
Support and stretch
Support
- Review first: Cube roots, including negatives.
- Use concrete materials: place value chart.
- 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: Find a missing radius or height from a volume.
- 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