Math lesson plan · 8th grade (Year 9 in England) · 60 minutes
Square roots and cube roots
Number sense
CCSS 8.EE.A.2CCSS 8.NS.A.2England: KS3 NumberEngland: GCSE Foundation Number
Objective and success criteria
Students will: Square roots and cube roots.
- 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: Primes, squares and cubes
Leads to: Rational and irrational numbers; Simplify surds (radicals); Pythagoras' theorem
Materials: Place value chart, Base-ten blocks or a number line, Mini whiteboards and pens, Printed student sheet (below).
Warm-up · 6 min
- Quick retrieval from earlier learning (Primes, squares and cubes). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- 5² = ? → 25Prompt: Squared means multiply the number by itself.
- Which of these is a prime number: 47, 57, 63, 93? (63 / 47 / 93 / 57) → 47Prompt: A prime has exactly two factors, 1 and itself.
- Which square number lies between 111 and 131? → 121Prompt: Square numbers are 1, 4, 9, 16, 25, …
Hook · 6 min
- Show a number in the news or a price tag and ask what each digit is worth.
- Share the objective: Square roots and cube roots. Read the success criteria together.
I do: model it · 12 min
- Work through the example out loud, saying why you do each step, not just what you do.
- Example: What is √256?
- Step 1: 16 × 16 = 256
- Step 2: 16
- Answer: 16
- Pause after each step and ask a student to say what comes next.
We do: guided practice · 12 min
- Do these together. Students try each step on whiteboards before you reveal it.
- Use the hints as prompts rather than giving the answer.
- What is √9? → 3Prompt: Which number multiplied by itself gives this?
- √150 lies between which two whole numbers? (10 and 11 / 13 and 14 / 12 and 13 / 11 and 12) → 12 and 13Prompt: List the square numbers near it.
You do: independent practice · 17 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 · 7 min
- Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
- √97 lies between which two whole numbers? (8 and 9 / 7 and 8 / 9 and 10 / 10 and 11) → 9 and 10Prompt: List the square numbers near it.
- Sam's square garden has an area of 36 m². How long is one side, in metres? → 6Prompt: Area of a square = side × side.
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: Primes, squares and cubes.
- 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: Rational and irrational numbers; Simplify surds (radicals); Pythagoras' theorem.
- 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