Math lesson plan · 6th grade (Year 7 in England) · 30 minutes
Perfect squares and whole-number square roots
Number sense
CCSS 6.EE.A.1CCSS 8.EE.A.2England: Y6 NumberEngland: KS3 Number
Objective and success criteria
Students will: Perfect squares and whole-number square 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: Square roots of fractions and decimals
Materials: Place value chart, Base-ten blocks or a number line, Mini whiteboards and pens, Printed student sheet (below).
Warm-up · 4 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.
- 3² = ? → 9Prompt: Squared means multiply the number by itself.
- Which of these is a prime number: 33, 49, 93, 97? (49 / 93 / 33 / 97) → 97Prompt: A prime has exactly two factors, 1 and itself.
- Which square number lies between 21 and 29? → 25Prompt: Square numbers are 1, 4, 9, 16, 25, …
Hook · 3 min
- Show a number in the news or a price tag and ask what each digit is worth.
- Share the objective: Perfect squares and whole-number square roots. 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: Find √49.
- Step 1: 7 × 7 = 49
- Step 2: √49 = 7
- Answer: 7
- 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.
- Find √256. → 16Prompt: Which number times itself gives this?
- Is 169 a perfect square? (Yes / No) → YesPrompt: A perfect square is a whole number times itself.
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.
- Is 66 a perfect square? (Yes / No) → NoPrompt: A perfect square is a whole number times itself.
- Find √196. → 14Prompt: Which number times itself gives this?
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: Square roots of fractions and decimals.
- 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-6.
Free lesson plan from eurekami.com/lesson-plan-builder