Math lesson plan · 8th grade (Year 9 in England) · 30 minutes
Order numbers including square roots and π
Number sense
CCSS 8.NS.A.2England: KS3 Number
Objective and success criteria
Students will: Order numbers including square roots and π.
- 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: Estimate square roots between whole numbers; Classify numbers as rational or irrational
Leads to: the next skill in this area.
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 (Estimate square roots between whole numbers; Classify numbers as rational or irrational). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- √89 lies between which two consecutive whole numbers? Give the smaller one. → 9Prompt: Find the perfect squares just below and just above.
- Is π rational or irrational? (Rational / Irrational) → IrrationalPrompt: Rational numbers can be written as a fraction of two integers.
- To the nearest whole number, what is √105? → 10Prompt: Which perfect square is closest to the number?
Hook · 3 min
- Show a number in the news or a price tag and ask what each digit is worth.
- Share the objective: Order numbers including square roots and π. 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: On a number line, √85 is between 9 and 10. Is it closer to 9 or to 10?
- Step 1: √85 ≈ 9.22
- Step 2: 9
- Answer: 9
- 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.
- On a number line, √10 is between 3 and 4. Is it closer to 3 or to 4? (3 / 4) → 3Prompt: Compare 10 with 3² = 9 and 4² = 16.
- On a number line, √17 is between 4 and 5. Is it closer to 4 or to 5? (4 / 5) → 4Prompt: Compare 17 with 4² = 16 and 5² = 25.
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.
- On a number line, √58 is between 7 and 8. Is it closer to 7 or to 8? (7 / 8) → 8Prompt: Compare 58 with 7² = 49 and 8² = 64.
- On a number line, √41 is between 6 and 7. Is it closer to 6 or to 7? (6 / 7) → 6Prompt: Compare 41 with 6² = 36 and 7² = 49.
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: Estimate square roots between whole numbers.
- 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
- 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