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.
- √120 lies between which two consecutive whole numbers? Give the smaller one. → 10Prompt: Find the perfect squares just below and just above.
- Is 0.25 rational or irrational? (Rational / Irrational) → RationalPrompt: Rational numbers can be written as a fraction of two integers.
- To the nearest whole number, what is √30? → 5Prompt: 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, √23 is between 4 and 5. Is it closer to 4 or to 5? (4 / 5) → 5Prompt: Compare 23 with 4² = 16 and 5² = 25.
- On a number line, √80 is between 8 and 9. Is it closer to 8 or to 9? (8 / 9) → 9Prompt: Compare 80 with 8² = 64 and 9² = 81.
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, √45 is between 6 and 7. Is it closer to 6 or to 7? (6 / 7) → 7Prompt: Compare 45 with 6² = 36 and 7² = 49.
- On a number line, √88 is between 9 and 10. Is it closer to 9 or to 10? (9 / 10) → 9Prompt: Compare 88 with 9² = 81 and 10² = 100.
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