Math lesson plan Β· 8th grade (Year 9 in England) Β· 45 minutes
Estimate square roots between whole numbers
Number sense
CCSS 8.NS.A.2England: KS3 NumberEngland: GCSE Foundation Number
Objective and success criteria
Students will: Estimate square roots between whole numbers.
- 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: Square roots of fractions and decimals
Leads to: Order numbers including square roots and Ο
Materials: Place value chart, Base-ten blocks or a number line, Mini whiteboards and pens, Printed student sheet (below).
Warm-up Β· 5 min
- Quick retrieval from earlier learning (Square roots of fractions and decimals). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Find β(25/16). β 5/4 (1 1/4)Prompt: Take the square root of the top and of the bottom.
- Find β0.09. β 0.3Prompt: Write it as a fraction: 9/100.
- Amara says β144 = 72 because the square root halves the number. What is β144 really? β 12Prompt: A square root asks: what number times ITSELF gives this?
Hook Β· 5 min
- Show a number in the news or a price tag and ask what each digit is worth.
- Share the objective: Estimate square roots between whole numbers. Read the success criteria together.
I do: model it Β· 10 min
- Work through the example out loud, saying why you do each step, not just what you do.
- Example: β138 lies between which two consecutive whole numbers? Give the smaller one.
- Step 1: 121 < 138 < 144
- Step 2: 11 < β138 < 12
- Answer: 11
- Pause after each step and ask a student to say what comes next.
We do: guided practice Β· 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.
- β60 lies between which two consecutive whole numbers? Give the smaller one. β 7Prompt: Find the perfect squares just below and just above.
- To the nearest whole number, what is β158? β 13Prompt: Which perfect square is closest to the number?
You do: independent practice Β· 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 Β· 5 min
- Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
- To the nearest whole number, what is β113? β 11Prompt: Which perfect square is closest to the number?
- Estimate β94 to 1 decimal place (you may use a calculator to check). β 9.7Prompt: Start with the two whole numbers it lies between.
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: Square roots of fractions and decimals.
- 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: Order numbers including square roots and Ο.
- 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