Math lesson plan · 8th grade (Year 9 in England) · 45 minutes
Square roots of fractions and decimals
Number sense
CCSS 8.EE.A.2England: KS3 NumberEngland: GCSE Foundation Number
Objective and success criteria
Students will: Square roots of fractions and decimals.
- 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 and cube roots; Perfect squares and whole-number square roots
Leads to: Estimate square roots between whole numbers; Solve x² = p and x³ = p; Use Pythagoras to find the hypotenuse
Materials: Place value chart, Base-ten blocks or a number line, Mini whiteboards and pens, Printed student sheet (below).
Warm-up · 5 min
- Quick retrieval from earlier learning (Square roots and cube roots; Perfect squares and whole-number square roots). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- What is ∛125? → 5Prompt: Which number, used three times in a multiplication, gives this?
- Find √16. → 4Prompt: Which number times itself gives this?
- √145 lies between which two whole numbers? (11 and 12 / 10 and 11 / 13 and 14 / 12 and 13) → 12 and 13Prompt: List the square numbers near it.
Hook · 5 min
- Show a number in the news or a price tag and ask what each digit is worth.
- Share the objective: Square roots of fractions and decimals. Read the success criteria together.
I do: model it · 10 min
- Work through the example out loud, saying why you do each step, not just what you do.
- Example: Find √(9/4).
- Step 1: √9 = 3, √4 = 2
- Step 2: 3/2
- Answer: 3/2 (1 1/2)
- Pause after each step and ask a student to say what comes next.
We do: guided practice · 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.
- Find √(9/16). → 3/4Prompt: Take the square root of the top and of the bottom.
- Find √0.09. → 0.3Prompt: Write it as a fraction: 9/100.
You do: independent practice · 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 · 5 min
- Two questions on their own. Sort answers into got it / nearly / not yet to plan the next lesson.
- Maya says √121 = 60.5 because the square root halves the number. What is √121 really? → 11Prompt: A square root asks: what number times ITSELF gives this?
- Find √(49/16). → 7/4 (1 3/4)Prompt: Take the square root of the top and of the bottom.
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 and cube roots.
- 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: Estimate square roots between whole numbers; Solve x² = p and x³ = p; Use Pythagoras to find the hypotenuse.
- 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