Math lesson plan · 9th grade (Year 10 in England) · 45 minutes
Simplify surds (radicals)
Number sense
CCSS HSN.RN.A.2England: GCSE Higher Number
Objective and success criteria
Students will: Simplify surds (radicals).
- 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; Prime factorisation
Leads to: Rationalise the denominator; The quadratic formula; Exact trig values (0°, 30°, 45°, 60°, 90°)
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; Prime factorisation). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- What is √121? → 11Prompt: Which number multiplied by itself gives this?
- Which is 252 written as a product of prime factors? (2² × 3² × 7 / 2 × 3² × 7 / 2³ × 3² × 7 / 2² × 3³) → 2² × 3² × 7Prompt: Keep dividing by the smallest prime that works (2, 3, 5, 7…).
- √14 lies between which two whole numbers? (3 and 4 / 1 and 2 / 4 and 5 / 2 and 3) → 3 and 4Prompt: 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: Simplify surds (radicals). 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: Simplify √80. It can be written as k√5. What is k?
- Step 1: √80 = √(16 × 5)
- Step 2: = √16 × √5
- Step 3: = 4√5
- Answer: 4
- 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.
- Simplify √96. It can be written as k√6. What is k? → 4Prompt: Look for the largest square number that divides it.
- Simplify √3 + √3. Write it as k√3; what is k? → 2Prompt: Simplify each surd first.
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.
- Simplify √125. It can be written as k√5. What is k? → 5Prompt: Look for the largest square number that divides it.
- Simplify √32 + √32. Write it as k√2; what is k? → 8Prompt: Simplify each surd first.
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: Rationalise the denominator; The quadratic formula; Exact trig values (0°, 30°, 45°, 60°, 90°).
- 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-9.
Free lesson plan from eurekami.com/lesson-plan-builder