Math lesson plan · 9th grade (Year 10 in England) · 45 minutes
Add and subtract surds
Number sense
CCSS HSN.RN.B.3England: GCSE Higher Number
Objective and success criteria
Students will: Add and subtract surds.
- 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: Simplify surds (radicals)
Leads to: Rationalise denominators like a + √b
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 (Simplify surds (radicals)). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Simplify √28. It can be written as k√7. What is k? → 2Prompt: Look for the largest square number that divides it.
- Work out √48 × √3. → 12Prompt: √a × √b = √(ab).
- Simplify √63. It can be written as k√7. What is k? → 3Prompt: Look for the largest square number that divides it.
Hook · 5 min
- Show a number in the news or a price tag and ask what each digit is worth.
- Share the objective: Add and subtract surds. 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: 6√5 + 3√5 − 3√5
- Step 1: (6 + 3 − 3)√5
- Step 2: = 6√5
- Answer: 6√5
- 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: 2√2 + 8√2 − √2 → 9√2Prompt: Treat √2 like a letter: these are like terms.
- Simplify: √32 − √8. Give your answer in the form a√b. → 2√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: √150 + √54. Give your answer in the form a√b. → 8√6Prompt: Simplify each surd first.
- Expand and simplify: (8 + √5)(8 − √5) → 59Prompt: This is a difference of two squares: (p + q)(p − q) = p² − q².
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: Simplify surds (radicals).
- 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 denominators like a + √b.
- 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