Math lesson plan · 9th grade (Year 10 in England) · 30 minutes
Multiply and divide surds
Number sense
CCSS HSN.RN.B.3CCSS 8.EE.A.2England: GCSE Higher Number
Objective and success criteria
Students will: Multiply and divide 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: 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 (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.
- Simplify √80 + √45. Write it as k√5; what is k? → 7Prompt: Simplify each surd first.
- Simplify √72. It can be written as k√2. What is k? → 6Prompt: Look for the largest square number that divides it.
Hook · 3 min
- Show a number in the news or a price tag and ask what each digit is worth.
- Share the objective: Multiply and divide surds. 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: Simplify √10 × √5. Give your answer in the form a√b (or a whole number).
- Step 1: √50 = √(25 × 2)
- Step 2: = 5√2
- Answer: 5√2
- 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.
- Simplify √18 × √3. Give your answer in the form a√b (or a whole number). → 3√6Prompt: √a × √b = √(ab).
- Simplify 2√15 × 4√3. Give your answer in the form a√b. → 24√5Prompt: Multiply the whole numbers, then multiply the surds.
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.
- Simplify 4√21 × 3√3. Give your answer in the form a√b. → 36√7Prompt: Multiply the whole numbers, then multiply the surds.
- Simplify √250 ÷ √2. Give your answer in the form a√b or as a whole number. → 5√5Prompt: √a ÷ √b = √(a ÷ b).
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
- 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