Math lesson plan · 6th grade (Year 7 in England) · 30 minutes
Find the whole when you know a percentage of it
Decimals and percentages
CCSS 6.RP.A.3.CEngland: KS3 NumberEngland: GCSE Foundation Ratio
Objective and success criteria
Students will: Find the whole when you know a percentage of it.
- 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: Find 50%, 25%, 10%, 5% and 1% mentally
Leads to: the next skill in this area.
Materials: Place value chart with tenths and hundredths, Hundred squares, Number lines, Mini whiteboards and pens, Printed student sheet (below).
Warm-up · 4 min
- Quick retrieval from earlier learning (Find 50%, 25%, 10%, 5% and 1% mentally). Students answer on mini whiteboards.
- Show answers together and note who needs support in the main task.
- Find 25% of 140 in your head. → 35Prompt: For 25%: halve it, then halve again.
- Find 15% of 200 by building it from 10% and 5%. → 30Prompt: 10% of 200 is 20.
- Ravi says: “15% of 520 is 10% of 520 plus 5, so it is 57.” What is 15% of 520 really? → 78Prompt: 5% is not the number 5: it is half of 10%.
Hook · 3 min
- Show two prices or race times with decimals and ask which is bigger, then why.
- Share the objective: Find the whole when you know a percentage of it. 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: 40% of a number is 80. What is the number?
- Step 1: 100 ÷ 40 = 2.5
- Step 2: 80 × 2.5 = 200
- Answer: 200
- 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.
- 5% of a number is 10. What is the number? → 200Prompt: How many lots of 5% make 100%?
- A download is 45% complete. So far 81 MB have downloaded. How big is the whole file, in MB? → 180Prompt: Find 1% first: divide by 45.
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.
- 20% of a number is 48. What is the number? → 240Prompt: How many lots of 20% make 100%?
- 32 students in a year group chose football as their favourite sport. That is 20% of the year group. How many students are in the year group? → 160Prompt: 32 is 20% of the total.
Watch out for
- Thinking 0.45 is bigger than 0.5 because 45 is bigger than 5.
- Moving the digits the wrong way when multiplying or dividing by 10.
Support and stretch
Support
- Review first: Find 50%, 25%, 10%, 5% and 1% mentally.
- Use concrete materials: place value chart with tenths and hundredths.
- 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-6.
Free lesson plan from eurekami.com/lesson-plan-builder