Cogito
Grade 6 Math · Chapter 2 · Lesson 5
Finding the Whole from a Percent
Working backwards to the total.
10 problems · about 18 minutes · 6.RP.A.3
What this lesson teaches
The child finds the whole when a percent and the matching part are known.
- A percent question has three parts: the part, the percent, and the whole.
- Knowing two of them is enough to find the third.
- Divide down to 1%, then multiply up to 100%.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
3 problemsReview — Comparing with Unit Rates: 6 cakes for £9. Price for one, in pounds?
Answer 1.5
Why £1.50 each.
Review — Finding a Percent of a Number: What is 30% of 90?
Answer 27
Why 3 × 9 = 27.
Review — Percent as a Rate per Hundred: 17 out of 20 as a percent?
Answer 85
Why 85%.
Warm Up
Straightforward practice. Get the method working first.
3 problems25% of a number is 11. What is the number?
Answer 44
Why 44.
10% of a number is 7. What is the number?
Answer 70
Why Ten lots of 7.
25% of a number is 9. What is the number?
Answer 36
Why Four lots of 9.
Build It Up
The same ideas with more to keep track of.
2 problems50% of a number is 30. What is the number?
Answer 60
Why Double it.
20% of a number is 12. What is the number?
Answer 60
Why Five lots of 12.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsThe Discount: 10% of a price is £4. What is the full price, in pounds?
Answer 40
Why £40.
The Survey: 50% of the group is 21 people. How many in the group?
Answer 42
Why 42 people.