Cogito
Grade 6 Math · Chapter 1 · Lesson 2
Equivalent Ratios
Scaling up keeps the comparison the same.
10 problems · about 17 minutes · 6.RP.A.3
What this lesson teaches
The child generates equivalent ratios by multiplying both quantities and uses a ratio table.
- Equivalent ratios are the same comparison written with different numbers.
- Multiply both quantities by the same number.
- A ratio table lays the pattern out in rows.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
2 problemsReview — What a Ratio Says: 6 pens and 9 pencils. Pens to total: what is the second number?
Answer 15
Why 6 : 15.
Review — What a Ratio Says: What does a ratio do?
Answer Compares two amounts.
Why A ratio is a comparison.
Warm Up
Straightforward practice. Get the method working first.
4 problems4 : 5. With 16 of the first, how many of the second?
Answer 20
Why 16 : 20.
To keep a ratio the same, what must you do?
Answer Multiply both quantities by the same number.
Why Both, by the same factor.
5 : 2 scaled by 3. What is the second number?
Answer 6
Why 2 × 3.
3 : 7. With 9 of the first, how many of the second?
Answer 21
Why Scaled by 3.
Build It Up
The same ideas with more to keep track of.
2 problems6 : 8. Scaled down, what is the simplest first number?
Answer 3
Why Both divide by 2.
Is 4 : 6 the same comparison as 6 : 9?
Answer Yes. Both are 2 : 3.
Why Simplify both.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsThe Paint: 2 : 3 blue to yellow. With 8 blue, how much yellow?
Answer 12 yellow
Why 8 : 12.
The Class: 3 : 4 teachers to helpers. With 12 teachers, how many helpers?
Answer 16 helpers
Why 12 : 16.