Cogito
Grade 6 Math · Chapter 1 · Lesson 6
Comparing Two Ratios
Which mix is stronger?
10 problems · about 18 minutes · 6.RP.A.3
What this lesson teaches
The child decides whether two ratios are equivalent and which of two ratios is greater.
- Two ratios are equivalent when one scales to the other.
- To compare, scale until one quantity matches in both.
- Then whichever has less of the other quantity is the stronger mix.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
3 problemsReview — Double Number Lines: Ratio 2 : 9. If the top shows 6, what does the bottom show?
Answer 27
Why 3 × 9 = 27.
Review — Tape Diagrams and Ratio Problems: Share 48 in the ratio 1 : 3. What is the larger share?
Answer 36
Why 3 × 12 = 36.
Review — Why You Multiply and Not Add: 6 : 9 scaled so the first is 12. What is the second?
Answer 18
Why 12 : 18.
Warm Up
Straightforward practice. Get the method working first.
3 problemsScale 4 : 7 so the first number is 12. What is the second?
Answer 21
Why 12 : 21.
Scale 3 : 5 so the first number is 12. What is the second?
Answer 20
Why Multiply both by 4.
Scale 5 : 2 so the first number is 20. What is the second?
Answer 8
Why Multiply both by 4.
Build It Up
The same ideas with more to keep track of.
2 problemsIs 6 : 8 equivalent to 9 : 12?
Answer Yes.
Why Both reduce to 3 : 4.
Is 2 : 5 equivalent to 3 : 7?
Answer No.
Why Scale both to 6 of the first.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsTwo Recipes: Scale 2 : 3 so the first number is 6. What is the second number?
Answer 9
Why 6 : 9.
The Comparison: Is 4 : 6 equivalent to 6 : 9?
Answer Yes. Both are 2 : 3 scaled.
Why Both reduce to 2 : 3.