Cogito
Grade 6 Math · Chapter 1 · Lesson 5
Double Number Lines
Two rulers that move together.
10 problems · about 17 minutes · 6.RP.A.3
What this lesson teaches
The child uses a double number line to find equivalent ratios and to answer ratio questions.
- A double number line marks two quantities so their pairs line up.
- Both lines take the same number of steps.
- Find the value you know, then read straight across.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
3 problemsReview — 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.
Review — Equivalent Ratios: 4 : 5. With 16 of the first, how many of the second?
Answer 20
Why 16 : 20.
Warm Up
Straightforward practice. Get the method working first.
3 problemsRatio 2 : 9. If the top shows 6, what does the bottom show?
Answer 27
Why 3 × 9 = 27.
Ratio 3 : 5. If the top shows 9, what does the bottom show?
Answer 15
Why 9 is 3 lots of 3.
Ratio 4 : 7. If the top shows 12, what does the bottom show?
Answer 21
Why 12 is 3 lots of 4.
Build It Up
The same ideas with more to keep track of.
2 problemsRatio 5 : 2. If the bottom shows 8, what does the top show?
Answer 20
Why 8 is 4 lots of 2.
On a double number line, do both lines take the same number of steps?
Answer Yes. The columns line up.
Why Every column is one pair.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
2 problemsThe Paint Mix: Blue to white is 2 : 5. For 8 litres of blue, how much white?
Answer 20
Why 4 × 5 = 20 litres.
The Same Mix: Blue to white is 2 : 5. For 15 litres of white, how much blue?
Answer 6
Why 3 × 2 = 6 litres.