Cogito
Grade 6 Math · Chapter 1 · Lesson 4
Tape Diagrams and Ratio Problems
Drawing the parts before you count them.
10 problems · about 18 minutes · 6.RP.A.3
What this lesson teaches
The child solves ratio problems involving a total by using a tape diagram.
- Draw the ratio as parts of a bar.
- Divide the total by the number of parts to find one part.
- Then build each share from the parts it has.
Warm-Up Review
From earlier lessons. Loosen up before the new work.
1 problemReview — 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.
4 problemsShare 48 in the ratio 1 : 3. What is the larger share?
Answer 36
Why 3 × 12 = 36.
To share a total in a ratio, what do you find first?
Answer What one part is worth.
Why One part, then build each share from it.
Share 24 in the ratio 1 : 2. What is the smaller share?
Answer 8
Why 3 parts.
Share 35 in the ratio 2 : 5. What is the larger share?
Answer 25
Why 7 parts, one part is 5.
Build It Up
The same ideas with more to keep track of.
2 problemsShare 50 in the ratio 3 : 7. What is one part worth?
Answer 5
Why 10 parts.
Share 36 in the ratio 4 : 5. What is the smaller share?
Answer 16
Why 9 parts, one part is 4.
Stretch Yourself
Mixed problems. Work out what kind of question it is before you start.
3 problemsThe Sweets: Share 30 in the ratio 2 : 3. What is the smaller share?
Answer 12
Why 2 × 6 = 12.
The Money: Share 60 pounds in the ratio 1 : 5. What is the larger share?
Answer 50 pounds
Why 5 × 10 = 50.
The Difference: Share 45 in the ratio 4 : 5. How much bigger is the larger share?
Answer 5
Why 25 − 20 = 5, which is exactly one part.