1. A ratio is a comparison of any two quantities or measures
What relationships do you see between the two numbers of this ratio?
10:20
Answers may vary but focus in on the following>
Look for 2 additive answers
The first number is 10 less than the second number.
2. The second number is 10 more than the first number.
Look for 2 multiplicative answers.
3.The first number is ½ of the second.
4. The second number is two times the first number.

2. What 2 multiplicative relationships do you see in these ratios?
B) 9:3
C) 4:6
D) 16:12
E) 4:10
The first is one-fourth the second. The second is four times the first.
B) The first is three times the second. The second is one-third the first.
c) The first is two-thirds times the second. The second is three-halves times the first or one and one-half times the first.
d) The first is four-thirds or one and one-third times the second. The second is three fourths times the first.
E) The first is two-fifths times the second. The second is five-halves or two and one-half times the first.

3. We describe this as a relationship “within” the ratio.
A ratio of two quantities in the same setting is a “within” ratio.
The 2nd bullet is found in Teaching Student Centered Mathematics Grades 5-9, page 169.

4. On which cards is the ratio of trucks to boxes the same?
This is a “within” relationship.

5. This could be printed as a handout.

6. Solve this using a “within” relationship5 10
1.4 ? = 1 2 1 2
Since 5 is of 10, think 1.4 = of ?
? = 2.8

7. A proportion is a statement of equality between two ratios.1 2 3 6
= is a proportion

8. Solve this proportion = Since 12 is 4 times 3, then ? is 4 times 2.
? = 8 OR
Since 3 is of 12, then 2 is of ? 1 4 1 4

9. We describe this as a “between” relationship.
A “between” relationship is a ratio of two corresponding quantities in different situations.

10. On which cards is the ratio of trucks to trucks the same as the ratio of boxes to boxes?
This is a “between” relationship.

12. Solve this using a “between” relationship7 15 ? 30 =

13. Solve each one using a different method (within or between)2 9 10 ? = ? 30 6 18 =
In this slide and the next, teachers should be able to decide which is the better method to choose for each problem and why.

14. Solve each one using a different method (within or between)
1.2
3.6 ?
4.5 = ? 25 6 10 =