This resource is about proportional relationships. To get started, read the following problem.
A group of kids are making lemonade to sell at their lemonade stand. Following the recipe, they use 6 lemons and make 8 cups of lemonade. The next week, they use the same recipe with 9 lemons and make 12 cups of lemonade. 
Sources of images used for this section:
Little boy, Microsoft clipart, office.com
Lemon tree  Korfu Zitronen, JeanLuc 2005, Wikimedia commons
Glass of lemonade  Shekanjbeen, Mainsari66, Wikimedia Commons
Copy the following table into your notes, and use the information from the problem to fill in the empty cells.
Lemons

Cups of Lemonade

3


6

8

9

12

12


15


Click here to see the completed table.
Use the table to answer the following questions.
1. What happens to the amount of lemonade the recipe makes if you double the number of lemons?
2. What happens to the amount of lemonade the recipe makes if you triple the number of lemons?
3. What happens to the amount of lemonade the recipe makes if you change the number of lemons by any scale factor?
4. What rule did you use to fill out the missing information?
The kids decide to sell lemonade one more time. When they go to the fruit bowl they find that they have 5 lemons. How much lemonade can they make now?
Lemons

Cups of Lemonade

3

4

5

?

6

8

9

12

12

16

15

20

Solve the problem on a separate piece of paper, then watch the video to check your answer.
Answer the following questions based on what you saw in the video.
 What was the scale factor used in the first method of solving the problem?
Check Your Answer  What did this scale factor mean?
Check Your Answer  What was the constant of proportionality used in the second method of solving the problem?
Check Your Answer  What did this constant of proportionality mean?
Check Your Answer
This problem required proportional reasoning. Whatever factor you use to change one variable—in this case, the number of lemons, you also use that factor to change the other variable—the number of cups of lemonade.
Danny is helping to decorate the gym for a school dance. It takes Danny 10 minutes to hang 4 strings of flashing lights. If Danny continues to work at the same pace how long will it take him to hang 7 strings of lights?
Source: Platonic solids Lantern, The Playful Geometer, Flickr
Copy the following table into your notes, and fill it in with the values from the problem.
Strings  Minutes 

Click here to see the completed table.
Answer the following questions based on the information in the table.