1. Lesson 4.2.1 – Teacher Notes Standard: 7.RP.A.2a
Recognize and represent proportional relationships between quantities.
Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin.
Full mastery by end of chapter
Lesson Focus:
The focus is for students to understand what a proportional relationship looks like and how growth is shown in a table and graph. (4-25, 4-26, and 4-27) ***It may be a good idea for teachers to have students create a table and/or graph to prove their work in 4-27.
I can translate a proportion into a table to determine equivalency.
Graph ordered pairs on a coordinate plane.
Represent ratios as ordered pairs on the coordinate plane.
Recognize that ordered pairs are proportional if they form a straight line through the origin.
Calculator: Yes
Literacy/Teaching Strategy: Think-Pair-Share (4-21 and 4-27); Walk and Talk (4-26)

2. Bell Work

3. Grocery stores often advertise special prices for fruits and vegetables that are in season. You might see a sign that says, “Special Today!  Buy 2 pounds of apples for $1.29!” How would you use that information to predict how much you need to pay if you want to buy six pounds of apples? Or just 1 pound of apples? 
The way that the cost of apples grows or shrinks allows you to use a variety of different strategies to predict and estimate prices for different amounts of apples. In this section, you will explore different kinds of growth patterns. You will use those patterns to develop strategies for making predictions and deciding if answers are reasonable. 

4. As you work in this section, ask yourself these questions to help you identify different patterns:
How are the entries in the table related?
Can I double the values?
What patterns can I see in a graph?

5. 4-25. FOR THE BIRDS
When filling her bird feeder, Sonja noticed that she paid $27 for four pounds of bulk birdseed.  “Next time, I’m going to buy 8 pounds instead so I can make it through the spring. That should cost $54.”
a. Does Sonja’s assumption that doubling the amount of birdseed would double the price make sense? Why or why not? How much would you predict that 2 pounds of birdseed would cost? 

6. 4-25. FOR THE BIRDS
When filling her bird feeder, Sonja noticed that she paid $27 for four pounds of bulk birdseed.  “Next time, I’m going to buy 8 pounds instead so I can make it through the spring. That should cost $54.”
b. To check her assumption, she found a receipt for 1 pound of birdseed. She decided to make a table, which is started below. Copy and complete her table.
Pounds 1 2 3 4 5 6 8
Cost
$6.75
$27

7. c. How do the amounts in the table grow?
4-25. FOR THE BIRDS
When filling her bird feeder, Sonja noticed that she paid $27 for four pounds of bulk birdseed.  “Next time, I’m going to buy 8 pounds instead so I can make it through the spring. That should cost $54.”
c. How do the amounts in the table grow? 
d. Does the table confirm Sonja’s doubling relationship? Give two examples from the table that show how doubling the pounds will double the cost. 
Pounds 1 2 3 4 5 6 8
Cost
$6.75
$27

8. 4-26. Examine the graphs below.
a. With your team:
Describe how each graph is the same.
Describe what makes each graph different.
b. How do the differences explain why doubling works in one situation and not in the other? Generalize why doubling works in one situation and not in another. 
Gustavo
Sonja

9. 4-26. Examine the graphs below.
c. The pattern of growth in Sonja’s example of buying birdseed is an example of a proportional relationship. In a proportional relationship, if one quantity is multiplied by a scale factor, the other is scaled by the same amount. Gustavo’s bank account is not proportional, because it grows differently; when the number of years doubled, his balance did not.
Gustavo
Sonja

10. 4-26. Examine the graphs below.
d. Work with your team to list other characteristics of proportional relationships, based on Sonja’s and Gustavo’s examples. Be as specific as possible. 
Gustavo
Sonja

11. 4-27. IS IT PROPORTIONAL? (also on the handout)
When you are making a prediction, it is important to be able to recognize whether a relationship is proportional or not.
Your Task: Work with your team to read each new situation below. Decide whether you think the relationship described is proportional or non-proportional and justify your reasoning. Be prepared to share your decisions and justifications with the class. Make a table for each situation to prove your answer.         
Carlos wants to buy some new video games. Each game he buys costs him $36. Is the relationship between the number of games Carlos buys and the total price proportional? 
b. A single ticket to a concert costs $56, while buying five tickets costs $250. Is the relationship between the number of tickets bought and the total price proportional?  

12. 4-27. IS IT PROPORTIONAL? (also on the handout)
When you are making a prediction, it is important to be able to recognize whether a relationship is proportional or not.
Your Task: Work with your team to read each new situation below. Decide whether you think the relationship described is proportional or non-proportional and justify your reasoning. Be prepared to share your decisions and justifications with the class. Make a table for each situation to prove your answer.       
c. Vu is four years older than his sister.  Is the relationship between Vu and his sister’s age proportional?  
d. Janna runs at a steady pace of 7 minutes per mile.  Is the relationship between the number of miles she ran and the distance she covered proportional?  

13. 4-27. IS IT PROPORTIONAL? (also on the handout)
When you are making a prediction, it is important to be able to recognize whether a relationship is proportional or not.
Your Task: Work with your team to read each new situation below. Decide whether you think the relationship described is proportional or non-proportional and justify your reasoning. Be prepared to share your decisions and justifications with the class. Make a table for each situation to prove your answer.       
e. Carl just bought a music player and plans to load 50 songs each week. Is the relationship between the number of weeks after Carl bought the music player and the number of songs on his player proportional?  
f. Anna has a new video game. It takes her five hours of playing the game to master level one. After so much time, Anna understands the game better and it only takes her three hours of playing the game to master level two. Is the number of hours played and the game level proportional?  

14. Practice
Drew is an artist. He paints portraits. The table below shows the number of portraits painted in hours. the Do the numbers in the table represent a proportional relationship?
Daisy made an envelope from sheets of paper The table below shows the number of envelopes made by the number of sheets. Do the numbers in the table represent a proportional relationship?
Alice went to market and bought comics. The table below shows the price for different numbers of comics. Do the numbers in the table represent a proportional relationship?