1. Lesson 7.1.1 – Teacher Notes Standard:
7.RP.A.2d Recognize and represent proportional relationships between quantities.
Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0, 0) and (1, r) where r is the unit rate.
Full mastery can be expected by the end of the chapter.
Lesson Focus:
The focus of the lesson is for students to understand how to read a graph, paying close attention to unit rate. Students will also need to apply knowledge of unit rate. If you decide to use the toys, it is a good idea to only use one toy per table.
(7-2, 7-3, and 7-7)
I can explain what a point (x, y) on a graph of a proportional relationship means in terms of the situation.
Calculator: No
Literacy/Teaching Strategy: Teammates Consult and Whiparound (7-1); Huddle (Struggling learners); Walk and Talk (Closure)

2. Bell Work

3. In this course, you have looked at several relationships between two sets of information and investigated how one piece of information can or cannot be found from the other.  To continue your investigation of proportional relationships from Chapter 4, you will look at the mathematical relationship between distance, rate, and time.  Later, in the final section of this chapter, you will identify proportional relationships and use your understanding of proportionality to solve problems.

4. 7-1. George stood on the train platform and waved goodbye to his sister as she left for summer camp.  Later, as he was getting in his car to drive home, he saw a light flashing inside the train station and heard an announcement that his sister’s train had malfunctioned and was stuck on the tracks.  George had a map of the train’s route and decided to drive to where the train was stuck and pick up his sister. 
- How can he figure out where the train is? 
- What information would help him to figure it out?  Be prepared to share your ideas with the class. 

5. 7-2. TOYS
If you needed to predict how far a car, train, or plane had gone, it would be helpful to know something about how fast it was going and how long it had been moving.  You will work with your team to investigate the relationship between distance, speed (or rate), and time in the following experiment.    
Obtain a meter stick, a toy (such as a wind-up car), a long piece of paper, and a stopwatch from your teacher.  Put the paper on the floor, draw a starting line near one end of it, and place the toy on the edge of the paper facing the starting line as shown at right.  Place the toy a short distance behind the starting line so that it can reach a constant speed by the time it gets to the starting line. 

6. Read the directions below for taking data before starting your toy:

7. Do a “dry run” of the experiment one time without collecting data, and talk with your team about how, exactly, you will collect the data.
Work with your team to take data comparing the time that has passed (in seconds) to the distance (in cm) that the toy is from the starting line, following the directions you were given. 

8. Obtain a Lesson 7. 1. 1 Resource Page from your teacher
Obtain a Lesson Resource Page from your teacher.  Work with your team to organize your data into a table and graph it.  Be prepared to share your table and graph with the class.  Then think about the following questions.
a. Where does your graph begin?  Should your graph “stop”?  Would it make sense to continue your graph to show how your toy would travel if you were to continue measuring for more time?
b. How far would you expect your toy to
Have traveled after 7 seconds have
passed? What about after 2.3 seconds? 
Does it make sense to connect the points
on the graph?  Why or why not?

9. 7-3. What is the unit rate of your toy
7-3. What is the unit rate of your toy?  That is, approximately how far does your toy travel each second?  How can you see this in your table?  How can you see it on your graph?  Be prepared to explain your ideas to the class. 
7-4. How can you use your answer to problem 7-3 to write an equation relating the time the car has been moving to the distance it has traveled?  Work with your team to write an equation relating distance and time.  
7-5. If your toy were twice as fast, how far would it travel each second?  How would you see this in the table?  How would you see it on the graph?  Again, be prepared to explain your ideas to the class.   

10. 7-6. If your toy travels at a constant speed, then the distance your toy has traveled and the time it has taken are related to each other proportionally.  In a proportional relationship, two quantities are related by a constant of proportionality (or a constant multiplier).  For your toy, the constant of proportion is called the rate.  In this case, it is also the speed. 
Where else in this course have you seen two quantities related by a constant multiplier?  Work with your team to come up with examples of proportional relationships and be ready to contribute your ideas to the class discussion. 

11. 7-7. Answer each of the following questions and be ready to explain how you could use your table or graph to get each answer.
a. What distance would your toy travel in 9 seconds?   
b. How far would your toy travel in 25 seconds?   
c. How many seconds would it take your toy to travel 300 cm? 

12. Bella wants to use her toy car to deliver a secret note to Edward, who is sitting all the way across the cafeteria, approximately 20 meters from her.  She plans to get the car started and then leave the cafeteria so Edward will not see her.  If her car travels at 1.1 meters per second, about how much time will she have to get out of the cafeteria before Edward gets the note?  

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