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Proportional Relationships

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1 Proportional Relationships
Engage NY Module 1 - Lesson 2 Proportional Relationships

2 Materials Needed Student packet with: Class Notes Exit Ticket
Problem Set

3 Proportional Relationships
7th Grade Module 1; Lesson 2 Student Outcomes Click to reveal student outcomes

4 Classwork Module 1 Lesson 2 TAKE OUT LESSON 2 CLASSWORK - Pg S.4 yum!

5 Classwork Example 1 Questions to Discuss: Module 1 Lesson 2
(Lower the screen shade for discussion questions.) Questions to Discuss:  Does everyone pay the same cost per ounce? How do you know?  Isabelle’s brother takes an extra-long time to create his dish. When he puts it on the scale, it weighs 15 ounces. If everyone pays the same rate in this store, how much will his dish cost? How did you calculate this cost? (Have students complete the statement in their materials.)  Since this is true, we say “cost is proportional to weight”.  What happens if you don’t serve yourself any yogurt or toppings, how much do you pay?  And does the relationship above still hold true? In other words, if you buy 0 ounces of yogurt, then multiply by the cost per ounce, do you get 0?

6 place the x and y variables in the appropriate rows
Example 1 ... Continued (Pause with students to note that any variables could be chosen but for the sake of this discussion, they are x and y. )  You always multiply the number of ounces, x , by the constant that represents cost per ounce, to get the total cost, y . Let's fill in our table: (Have students write 'x 0.40' beside each x value)  For any measure x, how do we find y? x place the x and y variables in the appropriate rows y (drag variables)

7 Example 2 Questions to Discuss:  What does the diagram tell us?
 Is the number of ounces proportional to the number of cups? How do you know?  There are 8 ounces for every cup and to get the number of ounces. You can always multiply the number of cups by 8.

8 A Cooking Cheat Sheet How many ounces are there in 4 cups? 5 cups?
Have students complete statement on their materials, ounces is proportional to cups, and note how they can tell. It is important to acknowledge that you could also divide by 8 if you know the number ounces and are trying to find the number of cups. This discussion should lead to the importance of defining the quantities clearly. pull How many ounces are there in 4 cups? pull 5 cups? pull 8 cups? pull How do you know?

9 let’s represent the cups with x, and the ounces with y .
For any number of cups x, how do we find the number of ounces, y? use this to push the students to represent the relationship as an equation (y=8x) Have students substitute quantities to make sure the equation is an accurate representation.

10 Exercise 1 Classwork Module 1 Lesson 2
Look at "Exercise 1" on page S.5. Let's read it together as a class. Take 5 minutes to complete this problem INDEPENDENTLY. talking

11 Questions: How much do you think Alex had earned by the end of 2 weeks? How will a table help us to check Alex’s prediction? Where did the two given pairs of data come from? Is this reasonable? What other pair could we complete fairly easily? How will we find out his earnings after 2 weeks? 3 weeks?

12 How do we know if two quantities are proportional to each other?
Closing How do we know if two quantities are proportional to each other? How can we recognize a proportional relationship when looking at a table or a set of ratios? (Pair-Share out)

13 Exit Ticket Answer the following question independently and be prepared to hand it in. Ms. Albero decided to make juice to serve along with the pizza at the Student Government party. The directions said to mix 2 scoops of powdered drink mix with a half a gallon of water to make each pitcher of juice. One of Ms. Albero’s students said she will mix 8 scoops with 2 gallons of water to get 4 pitchers. How can you use the concept of proportion to decide whether the student is correct?

14 Problem Set Module 1 Lesson 2 Homework... Due tomorrow


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