Name: ______________________________

Date: September 22, 2016

Homeroom:

7th Grade Math:

Unit: Ratios and Proportions

Packet 16: Proportional Relationships and Equations

Objectives: Scholars will be able to use the constant of proportionality to represent

proportional relationships with equations in real-world contexts. Scholars will be able to represent proportional relationships with

equations, graphs and ratio tables. Scholars will be able to convert between representations of

proportional relationships. Agenda:

1. Review Do Now 6. Independent Practice2. Points to Remember 7. Exit Ticket3. College-Ready Vocabulary 8. Homework Overview4. Do we have enough to make it?5. Andrea’s Portraits Homework 16: Proportional

Relationships and EquationsDo Now:

1. What is the constant of proportionality in the following table?

Cans of Paint 5 10 6 9 2Birdhouses

Painted15 30 18 27 6

____________________________________________________________________________________________________________________________________________________________

2. What does the constant of proportionality mean in the context of this problem? ________________________________________________________________________________________________________________________________________________

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Points to Remembero _______________________________ relationships have a

_____________________ ratio, or ______________________ ________________.

o The constant ratio, or unit rate of ________________, can also be called

the ________________________________ ______________

______________________________________.

College-Ready VocabularyWord Definition Example

Independent Variable

Dependent Variable

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Do we have enough to make it?Your mother has accelerated onto the interstate beginning a long road trip and you notice that the low fuel light is on, indicating that there is a half a gallon left in the gas tank. The nearest gas station is 26 miles away. Your mother keeps a log where she records the mileage and the number of gallons purchased each time she fill up the tank. Use the information in the table below to determine the amount of gas that he car consumes in a particular number of miles, then you can determine whether or not you can make it to the next gas station.

Mother’s Gas Record

Gallons Miles Driven8 22410 2804 112

1. Find the constant of proportionality and explain what it represents in this situation. ________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

2. Write an equation that will relate the miles driven to the number of gallons of gas.

3. Knowing that there is a half-gallon left in the gas tank when the light comes on, will she make it to the nearest gas station? Explain why or why not. ________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

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4. Determine how far your mother can travel on 18 gallons of gas. Solve this problem 2 ways!

5. Determine how many gallons of gas would be needed to travel 750 miles. Solve this problem 2 ways!

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Andrea’s PortraitsAndrea is a street artist in New Orleans. She draws caricatures (cartoon-like portraits) of tourists. People have their portrait drawn and then come back later to pick it up from her. The graph below shows the relationship between the number of portraits she draws and the amount of time in hours she needs to draw the portraits.

1. Write several ordered pairs from the graph and explain what each ordered pair means in the context of this graph.

2. Determine the constant of proportionality and explain what it means in this situation. ________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

3. Write an equation that would relate the number of portraits drawn to the time spent drawing the portraits.

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Independent PracticeDirections: Write an equation that will model the proportional relationship given in each real-world situation.

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1. It costs $15 to send 3 packages through a certain shipping company. Consider the number of packages per dollar.

a. Find the constant of proportionality for this situation. ______________________________________________________________________________________________________________________________________________________________________________________________________

b. Write an equation to represent the relationship.

2. On average, Susan downloads 60 songs per month. An online music vendor sells package prices for songs that can be downloaded on to personal digital devices. The graph below shows the package prices for the most popular music promotions. Susan wants to know if she should buy her music from this company or pay a flat fee of $58.00 per month offered by another company. Which is the better buy?

1. Find the constant of proportionality for this situation. ________________________________________________________________________________________________________________________________________________________________________________________________________________________

2. Write an equation to represent the relationship.

3. Which is the better buy?

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Practice beyond Perfection! (Turn in for $$)

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Name: ______________________________

Date: September 22, 2016

Homeroom:

Ms. Petrozzi: (614) 725-9693

7th Grade Math:

Unit: Ratios and Proportions

Packet 16: Proportional Relationships and Equations

Redo: Score: ________/5 _________% DNG A B C D F

Directions: Answer the following questions. Show all of your work.

1. It costs $75 to buy 15 pictures at a store. Determine how much it costs per picture.

a. Find the constant of proportionality in this situation. _____________________________________________________________________________________________________________________________________________________________________________________________________

b. Write an equation to represent this relationship.

2. Ms. Rogers is shopping for groceries. She pays $3.15 per pound of raspberries.

a. Find the constant of proportionality in this situation. ______________________________________________________________________________________________________________________________________________________________________________________________________

b. Write an equation to represent this relationship.

Allison’s middle school volleyball team has designed t-shirts containing their team name and color. Allison and her friend Nicole have volunteered to call

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local stores to get an estimate on the total cost of purchasing t-shirts. The store sends them the graph below.

3. Does this graph represent a proportional relationship? ________________________________________________________________________________________________________________________________________________________________________________________________________________________

4. What is the constant of proportionality? What does it represent in this situation? ________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

5. Write an equation relating the cost and the number of shirts.

Name: ______________________________

Date: September 22, 2016

Homeroom:

7th Grade Math:

Unit: Ratios and Proportions

Packet 16: Proportional Relationships and Equations

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Directions: Answer the questions below. Once you have finished, flip this paper over and assign yourself to your independent reading book.

John and Amber work at an ice cream shop. The hours worked and wages earned are given for each person.

1. Are John’s wages proportional to time? If so, what is the constant of proportionality? Write an equation to represent this relationship.

2. Are Amber’s wages proportional to time? If so, what is the constant of proportionality? Write an equation to represent this relationship.

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Self-Assessment: _______ Test-Ready _______ More Practice ________ Help!

Mastery: ___________/4 Mastered Progressing Not-Mastered

John’s wagesTime (h) Wages ($)

2 183 274 36