Name: ______________________________

Date: September 14, 2016

Homeroom:

7th Grade Math:

Unit: Ratios and Proportions

Packet 11: Proportional Relationships

Objectives: Scholars will be able to identify whether proportional relationships exist

between a set of quantities. Scholars will be able to identify the unit rate given a proportional

relationship. Agenda:

1. Review Do Now 6. Exit Ticket2. Pay by the ounce frozen yogurt! 7. Homework Overview3. A cooking cheat sheet Homework 6: Proportional

Relationships4. Summer Job5. Independent Practice

Do Now: 1. Find each rate and unit rate. INCLUDE UNITS!

Rate Unit Rate

40 hours in 5 days

66 miles in 3 gallons

9 pounds for $2

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College-Ready VocabularyWord Definition Example

Proportion

Proportional Relationship

Example 1: Pay by the ounce frozen yogurt! A new self-serve yogurt store opened this summer that sells its yogurt at a price based upon the total weight of the yogurt and its toppings in a dish. Each member of Isabelle’s family weighed their dish and this is what they found. Determine if the cost is proportional to the weight.

Weight (ounces)

12.5 10 5 8

Cost ($) 5 4 2 3.20

The cost is ______________________________ to the weight.

1. Does everyone pay the same cost per ounce? How do you know? ________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

2. 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?

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3. What happens if you don’t serve yourself any yogurt or toppings? How much do you pay? ________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

Example 2: A Cooking Cheat Sheet! In the back of a recipe book, a diagram provides easy conversions to use while cooking.

The ounces _____________________________________________ to the cups.

1. What does the diagram tell us? ________________________________________________________________________________________________________________________________________________________________________________________________________________________

2. Is the number of ounces proportional to the number of cups? How do you know? ________________________________________________________________________________________________________________________________________________________________________________________________________________________

3. How many ounces are there in 4 cups? 5 cups? 8 cups? How do you know? ________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

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Ounces

Cups

0 ½ 1 21 ½

0 4 8 1612

4. For any number of cups x, how do we find the number of ounces, y?________________________________________________________________________________________________________________________________________________

Try the following problem on your own!

During Jose’s physical education class today, students visited activity stations. Next to each station was a chart depicting how many calories (on average) would be burned by completing the activity.

Calories burned while jumping rope:

1. Is the number of calories burned proportional to time? How do you know? ________________________________________________________________________________________________________________________________________________________________________________________________________________________

2. If Jose jumped rope for 6 minutes, how many calories would he expect to burn? What if he jumped rope for 7.5 minutes? ________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

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Calories Burned

Time (minutes)

0 1 2 43

0 11 22 4433

Example 3: Summer Job Alex spent the summer helping out at his family’s business. He was hoping to earn enough money to buy a new $220 gaming system by the end of the summer. Halfway through the summer, after working for 4 weeks, he had earned $112. Alex wonders, “If I continue to work and earn money at this rate, will I have enough money to buy the gaming system by the end of the summer?”

To determine if he will earn enough money, he decided to make a table. He entered his total money earned at the end of week 1 and his total money earned at the end of week 4.

Week

0 1 2 3 4 5 6 7 8

Total $ $28 $112

Fill in the rest of the table. Show your work in the space below.

1. Are Alex’s total earnings proportional to the number of weeks he worked? How do you know? ________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

2. Will Alex have enough money to buy the gaming system by the end of the summer (week 8?) ________________________________________________________________________________________________________________________________________________________________________________________________________________________

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Independent Practice:Directions: Determine whether the set of numbers in each table are proportional.

1.

The relationship between the number of shaded squares to total squares ___________________________________ (is or is not) proportional.

2.

The relationship between the number of junk e-mails to total e-mails ___________________________________ (is or is not) proportional.

3.

The relationship between the numbers of weeks and days __________________________ (is or is not) proportional.

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1. A cran-apple juice blend is mixed in a ratio of cranberry to apple of 3 to 5.

a. Complete the table to show different amounts that are proportional.

Amount of CranberryAmount of

Apple

b. Why are these quantities proportional? ________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

2. John is filling a bathtub that is 18 inches deep. He notices that it takes two minutes to fill the tub with three inches of water. He estimates it will take ten more minutes for the water to reach the top of the tub if it continues at the same rate. Is he correct? Explain.

MinutesWater

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Practice beyond Perfection: Turn in for dollars!

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Name: ______________________________

Date: September 14, 2016

Homeroom:

Ms. Petrozzi: (614) 725-9693

7th Grade Math:

Unit: Ratios and Proportions

Packet 11: Proportional Relationships

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

Directions: Determine whether the set of numbers in each table are proportional to each other. If they are proportional, write “proportional” on the line. If they are not proportional, write “non-proportional” on the line.

1. The table below shows the amount of blue paint to yellow paint necessary to make green paint.

The amount of blue paint is _________________________________ to the amount of yellow paint.

Explain your answer in the box below:

2. The table below shows the amount of sugar and ice tea mix you need to make sweet tea.

The amount of ice tea mix is ________________________________ to the amount of sugar.

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Help?! See page 4

3. The relationship between the number of shaded to total squares is ______________________________.

4. The relationship between the number of weeks to the number of days is ________________________________.

Explain your answer in the space below:

5. Andrew earns $18 per hour for mowing lawns. Is the amount of money he earns proportional to the number of hours he spends mowing? Fill in the table below to defend your answer!

$ $18Hours 1 hour

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Is this relationship proportional?

Help?! See page 5

Help?! See page 4

Name: ______________________________

Date: September 14, 2016

Homeroom:

7th Grade Math:

Unit: Ratios and Proportions

Packet 11: Proportional Relationships

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

1. The price of coffee is shown in the table below.

The amount of coffee (in pounds) ____________________ (is/is not) proportional to the cost in dollars.

Explain your answer below:

2. The table below shows the distance traveled per hour by a train going up a large mountain.

The time traveled __________________________ (is/is not) proportional to the distance traveled.

Explain your answer below:

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

Mastery: ___________/4 Mastered Progressing Not-Mastered