Name: ______________________________

Date: September 20, 2016

Homeroom:

7th Grade Math:

Unit: Ratios and Proportions

Packet 15: Constant of

Proportionality

Objectives: Scholars will be able to calculate the constant of proportionality. Scholars will be able to find and interpret the constant of

proportionality within the context of a problem. Agenda:

1. Review Do Now 6. Independent Practice2. National Forest Deer Population 7. Exit Ticket3. College-Ready Vocab 8. Homework Overview4. You Need What???5. French Cooking Class Homework 15: Constant of

Proportionality

Do Now: 1. What are the characteristics of the graphs that represent proportional

relationships?

1. Find the quotient of the following numbers.

16,536 ÷ 24

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National Forest Deer PopulationWildlife conservationists are concerned that the deer population might not be constant across the National Forest. The scientists found that there were 144 deer in a 16 square mile are of the forest. In another part of the forest, conservationists counted 117 deer in a 13 square mile area. Yet a third conservationist counted 216 deer in a 24 square mile plot of the forest. Do conservationists need to be worried?

1. Why does it matter if the deer population is not constant in a certain area of the National Forest? ________________________________________________________________________________________________________________________________________________________________________________________________________________________

2. What is the population density of deer per square mile?

Square Miles (x) Number of Deer (y)

3. What is the constant of proportionality in this problem? ________________________________________________________________________________________________________________________________________________

4. Explain the meaning of the constant of proportionality in the context of this problem. ________________________________________________________________________________________________________________________________________________

5. How many deer would you expect to find in 207 square miles? ________________________________________________________________________________________________________________________________________________________________________________________________________________________

6. How many square miles would you expect to need in order to find 486 deer?

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________________________________________________________________________________________________________________________________________________________________________________________________________________________

7. Based on our work above, do conservationists need to be worried? ________________________________________________________________________________________________________________________________________________________________________________________________________________________

College-Ready Vocabulary!Word Definition Example

Constant of Proportionality

You Need WHAT????Brandon came home from school and informed his mother that he had volunteered to make cookies for his entire grade level. He needs 3 cookies for each of the 96 students in the 7th grade. Unfortunately, he needs the cookies the very next day! Brandon and his mother determined that they can fit 36 cookies on two cookie sheets.

1. Is the number of cookies proportional to the number of cookie sheets used in baking? Create a table that shows data of the number of sheets needed for the total number of cookies baked.

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Space for work:

2. What is the constant of proportionality? ________________________________________________________________________________________________________________________________________________

3. Explain what the constant of proportionality means in the context of this problem. ________________________________________________________________________________________________________________________________________________

4. It takes 2 hours to bake 8 sheets of cookies. If Brandon and his mother begin baking at 4:00 p.m., when will they finish baking the cookies? ________________________________________________________________________________________________________________________________________________________________________________________________________________________

French Cooking ClassSuzette and Margo want to prepare crepes for all of the students in their French class. A recipe makes 20 crepes with a certain amount of flour, milk and 2 eggs. The girls already know that they have plenty of flour and milk to

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Space for Work:

make 50 crepes, but they need to determine the number of eggs they will need for the recipe because they are not sure they have enough.

1. Considering the amount of eggs necessary to make the crepes, what is the constant of proportionality?

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

3. How many eggs are needed to make 50 crepes?

Independent PracticeDirections: Calculate the constant of proportionality in the tables below. Show all of your work and write your answers in complete sentences.

1.

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X 7.5 10 17.5 20Y 4.5 6 10.5 12

2.

3.

4.

5.

6

X 1.5 2 3.5 5Y 10.5 14 24.5 35

X 2 4 5 7Y 1 2 2.5 3.5

X 2 3 5 6Y 6 9 15 18

X 2 4 7 9Y 0.4 0.8 1.4 1.8

6.

7. The dry cleaning fee for 3 pairs of pants is $18. a. What is the constant of proportionality?

______________________________________________________________________________________________________________________________________________________________________________________________________

b. How much will the dry cleaner charge for 11 pairs of pants? ____________________________________________________________________________________________________________________________________

8. Bananas are $0.59 per pound.a. What is the constant of proportionality?

______________________________________________________________________________________________________________________________________________________________________________________________________

b. How much will 25 bananas cost? ____________________________________________________________________________________________________________________________________

Practice beyond Perfection! (Turn in for $$)

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X 1.5 3 4.5 12Y 1 2 3 8

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Name: ______________________________

Date: September 20, 2016

Homeroom:

Ms. Petrozzi: (614) 725-9693

7th Grade Math:

Unit: Ratios and Proportions

Packet 15: Constant of

ProportionalityRedo: Score: ________/5 _________%

DNG A B C D F

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

Each school year, the 7th graders who study Life Science participate in a special field trip to the city zoo. In 2010, the school paid $1,260 for 84 students to enter the zoo. In 2011, the school paid $1,050 for 70 students to enter the zoo. In 2012, the school paid $1,395 for 93 students to enter the zoo.

1. Is the price the school pays each year in entrance fees proportional to the number of students entering the zoo? Create a table below.

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2. Is this relationship proportional? Explain why or why not. ________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

3. Identify the constant of proportionality and explain what it means in the context of this situation. ________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

4. What would the school pay if 120 students entered the zoo? ________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

5. How many students would enter the zoo if the school paid $1,425? ________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

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Work for question #4: Work for question #5:

Name: ______________________________

Date: September 20, 2016

Homeroom:

7th Grade Math:

Unit: Ratios and Proportions

Packet 15: Constant of

Proportionality

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

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? ________________________________________________________________________________________________________________________________________________

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

Cans of Paint 2 10 6 9 1Birdhouses

Painted10 50 30 45 5

____________________________________________________________________________________________________________________________________________________________

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

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________________________________________________________________________________________________________________________________________________

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

Mastery: ___________/4 Mastered Progressing Not-Mastered