ccadana7.weebly.com€¦ · Web viewYou have decided to walk in a long distance race. There are two teams that you can join. Team A walks at a constant rate of 2.5 miles per hour

Name: ______________________________

Date: September 16, 2016

Homeroom:

7th Grade Math:

Unit: Ratios and Proportions

Packet 13: Proportional

Relationships in Tables 2

Objectives: Scholars will be able to determine whether two quantities are

proportional to each other when given a table. Scholars will be able to construct tables to determine whether two

quantities are proportional. Agenda:

1. Review Do Now 6. Independent Practice2. Skill Drill 7. Exit Ticket3. Which team will win the race? 8. Homework Overview4. Guided Practice Exercises5. Examine Reasoning Homework 13: Proportional


Do Now: 1. The table below shows the price, in dollars, for the number of roses

indicated.

Number of Roses 3 6 9 12 15

Price (Dollars) 9 18 27 36 45

a. Is the price proportional to the number of roses? How do you know?

b. Find the cost of purchasing 30 roses.

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Skill Drill!

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College-Ready Vocabulary!Word Definition Example

Constant Rate

Example 1: Which team will win the race? You have decided to walk in a long distance race. There are two teams that you can join. Team A walks at a constant rate of 2.5 miles per hour. Team B walks 4 miles for the first hour and then 2 miles an hour after that.

Task: Create a table for each team showing the distances that would be walked for times of 1, 2, 3, 4, 5, and 6 hours. Using your tables, answer the questions that follow.

3

Team BTime (h) Distance

(miles)

Team ATime (h) Distance

(miles)

1. For which team is distance proportional to time? Explain your reasoning. ________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

2. Explain how you know distance for the other team is not proportional to time. ________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

3. At what distance in the race would it be better to be on Team B than Team A? Explain. ________________________________________________________________________________________________________________________________________________________________________________________________________________________

4. If the members on each team ran for 10 hours, how far would each member run on each team? ________________________________________________________________________________________________________________________________________________________________________________________________________________________

5. Will there always be a winning team, no matter what the length of the course? Why or why not? ________________________________________________________________________________________________________________________________________________________________________________________________________________________

6. If the race is 12 miles long, which team would you choose to be on if you wish to win? Why would you choose this team? ________________________________________________________________________________________________________________________________________________________________________________________________________________________

7. How much sooner would you finish on that team compared to the other team? ________________________________________________________________________________________________________________________________________________________________________________________________________________________

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Guided Practice1. Bella types at a constant rate of 42 words per minute. Is the number of

words she can type proportional to the number of minutes she types? Create a table to determine the relationship.

Minutes 1 2 3 6 60Number of Words

2. Mark recently moved to a new state. During the first month he visited five state parks. Each month after he visited two more. Complete the table below and use the results to determine if the number of parks visited is proportional to the number of months.

Number of Months

Number of State Parks

123

23

3. The table below shows the relationship between the side length of a square and the area. Complete the table. Then determine if the length of the sides is proportional to the area. (To find area, multiply base * height).

Side Length Area1 12 43458

5

Is this a proportional relationship?

Is this a proportional relationship?

Is this relationship proportional?

Examine ReasoningA scholar notices in the table below that as the x-value increases by 3 the y-value increases by 4. Because there is a pattern, the scholar has determined that x is proportional to y. Do you agree with the student’s claim? Why or why not?

x y4 17 510 913 1316 17

Independent Practice1. Joseph earns $15 for every lawn he mows. Is the amount of money he

earns proportional to the number of lawns he mows? Make a table to help you identify the type of relationship.

Number of Lawns MowedEarnings ($)

2. At the end of the summer, Caitlin had saved $120 from her summer job. This was her initial deposit into a new savings account at the bank. As the school year starts, Caitlin is going to deposit another $5 each week from her allowance. Is her account balance proportional to the number of weeks of deposits? Use the table below. Explain your reasoning.

Time (weeks)

Account Balance ($)

6



3. Lucas and Brianna read three books each last month. The table shows the number of pages in each book and the length of time it took to read the entire book.

a.

a. Which of the tables, if any, shows a proportional relationship?

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

b. Both Lucas and Brianna had specific reading goals they needed to accomplish. What different strategies did each person employ in reaching those goals?

________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________

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Pages Brianna Read

168

120

348

Time (hours) 6 4 12

Pages Lucas Read

208

156

234

Time (hours) 8 6 9

Practice beyond Perfection: Turn in for dollars!

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Name: ______________________________


Homeroom:

Ms. Petrozzi: (614) 725-9693

7th Grade Math:




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

Directions: Answer the following questions in complete sentences.

1. Drew is an artist. He paints portraits. The table below shows the number of portraits painted in hours. Do the numbers in the table represent a proportional relationship?

Number of Portraits

Time (in hours)

1 52 103 154 20

2. This table shows the amount earned by Harry for selling cups of ice cream. Do the numbers in the table represent a proportional relationship?

Cups sold Earnings ($)3 125 207 289 36

9



Help?! See question 2 on page 5.

3. Fred wrote notes during an examination. The table below shows number of pages written in relation to the time it took to make the notes (in hours). Does this table represent a proportional relationship?

Notes (pages) Time (hours)8 169 1810 2011 23

4. The table below gives the distance covered by a train over time. Do the numbers in the table represent a proportional relationship?

Notes (pages) Time (hours)1 103 145 187 22

5. Betty makes and sells necklaces. The table below shows the number of necklaces made and the amount of money earned. The relationship between the number of necklaces made and the amount of money earned is proportional. Complete the table below.

Number of Necklaces Earnings ($)12 545

7.5020

10 25

10



Help?! See question 1 on page 5.

Name: ______________________________


Homeroom:

7th Grade Math:




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

1. The table below shows the relationship between the side lengths of a regular octagon and its perimeter.

Side Lengths, s (inches) Perimeter, P (inches)

1 8

2 16

3 24

4 32

9

12

a. Complete the table.b. Does this represent a proportional relationship?

c. If Gabby wants to make a regular octagon with a side length of 20 inches using wire, how much wire does she need?

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

Mastery: ___________/4 Mastered Progressing Not-Mastered

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ccadana7.weebly.com€¦ · Web viewYou have decided to walk in a long distance race. There are two teams that you can join. Team A walks at a constant rate of 2.5 miles per hour