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7th Grade Math: Unit 3

Last updated 9 months ago
25 questions
1

Unit 3 – Item 1
A cookie factory operates 8 cutting machines, with each machine capable of cutting 12
gingerbread cookies every 45 seconds. How many gingerbread cookies can all 8 machines cut in one minute?

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Unit 3 – Item 2
There are 30 students presenting projects at an engineering fair. Each student must present their project to a panel of judges. The time allotted for all the presentations is 4 hours. How many minutes does each student have to present their projects?

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Unit 3 – Item 3
The cost to play games at the Perry State Fair is shown in the table below.

Determine if the cost per number of games is proportional or nonproportional.

Unit 3 – Item 4
Paul started a lawn care business to make extra money during the summer. The amount Paul charges to mow a lawn is proportional to the time it takes him to mow the lawn. For a lawn that takes 3.5 hours to mow, Paul charges the customer $80.50.
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Part A
Write an equation that represents the relation between the amount of dollars, d, that Paul charges when it takes him h hours to mow the lawn?

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Part B
Paul estimated that it would take 5.5 hours to mow Mrs. Johnson’s lawn. He quoted her a price of $200.00. Is the price that Paul quoted Mrs. Johnson fair? Why or Why Not?

Unit 3 – Item 5
The graph below shows the profit Farmhouse Shakes can make from selling their shakes in the mall.

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PART A
Is the number of milkshakes sold proportional to the profit? Justify your answer.

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PART B
What does the point (30, 45) mean in the context of the situation?

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PART C
What is the unit rate? What point represents the unit rate on the graph?

Unit 3 – Item 6
While driving on the highway Sarah used her cruise control so that the number of miles she traveled was proportional to the time she spent driving. After six hours, Sarah had driven 420 miles.
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PART A
Determine how many miles Sarah traveled each hour and explain its meaning in the context of this situation.

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PART B
What distance would Sarah have covered if she continued to drive at the same constant rate for a total of 8 hours?

Unit 3 – Item 7
The Blue Water Company wanted to determine the rate of water flowing into two pools located in different locations on their site. They began to fill each pool with water, and then graphed the results, as shown.


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PART A
What is the constant of proportionality for graph A and what does it mean?

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PART B
What is the constant of proportionality for graph B and what does it mean?

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PART C
Which pool has the fastest flow rate? Justify your answer.

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Unit 3 – Item 8
Two years ago, the number of students in 7th grade was 150. Last year, the student population increased by 8%. This year, it increased about 8% again. What is the number of students this year?

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Unit 3 – Item 9
Two weeks ago, Sarah went to her favorite coffee shop which advertised a discount of 15% on all pastries. Sarah decided to buy a croissant that was originally priced at $3.50. How much did Sarah pay for the croissant before tax?

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Unit 3 – Item 10
At a shoe store, a pair of sneakers is priced at $80. When would a 25% discount provide a
better deal than a $15 discount off the original price?

Do you agree with Jake or Zack? Explain your reasoning.

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Unit 3 – Item 11


Instructions to care for a tomato plant advise watering it with 1 1/2 cups of water every day. However, the plant has been receiving 20% less water per day than recommended. How much water has the plant been getting?

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Unit 3 – Item 12
In a bakery, a loaf of bread is supposed to weigh 1 pound (16 ounces). However, when
Terry buys a loaf, he measures it to be only 14.5 ounces. What is the percent error in
the weight of the loaf? Justify your answer in the context of the problem.

Unit 3 – Item 13
A survey collected the ages (in years) of a random sample of 12 individuals for their
participation in three different hobbies: painting, playing video games, and gardening.
The ages are as follows:


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Part A
Calculate the mean age for one of the samples. Which hobby do you think the sample represents? Explain your reasoning.

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Part B
Using the sample, estimate the population mean age if 150 individuals were surveyed.

Unit 3 – Item 14
NBA Analytics
You are a data analyst working for a professional basketball team's analytics
department.

Your team is specifically interested in comparing the points per game (PPG) and assists
per game (APG) of selected NBA players to see if there is a proportional relationship
between these two statistics. Your analysis will help the team understand how scoring
efficiency (PPG) relates to playmaking ability (APG) among different players.
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Visit NBA.com/Stats All-Time Leaders and collect data on PPG and APG for at least five NBA players of your choice. Click on the players name to access the needed statistics.

Fill in the table to show the relationship between PPG and APG for each player

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Generate a graph to visually represent the data and identify any patterns that suggest a proportional relationship between PPG and APG.

  • Click the graph tab.
  • Choose the correct graph type.
  • Click on the graph background to add a point. Add two points to create a graph. Drag a point or type in x and y coordinates to edit its position. Click on a point to delete it.
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Formulate equations to represent the proportional relationships between PPG and APG for each player.

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Solve these equations to find the constant of proportionality and explain what this constant represents in terms of basketball performance.

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Prepare a presentation summarizing your analysis, including the tables, graphs, equations, solutions, and explanations of the proportional relationships.

Your findings will be crucial for the team's coaching staff and management to make informed decisions regarding player roles, strategies, and performance
evaluations.