Identifying Correct Quantities and Variables (Grade 10)

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Identifying Correct Quantities and Variables

1. 
Kent wants to grow some tomato plants in his back yard so that he is able to can them for the winter. He is hoping to have about 9 quarts of canned tomatoes. He knows that about every 3 pounds of fresh tomatoes yields one quart of canned tomatoes. What quantities would be useful for finding the number of tomato plants Kent needs to plant?
  1. The average number of tomatoes a tomato plant produces.
  2. The average weight of tomatoes a tomato plant produces.
  3. How long it takes to can one pound of tomatoes.
  4. The average weight of one can of tomatoes.
2. 
Kate bought some mangoes from the store. She also bought some other groceries. If her total bill came to $22, and she knows that she bought about 3 lb of mangoes, which of the following would be needed to know how much the mangoes cost per pound?
  1. The cost of her other groceries.
  2. The number of mangoes she bought.
  3. The weight of each mango.
  4. The cost of each mango.
3. 
Hannah wants to buy an indoor plant for her apartment. Which of the following factors would be important to investigate in order to determine which plant would be appropriate to buy? Choose all that apply.
  1. Amount of sunlight the plant will get.
  2. The size of the apartment.
  3. Whether she will put the plant on the floor or on a table.
  4. Average temperature of her apartment.
4. 
Aaron is the high school hockey coach for the boys team, and is holding tryouts for the hockey team this year. He is hoping to develop a model that will aid him in determining which players are the best fit for the team. Which of the following variables would be important for this model? Choose all that apply.
  1. Hockey skill.
  2. Number of classes a student is taking.
  3. What type of movies he likes.
  4. Whether the student intends on attending university after he graduates high school.
5. 
Angela sells baked goods at a summer market each year. The two main baked goods are apple turnovers and chocolate caramel cupcakes. Unfortunately, she does not keep very good records, and cannot remember exactly what price she sold each for last year. She remembers that one day she sold 50 cupcakes and 30 turnovers, and made about $135. Another day, she sold 40 cupcakes and 40 turnovers, and made $140. If she were to create a model to solve for how much she sold each baked good for, what would be a good variable(s) to create?
  1. Just one variable, the average cost of a baked good.
  2. Two variables, one for the cost to make the baked goods, and another for the total revenue of the baked goods.
  3. Two variables, one for the total number of turnovers sold, and another for the total number of cupcakes sold.
  4. Two variables, one for the cost of a turnover, and one for the cost of a cupcake.
6. 
There is a leak in the ceiling of Kara's room. She puts a bucket underneath the drip. After an hour, there's about a half liter of water. She checks back in another 3 hours, and there is about 2 liters of water. If she wants to determine how much water there will be in 12 hours, what quantity or quantities would she need to determine?
  1. The rate of the water's increase, in liters per hour.
  2. The amount of water in the bucket, in liters.
  3. The amount of water in the bucket in liters and the amount of time that has passed in hours.
  4. The size of the bucket in liters and the rate of the drip in liters per hour.
7. 
Carl is planting a vegetable garden, but will need to build a fence around it so the deer cannot eat the plants. He has 30 m of fencing, and wants to enclose an area of 50 square meters to accommodate all the plants he wants to grow. If Carl were to create a mathematical model to help him know how to build the fencing appropriately, what variable(s) would be useful to create?
  1. One variable, the length of the side of the garden.
  2. One variables, the total perimeter of the garden.
  3. Two variables, the length and width of the garden.
  4. Two variables, the amount of fence he has, and the area of the garden.
8. 
Michelle is a police officer, and is attempting to model the crime patterns in a certain neighborhood. She wants to know when crimes are usually committed and which types of criminal activity are most common. She hopes to use this to predict better how to police this neighborhood. Which of the following quantities would be important to include in this model? Choose all that apply.
  1. Number of calls placed to 9-1-1 from this neighborhood.
  2. When calls to 9-1-1 are placed from this neighborhood.
  3. Names of people arrested in this neighborhood.
  4. Criminal history of people arrested in this neighborhood.
9. 
A moving company chargers $65 per hour, plus a fee that depends on the distance between where the objects are being moved ($35 for every mile). What variable(s) would be good to define if one were to create an expression that would determine the total cost of moving?
  1. One variable: C, the cost of moving.
  2. One variable: t, for the amount of time.
  3. Two variables: C, for the total cost, and t, for the amount of time.
  4. Two variables: t, for the amount of time, and d, for the distance traveled.
10. 
Colin has been asked to create a mathematical model of the penguin population on a remote island. He wants to be able to predict the growth of the penguin colony. He decides that important variables and quantities to consider in the model include: availability of food, presence of predators, the current number of penguins, and the historic growth rate of penguin population. Is Colin's list correct? Why or why not?
  1. Yes, this is the correct model, and there are no more important factors to consider.
  2. No, this model leaves out many important variables, such as climate, water currents, diseases, and many more.
  3. No, only the current number of penguins and the historic rate of population growth are important. All the other factors are simply over-complicating the problem.
  4. Neither correct nor incorrect. Any real world problem can be modeled in multiple ways and with varying degrees of complexity.

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