More about Constant of Proportionality

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Finding Equivalent Amounts.

Use the numbers and units from the list to find as many equivalent measurements as you can. For example, you might write “30 minutes is  hour.” You can use the numbers and units more than once.

There is a proportional relationship between any length measured in centimeters and the same length measured in millimeters.

There are two ways of thinking about this proportional relationship. If you know the length of something in centimeters, you can calculate its length in millimeters. Complete the table.

(1). What is the constant of proportionality in the table above?

If you know the length of something in millimeters, you can calculate its length in centimeters. Complete the table.

(2). What is the constant of proportionality in the table above?

(3). How are the two constants of proportionality you found related to each other?

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Establishing the Proportional Relationship.

On its way from New York to San Diego, a plane flew over Pittsburgh, Saint Louis, Albuquerque, and Phoenix traveling at a constant speed.

(1). What is the distance between Saint Louis and Albuquerque?

(2). How many minutes did it take to fly between Albuquerque and Phoenix?

(3). What is the proportional relationship represented by this table?

(4). Diego says the constant of proportionality is 550. Andre says the constant of proportionality is . Do you agree with either of them? Explain your reasoning.

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More Investigation on Constant of Proportionality.

(1). Keeping the slider at 7, select three costs from the table and divide them by their corresponding quantities. What answer do you get?

(2). Change the slider to a different number, select three costs from the table and divide them by their corresponding quantities. What number on the slider did you choose? What number did you get?

(3). What name do you give to the value you found in questions 1 and 2 above?

(4). Describe the relationship between the quantity and the cost based on the “constant of proportionality.

(5). Describe the relationship between the “constant of proportionality” and the graph.

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Completing a Table to determine the constant of Proportionality.

(A). One kilometer is 1000 meters. Complete the table.

(B). One kilometer is 1000 meters. Complete the table.

(1). What is the constant of proportionality in the table above? What does the constant of proportionality tell us?

(2). What is the relationship between the constants of proportionality in the two tables above?

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Noah is running a portion of a marathon at a constant speed of 6 miles per hour. Complete the table to predict how long it would take him to run different distances at that speed, and how far he would run in different time intervals.

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The area of the Mojave desert is 25,000 square miles. A scale drawing of the Mojave desert has an area of 10 square inches. What is the scale of the map?

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Which of these scales is equivalent to the scale 1 cm to 5 km?