Proportional Relationships

Proportional Relationships

Objective:

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Students will recognize and represent proportional relationships between quantities using tables, graphs, and equations.

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Math Goals

• I can find the constant of proportionality

• I can identify proportions using tables, graphs, and equations.

• I can transfer my understanding of unit rates to real-world problems.

Key Terms

• Constant

• Proportional​

• Ratio

• Unit Rate

Characteristics of Proportional Graphs.

• They are in the shape of a straight line.

• They start or cross at the point of origin.

• Origin is: (0,0)

Multiple Choice

Is the graph proportional or non proportional?

• proportional

• non proportional

Fill in the Blank

Why might someone think this graph from the previous slide would be considered proportional?

Multiple Choice

Does this graph represent a proportional relationship?

• Yes

• No

Poll

Check in: Rate your level of understanding:

• I do not understand at all, and need a lot of practice.

• I kind of understand, but still need some practice.

• I have mastered this and I am ready to move on.

Constant of Proportionality

Multiple Choice

What is the constant of proportionality?

• $3

• $4

• $2

• $9

Writing Equations

• Format of the equation is: y = kx

• First, find the constant of proportionality

• Then, replace the k value with the constant of proportionality

Multiple Choice

In the equation y = 14x, what is the constant of proportionality?

• y

• x

• 14

• y = 14

Fill in the Blank

The table represents the price of McDonald's Value Meals. Determine the constant of proportionality.

Express your as y = kx

Open Ended

In the previous question, why would the answer "5.25" be marked incorrect , even though it was the correct constant of proportionality?

Poll

Check in: Rate your level of understanding:

• I do not understand at all, and need a lot of practice.

• I kind of understand, but still need some practice.

• I have mastered this and I am ready to move on.

Multiple Choice

The graph shows the relationship between the total cost (in dollars) and candy (in pounds) sold in a local school fundraiser.

Use the graph to determine the constant of proportionality.

Express your answer as y = kx

• y = 3k

• y = 3x

• y = 0.03x

• y = 9x

Multiple Choice

What does the constant, 3 represent in the previous question?

• Price for 1 pound of candy

• Pounds of candy per $1 spent