Proportional Relationships and Unit Rates

In this lesson, Mrs. Lopez teaches students how to interpret graphs of proportional relationships. The lesson includes examples using a cookie recipe to explore the relationship between flour and cookies, and another example using sugar. Students learn to model these relationships on graphs and calculate unit rates. The lesson also covers an example of calculating costs at an amusement park using proportional relationships. The session concludes with a summary and encouragement for students to ask questions if needed.

What is the first step in converting dozens of cookies to individual cookies in Grandma's recipe?

• Subtract 12 from the number of dozens

• Add 12 to the number of dozens

• Multiply the number of dozens by 12

• Divide the number of dozens by 12

How do you determine the unit rate in a proportional relationship?

• Divide the total by the number of units

• Subtract the number of units from the total

• Multiply the total by the number of units

• Add the total to the number of units

What does a straight line through the origin on a graph indicate?

• A quadratic relationship

• A proportional relationship

• A non-proportional relationship

• An inverse relationship

In the sugar and cookies example, what does the ordered pair (4, 6) represent?

• 6 cups of sugar with 4 dozen cookies

• 4 cups of sugar with 6 dozen cookies

• 6 dozen cookies with 4 cups of sugar

• 4 dozen cookies with 6 cups of sugar

How many dozen cookies can be made with one cup of sugar according to the unit rate?

• 1 dozen

• 1.5 dozen

• 2 dozen

• 2.5 dozen

What is the equation used to find the total cost for people entering the amusement park?

• C = 50 + P

• C = 50P

• C = P/50

• C = 50 - P

If 5 people enter the amusement park, what is the total cost?

• $200

• $250

• $300

• $350

What must be true for a graph to represent a proportional relationship?

• It must be a curved line

• It must pass through the origin

• It must have a negative slope

• It must be a horizontal line

What is the constant of proportionality in the amusement park example?

• $50

• $100

• $25

• $75

Would the point (7, 350) be on the graph of the amusement park costs?

• No, because the unit rate is inconsistent

• Yes, because it is a random point

• No, because it does not fit the pattern

• Yes, because the unit rate is consistent