7.RP.2 Analyze proportional relationships and use them to solve real-world and mathematical problems. Recognize and represent proportional relationships between quantities. a.Decide whether two quantities are in a proportional relationship, e.g. by testing for equivalent ratios in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin b.Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. c.Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased as a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn. d.Explain what a point (x,y) on the graph of a proportional relationship means in terms of the situation, with special attention to the points (0,0) and (1,r) where r is the unit rate.

For each slide, complete one section of the graphic organizer as a strategy to determine the constant of proportionality (unit rate).

⅜ of the fish tank can be filled in 5 minutes. How long will it take to fill the entire tank?

At a school, 4 out of every 7 girls play sports. There are x girls in the school, how many of them play sports?

Identify the constant of proportionality.

A student identified the constant of proportionality as 1. Is this student correct? Explain your reasoning.

Do these two models represent the same proportional relationship? Explain your reasoning.

Helen made a graph that represents the amount of money she earns, y, for the number of hours she works, x. The graph is a straight line that passes through the origin and the point (1, 12.5). Determine if each statement is true or false, and justify each response. A. The origin is 1. B. Helen earns $12.50 per hour. C. Helen works 12.5 hours per day. D. The unit rate is 12.5.

What information does the point (0,0) represent for each line? Identify k for each proportional relationship

Coffee costs $15.06 for 3 pounds Name the point for this graph that would be the location of the unit rate..

Which equation has a constant of proportionality equal to 4? 4y = 4x 4y = 12x 3y = 4x 3y = 12x

The coordinates of point A are (6.5, 5) The coordinates of point B are (13, 5) Are points A and B a proportional relationship? Jill said they are in a proportional relationship because 6.5 doubled is 13. Do you agree with Jill’s thinking? Explain.