Ratio and Proportional Relationships

7.RP.1 Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each ¼ hour, compute the unit rate as the complex fraction (1/2)/(1/4) miles per hour, equivalently 2 miles per hour.

7.RP.2 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 at 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 is the unit rate.
7.G.1 Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.
7.NS.2c. Apply properties of operations as strategies to multiply and divide rational numbers.

Ratio                             Equivalent Ratio                       Units (labels)                       Rate

Unit Rate                      Proportional To                         Proportional Relationship

Independent Variable –IV                                              Dependent Variable -DV

Coordinate plane         X-axis                                         Y-axis                                  X-coordinate

Y-coordinate                 Scale (increments)                    Origin                                 Plot

Constant                       Variable                                     Constant of Proportionality (unit rate)

y/x                                  Complex Fraction                    Numerator                          Denominator

Corresponding             Enlargement                             Reduction                            Scale Factor