Unit 1- Ratios and Proportional Relationships

Unit 3

This unit builds on the students’ knowledge and understandings of rate and unit concepts that were developed in Grade 6. This includes the need to develop proportional relationships through the analysis of graphs, tables, equations, and diagrams. Grade 7 will push for the students’ to develop a deep understanding of the characteristics of a proportional relationship. Mathematics should be represented in as many ways as possible in this unit by using graphs, tables, pictures, symbols, and words. Some examples of providing the students with this opportunity are the following: researching newspaper ads, constructing their own questions, keeping a log of prices (particularly sales), and determining savings by purchasing items on sale.

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MGSE7.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 miles in each 1/4 hour, compute the unit rate as the complex fraction (1/2)/(1/4) miles per hour, equivalently 2 miles per hour.

MGSE7.RP.2 Recognize and represent proportional relationships between quantities.

 

MGSE7.RP.2a 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.

 

MGSE7.RP.2b Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

 

MGSE7.RP.2c Represent proportional relationships by equations.

 

MGSE7.RP.2d 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.

 

MGSE7.RP.3 Use proportional relationships to solve multi-step ratio and percent problems. Examples: simple interest, tax, markups, and markdowns, gratuities and commissions, and fees.

 

MGSE7.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.