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Lakes, Mia » Unit 3: Ratios and Proportional Relationships

Unit 3: Ratios and Proportional Relationships

UNIT 3 BIG IDEAS:

This unit emphasizes key standards that assist students to develop a deeper understanding of numbers. They learn to express different representations of rational numbers (e.g., fractions, decimals, and percent’s), discover how to identify and explain the constant of proportionality, and represent proportional relationships and scale drawings within real-world contexts. Students are expected to learn the following ideas:

  • Fractions, decimals, and percents can be used interchangeably.
  • Ratios and rates use multiplication/division to represent relationships between two quantities.
  • The constant of proportionality is also considered to be the unit rate.
 

STANDARDS FOR MATHEMATICAL CONTENT

Analyze proportional relationships and use them to solve real-world and mathematical problems. 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.

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 multistep ratio and percent problems.

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.