Exploring Ratios and Proportional Relationships Overview

Introduction

In this module, students will extend their learning from 6th grade as they will learn to identify proportional relationships from tables and graphs. They will also learn to identify and create equivalent ratios and recognize the constant from a table or graph. They will be able to understand that if there is no constant, there is no proportional relationship. Students will learn to write equations from tables that represent the unit rate. This will prepare them for slope in 8th grade. Graphing on a plane will be an important concept in this module as students can use the graph to determine proportionality.

Essential Questions

How can you compare unit rates associated with fractions?
How can you use the definition of a proportional relationship to determine whether a relationship presented in a table or graph is proportional?
How can you represent proportional relationships by equations?
How can I identify the constant of proportionality?
How can I use proportional relationships to solve multistep percent problems?
How can I demonstrate the origin and unit rate on a graph?

Key Terms

The following key terms will help you understand the content in this module.

Complex fraction - A complex fraction is a fraction in which either the numerator or the denominator or both contain fractions.

Constant of proportionality - The constant of proportionality is the constant ratio between two quantities in a proportional relationship.

Coordinate plane - A plane formed by the intersection of a horizontal number line called the x-axis and a vertical number line called the y-axis.

Equivalent ratios - Equivalent ratios are ratios that name the same comparison.

Indirect measurement - Indirect measurement is the process of using similar figures and proportions to find a measure.

Origin - The origin is the point where the x-axis and y-axis intersect on the coordinate plane (0, 0).

Proportion - A proportion is an equation that states that two ratios are equivalent

Proportional relationship - A proportional relationship is a relationship between two quantities in which the ratio of one quantity to the other quantity is constant.

Unit rate - The unit rate is rate in which the second quantity in the comparison is one unit. (denominator is 1)

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