The study of proportions and proportional reasoning, generally emphasized in grades 6 and 7, forms important connections between the study of fractions and fraction operations to many key concepts in algebra and geometry.
View the Progressions for this content.
See the standards throughout the grades: http://www.corestandards.org/Math/Content/RP/
Topic & Indicator
NF5.a. Examine different ways to solve proportion problems with tables, double number lines, and tape diagrams.
NF5.b. Examine common errors students make when solving problems involving ratio and proportion.
NF6.a. Compare and contrast different ways to find values in proportional relationships and in inversely proportional relationships. For example, explain why linear interpolation can be used with proportional relationships but not with inversely proportional relationships.
NF7.a. Use unit rates to solve problems and to formulate equations for proportional relationships.
NF7.b. Graph proportional relationships, interpreting the unit rate as the slope of the graph.
Purpose
"Although it is traditional to move students quickly to solving proportions by setting up an equation, the Standards do not require this method in Grade 6. There are a number of strategies for solving problems that involve ratios. As students become familiar with relationships among equivalent ratios, their strategies become increasingly abbreviated and efficient. " {Progressions document]
Inverse proportionality forms an excellent contrasting relationship to deepen student understanding of proportion.
Making the connections between unit rates and tables and the equations and graphs which represent them builds the foundation for future work in algebra and geometry.
Selected Resources
NF5.a. "Movin and Groovin.." https://www.insidemathematics.org/sites/default/files/materials/movin%20%27n%20groovin.pdf
Building Proportional Reasoning Across Grades and Math Strands, K-8 Book (Marian Small)
Developing Essential Understanding of Ratios, Proportions, and Proportional Reasoning for Teaching Mathematics, Grades 6-8 Book (Joanne Lobato, Amy Ellis, Rose Mary Zbiek)
Putting Essential Understanding of Ratios and Proportions into Practice in Grades 6-8. Book (Travis Olson, Melfried Olson, and Hannah Slovin)
"Multiple ways to solve proportions." Article in Mathematics Teaching in the Middle School, vol. 16, issue 8, pgs. 482-490.
"Tasks to develop language for ratio relationships." Article in Mathematics Teaching in the Middle School, vol. 20, issue 1, pgs. 38-44.
Beckmann (2018) Resources:
Chapters 7
Activity 7A Mixtures: Same or Different?
Activity 7B Using Double Number Lines
Activity 7C Using Strip Diagrams
Activity 7M How Are The Quantities Related?
Activity 7N Can You Use a Proportion or Not?
Activity 7O A Proportional Relationship Versus an Inversely Proportional Relationship
Billstein (2016) Resources:
Section 6-4
Sowder (2017) Resources:
Chapter 9
Activity 1 Orange Juicy
Activity 2 Cupcakes and Perfume
Van De Walle (2019) Resources:
Chapter 17
Strategies for solving proportional situations
Common challenges and misconceptions