7.RP.A.2. Recognize and Connections: Background Knowledge: represent proportional In the first section (7.RP.A.1) students use various methods for finding unit Teaching Student-Centered relationships between rates and examining equivalent fractions. In this section, they make the Mathematics, Van de Wallle quantities. (M) connection between proportional relationships and graphs, tables, and Pages 154-178 function rules (in the form y=kx). They should be able to state what a point a. Decide whether two (x,y) or (1,r) means in the context of a proportional relationship on a graph. Lesson quantities are in a The connection is made to measurement when students convert between AIMS Proportional proportional relationship, e.g., different units of measure and write that relationship in the form of a table Reasoning: by testing for equivalent or graph. Proportional Practice (a) ratios in a table or graphing Rectangle Ratios (a) on a coordinate plane and Notes: Recognizing Proportions (a) observing whether the graph Students’ understanding of the multiplicative reasoning used with Patterns in Equivalent is a straight line through the proportions continues from 6th grade. Students determine if two quantities Fractions (a) origin. are in a proportional relationship from a table. Ratio (rate) tables are used Mixing Measures (d) to build equivalent ratios/rates. The Shadow Knows (c) b. Identify the constant of Proportional relationships can be represented symbolically (equation), proportionality (unit rate) in graphically (coordinate plane), in a table, in diagrams, and verbal tables, graphs, equations, descriptions. AIMS Looking at diagrams, and verbal Proportional relationships that are written in the form of an equation should The Thick of Things descriptions of proportional be written in the form y=kx. Proportions that are written in the form of two Shadow Lines relationships. equivalent fractions should be reserved for unit 3. Reflection Takes a Turn Students recognize that graphs that are not lines through the origin and c. Represent proportional tables in which there is not a constant ratio in the entries do not represent relationships by equations. proportional relationships. Special attention should be spent on analyzing the points (0, 0) and (1, For example, if total cost t is r) proportional to the number n where r is the unit rate. of items purchased at a Ratio and proportional reasoning strategies can be extended and applied to constant price p, the multi-step ratio and percent problems. relationship between the total
7.RP.A.2. Recognize and represent proportional relationships between quantities. (M) 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 Connections: In the first section (7.RP.A.1) students use various methods for finding unit rates and examining equivalent fractions. In this section, they make the connection between proportional relationships and graphs, tables, and function rules (in the form y=kx). They should be able to state what a point (x,y) or (1,r) means in the context of a proportional relationship on a graph. The connection is made to measurement when students convert between different units of measure and write that relationship in the form of a table or graph. Notes: Students’ understanding of the multiplicative reasoning used with proportions continues from 6th grade. Students determine if two quantities are in a proportional relationship from a table. Ratio (rate) tables are used to build equivalent ratios/rates. Proportional relationships can be represented symbolically (equation), graphically (coordinate plane), in a table, in diagrams, and verbal descriptions. Proportional relationships that are written in the form of an equation should be written in the form y=kx. Proportions that are written in the form of two equivalent fractions should be reserved for unit 3. Students recognize that graphs that are not lines through the origin and tables in which there is not a constant ratio in the entries do not represent proportional relationships. Special attention should be spent on analyzing the points (0, 0) and (1, r) where r is the unit rate. Ratio and proportional reasoning strategies can be extended and applied to multi-step ratio and percent problems. Background Knowledge: Teaching Student-Centered Mathematics, Van de Wallle Pages 154-178 Lesson AIMS Proportional Reasoning: Proportional Practice (a) Rectangle Ratios (a) Recognizing Proportions (a) Patterns in Equivalent Fractions (a) Mixing Measures (d) The Shadow Knows (c) AIMS Looking at The Thick of Things Shadow Lines Reflection Takes a Turn
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