Grade 7 Mathematics Module 4, Topic B, Overview

In Topic B, students create algebraic representations and apply their understanding of percent from Topic A to interpret and solve multi-step word problems related to markups or markdowns, simple interest, sales tax, commissions, fees, and percent error (7.RP.A.3, 7.EE.B.3).  They apply their understanding of proportional relationships from Module 1, creating an equation, graph, or table to model a tax or commission rate that is represented as a percent (7.RP.A.1, 7.RP.A.2).  Students solve problems related to changing percents and use their understanding of percent and proportional relationships to solve the following:  A soccer league has 300 players, 60% of whom are boys.  If some of the boys switch to baseball, leaving only 52% of the soccer players as boys, how many players remain in the soccer league?  Students determine that, initially, 100% = 60% = 40% of the players are girls and 40% of 300 equals 120.  Then, after some boys switched to baseball, 100% - 52% of the soccer players are girls, so 0.48p = 120, or p = 120/0.48.  Therefore, there are now 250 players in the soccer league. 

In Topic B, students also apply their understanding of absolute value from Module 2 (7.NS.A.1b) when solving percent error problems.  To determine the percent error for an estimated concert attendance of 5,000 people, when actually 6,372 people attended, students calculate the percent error as:
 (|5000 - 6372|)/|6372|, which is about 21.5%. 

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Common Core Learning Standards

CCLS State Standard
7.RP.1 Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and...
7.RP.2 Recognize and represent proportional relationships between quantities.
7.RP.3 Use proportional relationships to solve multistep ratio and percent problems. Examples: simple...

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