Grade 7 Mathematics Module 4, Topic A, Overview

Studying for Test

Topic A builds on students’ conceptual understanding of percent from Grade 6 (6.RP.3c), and relates 100% to “the whole.”  Students represent percents as decimals and fractions and extend their understanding from Grade 6 to include percents greater than 100%, such as 225%, and percents less than 1%, such as 1/2% or 0.5%.  They understand that, for instance, 225% means 225/100 , or equivalently, 2.25/1 = 2.25 (7.RP.A.1).  Students use complex fractions to represent non-whole number percents.   

Module 3’s focus on algebra prepares students to move from the visual models used for percents in Grade 6 to algebraic equations in Grade 7.  They write equations to solve multi-step percent problems and relate their conceptual understanding to the representation:  Quantity = Percent × Whole (7.RP.A.2c).  Students solve percent increase and decrease problems with and without equations (7.RP.A.3).  For instance, given a multi-step word problem where there is an increase of 20% and “the whole” equals $200, students recognize that $200 can be multiplied by 120% or 1.2 to get an answer of $240.  They use visual models, such as a double number line diagram, to justify their answers.  In this case, 100% aligns to $200 in the diagram and intervals of fifths are used (since 20% = 1/5) to partition both number line segments to create a scale indicating that 120% aligns to $240.  Topic A concludes with students representing 1% of a quantity using a ratio, and then using that ratio to find the amounts of other percents.  While representing 1% of a quantity and using it to find the amount of other percents is a strategy that will always work when solving a problem, students recognize that when the percent is a factor of 100, they can use mental math and proportional reasoning to find the amount of other percents. 

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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.c Represent proportional relationships by equations. For example, if total cost t is proportional to...
7.RP.3 Use proportional relationships to solve multistep ratio and percent problems. Examples: simple...

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