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.