Grade 7 Module 4: Percent and Proportional Relationships

In Module 4, students deepen their understanding of ratios and proportional relationships from Module 1 by solving a variety of percent problems. They convert between fractions, decimals, and percents to further develop a conceptual understanding of percent and use algebraic expressions and equations to solve multi-step percent problems. An initial focus on relating 100% to “the whole” serves as a foundation for students. Students begin the module by solving problems without using a calculator to develop an understanding of the reasoning underlying the calculations. Material in early lessons is designed to reinforce students’ understanding by having them use mental math and basic computational skills. To develop a conceptual understanding, students use visual models and equations, building on their earlier work with these. As the lessons and topics progress and students solve multi-step percent problems algebraically with numbers that are not as compatible, teachers may let students use calculators so that their computational work does not become a distraction.  (Excerpt taken from NYS Engage website)

Engage worksheets and Video Lessons for all lessons covered in Module

 http://www.onlinemathlearning.com/common-core-math-worksheets-grade7.html

§  A markup is the amount of increase in a price.

§  A markdown is the amount of decrease in a price.

§  The original price is the starting price.  It is sometimes called the cost or wholesale price.

§  The selling price is the original price plus the markup or minus the markdown. 

§  The markup rate is the percent increase in the price, and the markdown rate (discount rate) is the percent decrease in the price.

§  Most markup problems can be solved by the equation:  

          Selling Price =(1 + m)(Whole), where m is the markup rate, and the whole is the original price.

§  Most markdown problems can be solved by the equation:  

         Selling Price =(1 - m)(Whole), where m is the markdown rate, and the whole is the original price.