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New York State Common Core
7
Mathematics Curriculum
GRADE
GRADE 7 • MODULE 4
Topic D:
Population, Mixture, and Counting Problems Involving Percents 7.RP.A.2c, 7.RP.A.3, 7.EE.B.3 Focus Standard:
7.RP.A.2c
Recognize and represent proportional relationships between quantities. c.
Instructional Days:
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 cost and the number of items can be expressed as t = pn.
7.RP.A.3
Use proportional relationships to solve multi-step ratio and percent problems. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error.
7.EE.B.3
Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers, fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on the exact computation.
3
Lesson 16: Population Problems (P)
1
Lesson 17: Mixture Problems (P) Lesson 18: Counting Problems (P)
Related Topics: More Lesson Plans for Grade 7 Common Core Math 1
Lesson Structure Key: P-Problem Set Lesson, M-Modeling Cycle Lesson, E-Exploration Lesson, S-Socratic Lesson
Topic D: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org
Population, Mixture, and Counting Problems Involving Percents 3/19/14 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
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Topic D
NYS COMMON CORE MATHEMATICS CURRICULUM
7•4
Topic D provides students with additional experience solving word problems related to percents. Students see the relevance and purpose of their algebraic work in Module 3, as they use it to efficiently solve multistep word problems involving percents (7.RP.A.3, 7.EE.B.3). They also see percent applied to other areas of math and science. In Lessons 16 and 17, students represent and solve population and mixture problems using algebraic expressions and equations, along with their foundational understanding from Topic A of the expression (7.RP.A.2c). Topic D concludes with Lesson 18, where students solve counting problems involving percents, preparing them for future work with probability.
Topic D: Date: © 2013 Common Core, Inc. Some rights reserved. commoncore.org
Population, Mixture, and Counting Problems Involving Percents 3/19/14 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.
228
