Strand: THE NUMBER SYSTEM (7.NS)

Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers (Standards 7.NS.1-3).

Standard 7.NS.2

Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.

• Chapter 1 - Mathematical Foundation (UMSMP)
This is Chapter 1 of the Utah Middle School Math: Grade 7 textbook. It provides a Mathematical Foundation for Probability, Percent, Rational Number Equivalence.
• Chapter 1 - Student Workbook (UMSMP)
This is Chapter 1 of the Utah Middle School Math: Grade 7 student workbook. It covers the following topics: Probability, Percent, Rational Number Equivalence.
• Chapter 2 - Mathematical Foundation (UMSMP)
This is Chapter 2 of the Utah Middle School Math: Grade 7 textbook. It provides a Mathematical Foundation for Rational Number Operations.
• Chapter 2 - Student Workbook (UMSMP)
This is Chapter 2 of the Utah Middle School Math: Grade 7 student workbook. It covers Rational Number Operations.
• Decimal Expansions of Fractions
The goal of this task is to convert some fractions to decimals and then make conjectures about which fractions have terminating decimal expansions (as well as the length of those decimals).
• Distributive Property of Multiplication
The goal of this task is to study the distributive property for products of whole numbers, focusing on using geometry to help understand why (-1) x (-1) = 1.
• Drill Rig
The purpose of this task is to provide a context for multiplying and dividing signed rational numbers, providing a means for understanding why the signs behave the way they do when finding products.
• Equivalent fractions approach to non-repeating decimals
This task is most suitable for instruction. The purpose of the task is to get students to reflect on the definition of decimals as fractions (or sums of fractions), at a time when they are seeing them primarily as an extension of the base-ten number system and may have lost contact with the basic fraction meaning. Students also have their understanding of equivalent fractions and factors reinforced.
• Grade 7 Math Module 2: Rational Numbers (EngageNY)
In Grade 6, students formed a conceptual understanding of integers through the use of the number line, absolute value, and opposites and extended their understanding to include the ordering and comparing of rational numbers.This module uses the Integer Game: a card game that creates a conceptual understanding of integer operations and serves as a powerful mental model students can rely on during the module. Students build on their understanding of rational numbers to add, subtract, multiply, and divide signed numbers. Previous work in computing the sums, differences, products, and quotients of fractions serves as a significant foundation.
• Grade 7 Unit 1: Operations with Rational Numbers (Georgia Standards)
The units in this instructional framework emphasize key standards that assist students to develop a deeper understanding of numbers. They learn to express different representations of rational numbers (e.g., fractions, decimals, and percents) and interpret negative numbers in everyday context (e.g., sea level change). The big ideas that are expressed in this unit are integrated with such previous knowledge as estimation, mental and basic computation. All of these concepts need to be reviewed throughout the year.
• Modeling Fraction Division Using Comparison, Group Number Unknown
In this lesson students will learn how to solve a word problem involving the division of fractions by viewing an animation about a hedgehog's hibernation. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Number Sets video
The video introduces and explains the topic.
• Repeating decimal as approximation
The purpose of the task is to have students reflect on the meaning of repeating decimal representation through approximation. A formal explanation requires the idea of a limit to be made precise, but 7th graders can start to wrestle with the ideas and get a sense of what we mean by an "infinite decimal." Students can make observations which reinforce the topic at hand as well as lay groundwork for later developments.
• Repeating Decimal Rings
In this interactive activity you will explore the patterns that occur when expanding seventh and thirteenth fractions into decimals. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Repeating or Terminating?
The purpose of this task is to understand, in some concrete cases, why terminating decimal numbers can also be written as repeating decimals where the repeating part is all 9's.
• Temperature Change
The goal of this task is to provide a context for interpreting the expressions that match the last part of the standard 7.NS.2.b, ''Interpret quotients of rational numbers by describing real-world contexts,'' though in this case the numerator and denominator are integers. Because of the context, students will also gain experience working with rates.
• The Number System (7.NS) - 7th Grade Core Guide
The Utah State Board of Education (USBE) and educators around the state of Utah developed these guides for Mathematics Grade 7 - The Number System
• Why is a Negative Times a Negative Always Positive?
The purpose of this task is for students to understand the reason it makes sense for the product of two negative numbers to be positive.

http://www.uen.org - in partnership with Utah State Board of Education (USBE) and Utah System of Higher Education (USHE).  Send questions or comments to USBE Specialist - Lindsey  Henderson and see the Mathematics - Secondary website. For general questions about Utah's Core Standards contact the Director - Jennifer  Throndsen.

These materials have been produced by and for the teachers of the State of Utah. Copies of these materials may be freely reproduced for teacher and classroom use. When distributing these materials, credit should be given to Utah State Board of Education. These materials may not be published, in whole or part, or in any other format, without the written permission of the Utah State Board of Education, 250 East 500 South, PO Box 144200, Salt Lake City, Utah 84114-4200.