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.3

Solve real-world and mathematical problems involving the four operations with rational numbers. Computations with rational numbers extend the rules for manipulating fractions to complex fractions.

• Access Ramp - Student Task
This task has students design an access ramp, which complies with the Americans with Disabilities Act (ADA) requirements and include pricing based on local costs.
• 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.
• 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.
• Framing a House - student task
This task has students recreate house plans on graph paper and then determine how many linear feet of wall plate material will be needed.
• 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 and Mixed Number Division Using Arrays
Students will learn how to solve word problems that involve dividing fractions and mixed numbers by using a visual model. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• 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.
• Modeling Fraction Division, Equal Groups, Group Size Unknown
The skill of dividing two fractions by groups of unknown size is the focus of this video. Students will learn how to solve a word problem using this process. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Modeling Fraction Division, Equal Groups, Number of Groups Unknown
This animated video shows students a model they can use to solve word problems involving the division of fractions. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Sharing Prize Money
This task requires students to be able to reason abstractly about fraction multiplication as it would not be realistic for them to solve it using a visual fraction model. Even though the numbers are too messy to draw out an exact picture, this task still provides opportunities for students to reason about their computations to see if they make sense
• 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

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.