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Mathematics - Secondary Curriculum Mathematics Grade 7
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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.1

Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a horizontal or vertical number line diagram.

  • Adding Integers
    This Teaching Channel video and presentation help students to add and subtract integers using a number line and a song with motions. (14 min.)
  • Adding Rational Numbers on the Number Line
    In this interactive students must solve riddles about a wallaby jumping contest. But they must find equivalent fractions and common denominators to complete the riddle. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
  • Addition and Subtraction of Integers
    A card game in which positive and negative numbers are added together is the subject of this video teaching students how to add and subtract integers. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
  • Bookstore Account
    The purpose of this task is for students to use algebra and the number line to understand why it makes sense that we sometimes represent debt using negative numbers. If we agree that depositing money in an account adds a positive number to the balance, and buying somethings subtracts a positive number from the balance, then it is natural to represent debt with negative numbers.
  • 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.
  • Comparing Freezing Points
    This task is appropriate for assessing student's understanding of differences of signed numbers.
  • Differences and Distances
    The purpose of this task is to help students connect the distance between points on a number line with the difference between the numbers. This task assumes that students are familiar with the idea that differences between integers correspond to distances between them on the number line and asks them to analyze a situation involving non-integer quantities.
  • Differences of Integers
    The goal of this task is to subtract integers in a real world context. It will be very helpful for students to use number lines for this task.
  • Distances Between Houses
    The purpose of this task is for students to solve a problem involving distances between objects whose positions are defined relative to a specified location and to see how this kind of situation can be represented with signed numbers.
  • Distances on the Number Line 2
    The purpose of this task is meant to reinforce students' understanding of rational numbers as points on the number line and to provide them with a visual way of understanding that the sum of a number and its additive inverse (usually called its "opposite") is zero. Students should have lots of opportunities to represent adding specific rational numbers before they work on answering this one.
  • 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.
  • IXL Game: Rational numbers
    This game for seventh graders will help them understand rational numbers, specifically how to add and subtract rational numbers. This is just one of many online games that supports the Utah Math core. Note: The IXL site requires subscription for unlimited use.
  • Operations on the number line
    The purpose of this task is to help solidify students' understanding of signed numbers as points on a number line and to understand the geometric interpretation of adding and subtracting signed numbers.
  • Rounding and Subtracting
    This task addresses what happens to rounding discrepancies when arithmetic is performed on rounded numbers and would be a good problem for classroom discussion.
  • What's Your Sign: Integer Addition
    In this filmed lesson students master integer addition using number lines as a visual tool. (5 minutes)
  • Zero Pairs, Manipulatives, and a Real-World Scenario
    In this filmed lesson, students use manipulatives and zero pairs to understand integer subtraction. (6 minutes)

UEN logo - 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.