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).
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 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.
• Comparing Freezing Points
This task is appropriate for assessing student's understanding of differences of signed numbers.
• 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).
• 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.
• 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.
• 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.
In order to assist educators with the implementation of the Common Core, the New York State Education Department provides curricular modules in Pre-K-Grade 12 English Language Arts and Mathematics that schools and districts can adopt or adapt for local purposes.
• 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.
• Increasing and Decreasing Quantities by a Percent
This lesson unit is intended to help educators assess how well students are able to interpret percent increase and decrease.
• 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.
• 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.
• Number Sets video
The video introduces and explains the topic.
• 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.
• 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.
• 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.
• 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
In this task, students will look at problems in which the answer might be 100 divided by 6. They must decide whether this is true, and what would be a sensible answer to write down.
• 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
• Using Positive and Negative Numbers in Context
This lesson unit is intended to help educators assess how well students are able to understand and use directed numbers in context. It is intended to help identify and aid students who have difficulties in ordering, comparing, adding, and subtracting positive and negative integers.