Strand: THE NUMBER SYSTEM (6.NS)

Apply and extend previous understandings of multiplication and division of whole numbers to divide fractions by fractions (Standard 6.NS.1). Compute (add, subtract, multiply and divide) fluently with multi-digit numbers and decimals and find common factors and multiples (Standards 6.NS.2–4). Apply and extend previous understandings of numbers to the system of rational numbers (Standards 6.NS.5–8).

Standard 6.NS.5

Understand that positive and negative numbers are used together to describe quantities having opposite directions or values (for example, temperature above/below zero, elevation above/below sea level, credits/debits, positive/negative electric charge); use positive and negative numbers to represent quantities in real-world contexts, explaining the meaning of zero in each situation.

• 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.
• Chapter 3 - Student Workbook (UMSMP)
This is Chapter 3 of the Utah Middle School Math: Grade 6 student workbook. It covers the following topics: Extending the Number System.
• Chapter 3 - Mathematical Foundations (UMSMP)
This is Chapter 3 of the Utah Middle School Math: Grade 6 textbook. It provides a Mathematical Extending the Number System.
• Extending the Number Line
The purpose of this task is to understand that there are natural mathematical questions to ask for which there are no answers if we restrict ourselves to the positive numbers. The idea is to motivate the need for negative numbers and to see that there is a natural representation of them on the number line.
• Grade 6 Math Module 3: Rational Numbers (EngageNY)
Students are familiar with the number line and determining the location of positive fractions, decimals, and whole numbers from previous grades. Students extend the number line (both horizontally and vertically) in Module 3 to include the opposites of whole numbers. The number line serves as a model to relate integers and other rational numbers to statements of order in real-world contexts. In this module's final topic, the number line model is extended to two-dimensions, as students use the coordinate plane to model and solve real-world problems involving rational numbers.
• Grade 6 Unit 7: Rational Explorations: Numbers and their Opposites (Georgia Standards)
In this unit students will understand that positive and negative numbers are used together to describe quantities having opposite directions or values, understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates. Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line. Recognize that the opposite of the opposite of a number is the number itself.
• Harry Makes a Big Splash with Positive and Negative Numbers
A video about a swim relay team opens this lesson on combining positive and negative numbers. The classroom activity involves using a number line and a game board and die. Students will write equations that represent the addition of positive and negative numbers. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Integers on the Number Line 2
The goal of this task is to study, with a number line, why it makes sense for a whole number a that -(-a)=a.
• It's Warmer in Miami
The purpose of this task is for students to apply their knowledge of integers in a real-world context.
• Mile High
The first two parts of this task ask students to interpret the meaning of signed numbers and reason based on that meaning in a context where the meaning of zero is already given by convention.
• Rational Numbers on the Number Line
Riddles about a wallaby jumping contest must be solved in this lesson. Students must place fractions, decimals or mixed numbers representing the lengths of jumps, on a number line from -5 to +5. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• The Number System (6.NS) - 6th Grade Core Guide
The Utah State Board of Education (USBE) and educators around the state of Utah developed these guides for Mathematics Grade 6 - The Number System.
• Using the Pythagorean Theorem on the Cartesian Graph
Students place animals on a Cartesian graph in this interactive activity. They then use the Pythagorean Theorem to determine the distance between the animals. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.

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.