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.7

Understand ordering and absolute value of rational numbers.

• Above and Below Sea Level
The purpose of this task is to help students interpret signed numbers in a context as a magnitude and a direction and to make sense of the absolute value of a signed number as its magnitude.
• Absolute Value
This Math Shorts video uses a number line and a real-life example to explain the absolute value of a number. The classroom activity then has the student play a game where they move a penny in both positive and negative directions on a number line. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• 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.
• 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.
• Comparing Temperatures
The purpose of the task is for students to compare signed numbers in a real-world context. It could be used for either assessment or instruction if the teacher were to use it to generate classroom discussion.
• Fractions and Decimals from 0 to 1 on the Vertical Number Line
In this interactive students must solve riddles about jumping fleas by placing fractions and decimals on a 0 to 1 number line. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• Fractions on the Number Line
In this task students are given a number line and they must label a number of fractions on the line. When given a selection of statements about inequality they must state which are true.
• 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.
• Integers on the Number Line 1
Given a number line, students are asked to find and label two numbers. Then given several inequalities, they must decide whether the inequality is true or false.
• Jumping Flea
This purpose of this task is to help students understand the absolute value of a number as its distance from 0 on the number line. The context is not realistic, nor is meant to be; it is a thought experiment to help students focus on the relative position of numbers on the number line.
• 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.
• Sample Assessment Task: Cake Weighing
This four-part sample assessment task provides a novel situation in an authentic context that all students can understand, even though it is not likely to be in their everyday experience. Use the navigation at the upper right of this page to access the task.
• 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.