Mathematics Grade 6
Educational Links
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 multidigit 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.4
Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1–100 with a common factor as a multiple of a sum of two whole numbers with no common factor. For example, express 36 + 8 as 4 (9 + 2).

Adding Multiples
This task is appropriate for assessing students understanding of repeated reasoning and generalizing that understanding to prepare them for deeper algebraic thinking needed in the expressions and equations domain.

Bake Sale
This problem requires students to apply the concepts of factors and common factors in a context.

Chapter 0  Mathematical Foundations (UMSMP)
This is Chapter 0 of the Utah Middle School Math: Grade 6 textbook. It provides a Mathematical Foundation for Fluency.

Chapter 0  Student Workbook (UMSMP)
This is Chapter 0 of the Utah Middle School Math: Grade 6 student workbook. It covers the following topics: Fluency.

Chapter 6  Mathematical Foundations (UMSMP)
This is Chapter 6 of the Utah Middle School Math: Grade 6 textbook. It provides a Mathematical Foundation for Expressions and Equations.

Chapter 6  Student Workbook (UMSMP)
This is Chapter 6 of the Utah Middle School Math: Grade 6 student workbook. It covers the following topics: Expressions and Equations.

Distributive Property with Variables
Algebra tiles are used to generate equivalent expressions using the distributive property in this instructional video. The classroom activity asks student to further explore the distributive property. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.

Equivalent Expressions with the Distributive Property
This animated Math Shorts video explains how the distributive property can help students model and create equivalent expressions. In the accompanying classroom activity, students play a quick game where they identify common factors within an expression and work on a series of problems that expand their understanding of how to apply the distributive property. While the problems begin with whole number expressions, students soon work toward algebraic notation and eventually develop the idea that ax + bx can be rewritten as x(a + b). NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.

Factors
This lesson is designed to help students understand factors of whole numbers.

Factors and Common Factors
This task requires students to apply the concepts of factors and common factors in a context.

Finding Factors
This lesson plan's activities give students practice in finding the factors of whole numbers.

Grade 6 Unit 1: Number System Fluency (Georgia Standards)
In this unit students will find the greatest common factor of two whole numbers less than or equal to 100. Find the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1100 with a common factor as a multiple of a sum of two whole numbers with no common factor. Interpret and compute quotients of fractions. Solve word problems involving division of fractions by fractions using visual fraction models and equations to represent the problem. Fluently divide multidigit numbers using the standard algorithm. Fluently add, subtract, multiply, and divide multidigit decimals using the standard algorithm for each operation.

Grade 6 Unit 3: Expressions (Georgia Standards)
In this unit students will represent repeated multiplication with exponents. Evaluate expressions containing exponents to solve mathematical and real world problems. Translate verbal phrases and situations into algebraic expressions. Identify the parts of a given expression. Use the properties to identify equivalent expressions. Use the properties and mathematical models to generate equivalent expressions.

Greatest Common Factor
This video from Math Shorts shows students how to find the greatest common factor of 2 numbers. The classroom activity shows them how Venn diagrams, multiplication and prime factors can also be used to find the greatest common factor. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.

Multiples and Common Multiples
This task requires students to apply the concepts of multiples and common multiples in a context.

Patterns of Factors
This interactive activity asks students to sort numbers based on the number of factors or prime factors. They are asked to also identify one reallife example of the usefulness of divisibility. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.

Sets and the Venn Diagram
This lesson is designed to help students understand the ideas surrounding sets and Venn diagrams.

The Florist Shop
Students are given the scenario of a florist ordering roses and asked to find the smallest number of bunches she could order and explain their reasoning.

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.
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 
Joleigh Honey
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
841144200.