Strand: EXPRESSIONS AND EQUATIONS (6.EE)

Apply and extend previous understandings of arithmetic to algebraic expressions involving exponents and variables (Standards 6.EE.1–4). They reason about and solve one-variable equations and inequalities (Standards 6.EE.5–8). Represent and analyze quantitative relationships between dependent and independent variables in a real-world context (Standard 6.EE.9).

Standard 6.EE.3

Apply the properties of operations to generate equivalent expressions. For example, apply the distributive property to the expression 3(2 + x) to produce the equivalent expression 6 + 3x; apply the distributive property to the expression 24x + 18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations to y + y + y to produce the equivalent expression 3y.

• Algebra Four
This lesson contains a game activity designed to help students practice solving algebraic equations.
• Anna in D.C.
The purpose of this task is to give students an opportunity to solve a multi-step percentage problem that can be approached in many ways.
• 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.
• Commutative and Associative Equations
This lesson focuses on how to rearrange and combine parts of algebraic expressions by using the commutative and associative properties of addition. NOTE: You have to create a Free PBS Account to view this web page, but it is easy to do and worth the effort.
• 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.
• Expressions and Equations (6.EE) - 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 - Expressions and Equations.
• Grade 6 Math Module 4: Expressions and Equations (EngageNY)
In Module 4, Expressions and Equations, students extend their arithmetic work to include using letters to represent numbers in order to understand that letters are simply "stand-ins" for numbers and that arithmetic is carried out exactly as it is with numbers. Students explore operations in terms of verbal expressions and determine that arithmetic properties hold true with expressions because nothing has changedthey are still doing arithmetic with numbers. Students determine that letters are used to represent specific but unknown numbers and are used to make statements or identities that are true for all numbers or a range of numbers.
• Reciprocity
The purpose of this task is to help students understand why dividing by a fraction gives the same result as multiplying by its reciprocal. This is accomplished by writing the division equation along with related multiplication equations and diagrams showing the situation for several different contexts.

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.