Unit 3: Expressions and Equations
Dive deep into algebraic expressions and equations, mastering exponents and mathematical modeling
Unit 3 Overview
In this unit of study, you will learn about expressions and how they bring numbers and operations together. You will, therefore, be able to use exponents to tell in repeated multiplication how fast numbers grow and use this to express the multiplication in the base.
You will also see how to write algebraic expressions using words and decompose an expression into parts so that you understand what it means. We will use properties of operations to rewrite expressions into equivalent forms, which might seem to make problems simpler or more complex than they do in their original state but don't change their answers.
We will then proceed to apply real-world problems into this new mathematics skill and observe how solutions are viewed, first using models and diagrams.
Learning Objectives
- Understand what exponents are and how they represent repeated multiplication
- Evaluate expressions containing exponents using order of operations
- Translate verbal phrases into algebraic expressions
- Identify parts of algebraic expressions (terms, coefficients, constants)
- Use properties to identify and generate equivalent expressions
Your Progress
Representing Repeated Multiplication with Exponents
What You'll Learn:
- Understanding what exponents are and how they represent repeated multiplication
- Writing expressions using exponents (2 x 2 x 2 = 2³)
- Identifying base and exponent in an exponential expression
Khan Academy - Intro to Exponents
This video introduces the concept of exponents, explaining what they are and how they work. It covers basic exponent notation and provides clear examples to help you understand the concept.
Watch on YouTubeMath Antics - Exponents
This video explains the laws of exponents, including multiplication, division, zero exponents, and negative exponents. It provides a step-by-step guide to solving problems using these rules.
Watch on YouTubeEvaluating Expressions Containing Exponents
What You'll Learn:
- Substituting values for variables in expressions with exponents
- Applying the order of operations (PEMDAS) to solve expressions with exponents
- Evaluating expressions with positive, negative, and fractional exponents
Khan Academy - Evaluating Expressions with Exponents
This video explains how to evaluate algebraic expressions that include exponents, showing how to substitute values for variables and follow the correct order of operations.
Watch on YouTubeMath Antics - Order of Operations
This video covers the order of operations (PEMDAS), including how to correctly handle exponents when evaluating expressions. It uses clear examples to show each step.
Watch on YouTubeTranslating Verbal Phrases into Algebraic Expressions
What You'll Learn:
- Identifying keywords that indicate mathematical operations (e.g., "sum" means addition, "product" means multiplication)
- Converting word problems into algebraic expressions
- Recognizing how to write expressions that model real-world situations
Khan Academy - Writing Expressions with Variables
This video explains how to create and write algebraic expressions using variables, showing how to translate phrases and word problems into mathematical expressions.
Watch on YouTubeMath Antics - Algebra Basics: What Are Variables?
This video introduces variables, explaining what they are and how they are used in algebra. It covers basic examples to help students understand how variables represent unknown values.
Watch on YouTubeIdentifying Parts of a Given Expression
What You'll Learn:
- Understanding and identifying terms, coefficients, constants, factors, and variables in an algebraic expression
- Breaking down complex expressions into their basic parts
- Recognizing and defining the role of each part of an expression
Khan Academy - Parts of Algebraic Expressions
This video explains the key components of algebraic expressions, including terms, factors, coefficients, and constants. It helps students identify these parts in various examples.
Watch on YouTubeMath Antics - Expressions, Equations, and Inequalities
This video introduces the basics of expressions, equations, and inequalities, explaining how they are different and how to solve each type. It uses simple examples for clarity.
Watch on YouTubeUsing Properties to Identify Equivalent Expressions
What You'll Learn:
- Applying the distributive property, commutative property, and associative property to simplify expressions
- Identifying when two expressions are equivalent
- Understanding how to combine like terms to generate equivalent expressions
Khan Academy - Equivalent Expressions
This video explains how to identify and create equivalent expressions by using properties like the distributive property. It helps students understand how different expressions can represent the same value.
Watch on YouTubeMath Antics - Combining Like Terms
This video teaches how to simplify algebraic expressions by combining like terms. It shows how to identify like terms and add or subtract them to create a simplified expression.
Watch on YouTubeUsing Properties and Mathematical Models to Generate Equivalent Expressions
What You'll Learn:
- Using the distributive property to expand and factor expressions
- Combining like terms to simplify expressions
- Modeling real-world situations with equivalent algebraic expressions
Khan Academy - Distributive Property
This video explains how to use the distributive property to simplify algebraic expressions, including examples of distributing a number across terms inside parentheses.
Watch on YouTubeMath Antics - The Distributive Property
This video demonstrates the distributive property, using clear visuals and examples to show how multiplying a value across parentheses works. It covers both positive and negative values.
Watch on YouTubeMy Practice Problems
Unit 3 Practice Problems
Open in DriveReview: Worksheets + Practice
Khan Academy: Expressions and Variables
Comprehensive practice with expressions and variables for 6th grade
Practice NowKhan Academy: Exponents and Radicals
Pre-algebra level practice with exponents and radicals
Learn MoreMath-Aids: Algebraic Expressions
Printable worksheets for algebraic expressions practice
Get WorksheetsMath-Drills: Evaluating Algebraic Expressions
Worksheets for evaluating algebraic expressions
Practice