Numerical and Algebraic Expressions and Equations
Numerical and Algebraic Expressions and Equations
? 2011 Carnegie Learning ? 2011 Carnegie Learning
Sometimes it's hard to tell how a person is feeling when you're not talking to them face to face. People use emoticons in emails and chat messages to show different facial expressions. Each expression shows a different kind of emotion. But you probably already knew
that. ; )
6.1 What's It Really Saying? Evaluating Algebraic Expressions ................................295
6.2 Express Math
Simplifying Expressions Using
Distributive Properties ...............................................303
6.3 Reverse Distribution Factoring Algebraic Expressions ................................ 309
6.4 Are They the Same or Different? Verifying That Expressions Are Equivalent ...................317
6.5 It is time to justify!
Simplifying Algebraic Expressions Using
Operations and Their Properties .................................325
293
Models Worked Examples
Peer Analysis Talk the Talk Technology
Chapter 6 Overview
This chapter focuses on the use of properties to interpret, simplify, add, subtract, and factor linear expressions.
Lessons
CCSS Pacing
Highlights
6.1
Evaluating Algebraic Expressions
6.EE.6 7.NS.3
Simplifying
Expressions 7.NS.3
6.2
Using
7.EE.1
Distributive 7.EE.2
Properties
6.3
Factoring Algebraic Expressions
7.EE.1 7.EE.2
Verifying
6.4
That Expressions
Are
7.EE.1 7.EE.2
Equivalent
Simplifying
Algebraic
6.5
Expressions Using
Operations
7.EE.1 7.EE.2
and Their
Properties
This lesson explores the use of algebraic
expressions as efficient representations
for repeating patterns.
1
X
X
Questions ask students to use tables to
organize values when evaluating algebraic
expressions.
This lesson reviews all aspects of the distributive properties.
1
Questions ask students to analyze
X
X
models and explore various strategies for
simplifying expressions to gain a deep
understanding of how the properties work.
This lesson continues the development
1
of distributive properties to simplify and
X
factor expressions.
This lesson explores different methods,
1
including the use of graphing calculators, to determine if expressions are
equivalent.
X
X
This lesson requires the use of operations
1
and properties to justify the steps of the simplification process to determine if
X
expressions are equivalent.
? 2011 Carnegie Learning
293A ? Chapter 6 Numerical and Algebraic Expressions and Equations
Skills Practice Correlation for Chapter 6
Lessons
Problem Set
Evaluating
6.1
Algebraic
Expressions
1?6 7?14 15?20 21?26
Simplifying
6.2
Expressions UsingDistributive
Properties
1?10 11?20 21?26
Factoring
6.3
Algebraic
Expressions
VerifyingThat 6.4 ExpressionsAre
Equivalent
Simplifying Algebraic 6.5 ExpressionsUsing Operationsand TheirProperties
1?10 11?20 21?26 27?32 1?6 7?12 13?18
1?8
9?14
Objective(s)
Vocabulary Definevariablesandwritealgebraicexpressions Evaluatealgebraicexpressions Completetablesofexpressions Evaluatealgebraicexpressionsforgivenquantities Vocabulary Drawmodelsandcalculateorsimplifyexpressions UsetheDistributivePropertytorewriteexpressions Evaluateexpressionsforgivenvalues Vocabulary RewriteexpressionsbyfactoringouttheGCF Simplifyexpressionsbycombiningliketerms Evaluateexpressionsforgivenvaluesbyfactoring Evaluateexpressionsforgivenvaluesbycombiningliketerms Determinewhetherexpressionsareequivalentbyevaluatingfor givenvalues Determinewhetherexpressionsareequivalentbysimplifying Determinewhetherexpressionsareequivalentbygraphing
Completejustificationtablestodetermineifexpressionsare equivalent Givejustificationofstepstodetermineifexpressionsareequivalent bysimplifying
? 2011 Carnegie Learning
Chapter 6 NumericalandAlgebraicExpressionsandEquations ? 293B
? 2011 Carnegie Learning
294 ? Chapter 6 Numerical and Algebraic Expressions and Equations
What's It Really Saying?
Evaluating Algebraic Expressions
Learning Goal
In this lesson, you will:
Evaluate algebraic expressions.
Key Terms
variable algebraic expression
evaluate an algebraic
expression
Essential Ideas
? An algebraic expression is a mathematical phrase
involving at least one variable, and it can contain numbers and operational symbols.
? An algebraic expression is often used to represent
situations in which the same mathematical process is performed over and over again.
? To evaluate an expression, you replace each variable
in the expression with numbers and then perform all possible mathematical operations.
? When you substitute known measures into a formula
and simplify it to determine a new measure, you are evaluating the formula.
Common Core State Standards for Mathematics
6.EE Expressions and Equations Reason about and solve one-variable equations and inequalities.
6. Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.
7.NS The Number System Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.
3. Solve real-world and mathematical problems involving the four operations with rational numbers.
? 2011 Carnegie Learning
6.1 Evaluating Algebraic Expressions ? 295A
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