2008-2009 algebra i power point 2 unit 1.2

8/6/2019 2008-2009 Algebra I Power Point 2 Unit 1.2

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Algebra I Unit 1: Solving Equationsin One Variable

Learning Goal: 1.2

Michelle A. OMalley

8th Grade MathLeague Academy of Communication Arts

Greenville, South Carolina


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Unit 1: Learning Goal 1.2

Students will use the properties of real

numbers and the properties of equality tosimplify expressions, to prove mathematicalstatements, and to justify the steps of thesimplification.


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Unit 1: Learning Goal 1.2 Essential

Knowledge and Skills for Students

The students will use problem solving,reasoning, communication, connections and

representation to: Simplify mathematical expressions (numeric and

algebraic) and prove mathematical statements,using the properties to justify each step.

Identify the property that is illustrated by a givenmathematical statement.

Model the properties concretely.


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Unit 1: Learning Goal 1.2

Algebra I Standards: EA-2.5 and EA-1.1

EA-2.5 Carry out a procedure to simplifynumerical expressions, including expressionswith square roots, using the properties of realnumbers (including commutative, associative,and distributive).

EA-1.1 Communicate knowledge ofalgebraic relationships using mathematicalterminology appropriately.


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Identity and Equality Properties


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5/1 x 1/5 = 1 4/cx c/4 = 13/5 x 5/3 = 1 4/3 x 3/4 = 1

Note: the Multiplicative Inverse Property states

that for any number a/b, where a, b do not equal

0, there is exactly one number b/a such that the

product of a/b and b/a is 1.


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Multiplicative

Identity

Substitution

Property of

Equality

Multiplicative

Inverse

Multip

licativeProperty of Zero Ref

lexive AdditiveIdentity


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Example:

Evaluate

24 1 8 + 5(9 3 3). Name the property used in each step.24 1 8 + 5(9 3 3) = 24 1 8 + 5(3-3) Substitution

= 24 1 8 + 5(0) Substitution

= 24 8 + 5(0) Multiplicative Identity

(24 1 = 24)

= 24 8 + 0 Multiplicative Property of Zero(5 0 = 0)

= 16 + 0 Substitution (24 8 = 16)

= 16 Additive identity (16 + 0 = 16)


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The Distributive Property


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= 3 a + 3 4

= 3a + 12

= 2 x+ 2 3

= 2x+ 6

= 6 h 6 5

= 6h - 30


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6x Simplest form 16xy


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6x Simplest form 16xy

MentalMath How would you use the

Distributive Property to find

the product of 6 and 104 mentally? Show

your steps. 6(100 + 4)

600 + 24

624


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Commutative and Associative Properties


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Commutative (x)Commutative (+)

Commutative (+) Associative


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4x+ 2y 10a + 3n 10d+ 3c

The Commutative and Associative Properties can be used with other

properties when evaluating and simplifying expressions. For example,

Simplify 3c + 5(2+ c) == 3c + 5(2) + 5(c) Distributive Property

= 3c + 10 + 5c Multiply= 3c + 5c + 10 Commutative (+)

= (3c +5c) + 10 Associative (+)

= (3 + 5)c + 10 Distributive Property

= 8c + 10 Substitution


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Work Cited

Carter, John A., et. al. Glencoe MathematicsAlgebra I. New York: Glencoe/McGraw-

Hill, 2003. Greenville County Schools Math Curriculum

Guide

2008-2009 algebra i power point 2 unit 1.2

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