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Page 1: UUnniittUnit Unit BookBBooookkBook ~~~~ Real …tigertweets.weebly.com/uploads/3/2/2/7/32272677/unit_2_algebra...∞ Properties of Real Numbers* Distributive Property Commutative Property

Name: ______Name: ______Name: ______Name: ______________________________________________________________________________________________________________________________________________ DateDateDateDate ________________________________________________________ BlockBlockBlockBlock ________________________________

∞ Mathematics ∞ Virginia Beach City Public SchoolsVirginia Beach City Public SchoolsVirginia Beach City Public SchoolsVirginia Beach City Public Schools ∞

UnitUnitUnitUnit BookBookBookBook ~~~~ Real Numbers and AReal Numbers and AReal Numbers and AReal Numbers and Algebraic Conceptslgebraic Conceptslgebraic Conceptslgebraic Concepts For all vocabulary and concepts you must include: The definition from your textbook glossary

AND notes, symbols, examples, or a PERSONAL REFLECTION (what the concept means to you ~in

your own words) for each of the following: Unit Vocabulary & Concepts:

∞ Real Numbers

∞ Rational Number

∞ Whole Numbers

∞ Integers

∞ Natural Numbers

∞ Irrational Numbers

∞ Absolute value

∞ Expression

∞ Simplify

∞ Evaluate

∞ Order of Operations

∞ Variables

∞ Term

∞ Coefficient

∞ Like Terms

∞ Constants

∞ Equation

∞ Solution

∞ Inverse Operation(s)

∞ Properties of Real Numbers*

� Distributive Property

� Commutative Property of Addition

� Commutative Property of Multiplication

� Associative Property of Addition

� Associative Property of Multiplication

� Additive Identity

� Multiplicative Identity

� Multiplicative Inverse/Reciprocal

� Additive Inverse

� Multiplicative Property of Zero

(Zero Product Property)

Enduring UnderstandingsEnduring UnderstandingsEnduring UnderstandingsEnduring Understandings

∞ Reliable mathematical truths and rules help

us work with numbers.

∞ Algebraic language is necessary for building

the mathematical communication

foundations of relationships and patterns.

∞ Algebraic representations generalize

patterns and relationships.

∞ Mathematical relationships and can be

represented in tables, graphs, words and

symbolic equations may be used in

problem solving.

∞ Mathematical patterns can be identified in

order to predict the value of variables.

Essential QuestionsEssential QuestionsEssential QuestionsEssential Questions

∞ How do the properties of real numbers help

us justify the process of simplifying

expressions?

∞ Why are mathematical rules necessary?

∞ Why is it important to use mathematical

language precisely and appropriately?

∞ Why are equations needed and useful?

∞ What are the relationships between graphs,

tables, words and equations?

∞ When should patterns be represented in

graphs, tables, words and symbolic

equations?

∞ How do operations with integers compare to

operations with whole numbers?

∞ How can models represent mathematical

ideas?

* use chart on back page for the property definitions

Page 2: UUnniittUnit Unit BookBBooookkBook ~~~~ Real …tigertweets.weebly.com/uploads/3/2/2/7/32272677/unit_2_algebra...∞ Properties of Real Numbers* Distributive Property Commutative Property

Name: ______Name: ______Name: ______Name: ______________________________________________________________________________________________________________________________________________ DateDateDateDate ________________________________________________________ BlockBlockBlockBlock ________________________________

∞ Mathematics ∞ Virginia Beach City Public SchoolsVirginia Beach City Public SchoolsVirginia Beach City Public SchoolsVirginia Beach City Public Schools ∞

At the conclusion of this unit, the student will:At the conclusion of this unit, the student will:At the conclusion of this unit, the student will:At the conclusion of this unit, the student will:

know: be able to do:

∞ Absolute value (SOL 7.5, CE 7A.4)

∞ Additive Identity Property (SOL 7.3, NS 7A.3)

∞ Additive Inverse (SOL 8.2, NS 7A.2)

∞ Algebraic expression (SOL 7.20, 7.21)

∞ Associative property (SOL 7.3, NS 7A.3)

∞ Coefficient (SOL 6.23c)

∞ Constant (SOL 8.18, PF 7A.25, 7A.26)

∞ Commutative property (SOL 7.3, NS 7A.3)

∞ Dependent variable (SOL 8.18, PF 7A.25, 7A.26a)

∞ Distributive property (SOL 7.3, NS 7A.3)

∞ Equation (SOL 6.23, 7.22, PF 7A.20)

∞ Evaluate (SOL 7.22)

∞ Expression (SOL 7.21, NS 7A.1a)

∞ Formula (SOL 8.17, PF 7A.24)

∞ Graph (SOL 7.19, PF 7A.19)

∞ Independent variable (SOL 8.18, PF 7A.25, 7A.26a)

∞ Integer (SOL 6.3c, NS 7A.2)

∞ Inverse operation (SOL 7.22a, PF 7A.20)

∞ Like terms (SOL 7.22)

∞ Multiplicative Identity Property (SOL 7.3, NS 7A.3)

∞ Multiplicative Property of Zero (SOL 7.3, NS 7A.3)

∞ Opposite (SOL 8.2, NS 7A.2)

∞ Order of Operations (SOL 7.2, 8.4, NS 7A.1a)

∞ Solution (SOL 8.15, PF 7A.20)

∞ Table (SOL 8.14, PF 7A.19)

∞ Term (SOL 6.23c, 7.21)

∞ Variable (SOL 5.21a)

∞ x and y axis (SOL 8.16, PF 7A.23)

∞ Simplify numerical and algebraic expressions

using order of operations. (VBCPS NS 7A.1a,

SOL 8.1)

∞ Experience operations with real numbers and

expressions in order to make generalizations

leading to the use of properties of real numbers.

(VBCPS NS 7A.3, SOL 7.3)

∞ Form generalizations of operations with

integers by using multiple models to add,

subtract, multiply and divide integers.

(VBCPS CE 7A.3)

∞ Use integer rules to simplify a numerical

expression. (VBCPS CE 7A.3)

∞ Simplify algebraic expressions using order of

operations, combining like terms and replacing

values of variables. (VBCPS CE 7A.5, SOL 7.2,

8.4)

∞ Solve and write one and two-step equations

using multiple strategies. (VBCPS PF 7A.20, SOL

8.15)

∞ Create one and two-step equations that reflect

real life problems and use these equations to

solve problems. (VBCPS PF 7A.20, SOL 8.15)

∞ Construct tables, graphs and symbolic

expressions that describe patterns of change in

variables. (VBCPS PF 7A.19, SOL 8.14)

∞ Students will use the language of the discipline

appropriately and accurately. (VBCPS PF 7A.25,

SOL 8.18)

MA.6.CE.6.1 The student will determine the greatest common factor of two or more numbers using prime

factorization

Composite Number A number with more than two factors (3 or more factors).

Factor A number that is multiplied by another number.

Greatest Common

Factor The largest of the common factors of two or more numbers.

Prime Number A whole number greater than 1 that has exactly two unique factors, 1 and the number itself.

Prime Factoring A composite number expressed as a product of prime factors. For example, the prime

factorization of 63 is 3( 3)(7) or 32 ( 7)

MA.6.CE.6.2 The student will multiply and divide fractions and mixed numbers (SOL 6.6a)

MA.6.CE.6.3 The student will estimate solutions and then solve single-step and multistep practical problems

involving addition, subtraction, multiplication and division of fractions and decimals (SOL 6.6 b,

6.7)

Page 3: UUnniittUnit Unit BookBBooookkBook ~~~~ Real …tigertweets.weebly.com/uploads/3/2/2/7/32272677/unit_2_algebra...∞ Properties of Real Numbers* Distributive Property Commutative Property

Name: ______Name: ______Name: ______Name: ______________________________________________________________________________________________________________________________________________ DateDateDateDate ________________________________________________________ BlockBlockBlockBlock ________________________________

∞ Mathematics ∞ Virginia Beach City Public SchoolsVirginia Beach City Public SchoolsVirginia Beach City Public SchoolsVirginia Beach City Public Schools ∞

MA.6.NS.6.3 The student will investigate and describe fractions, decimals, and percents

as ratios and demonstrate equivalent relationships (SOL 6.2a, c)

MA.6.NS.6.4 The student will identify a given decimal, fraction, and/or percent from a representation (SOL 6.2b)

Fraction A number written as �

�where b ≠ 0. Part of a whole.

Numerator The expression written above the line in a common fraction that indicates the number of

parts of the whole.

Denominator The expression written below the line in a common fraction that indicates the number

of parts into which one whole is divided.

Mixed Number A number that contains both a whole number and a fraction.

Rational Numbers Any number that can be written in the form �

�, where a and b are integers and b ≠ 0.

Percent A ratio that compares a number to 100.

Proportion A statement of equality of two or more ratios.

Ratio A comparison of two quantities using a fraction or division.

MA.6.NS.6.5 The student will compare and order fractions, decimals, percents, and scientific notation using

manipulatives, pictorial representations, number lines, and the symbols >, <, ≤, ≥, = (SOL 6.2c, d,

7.1c)

Scientific Notation A number in scientific notation is expressed as a x 10n, where 1 ≤ a < 10 and n is an integer.

For example: 5,400,000 = 5.4 x 106

and 0.0043 = 4.3 x 10-3

Greater than > The symbol to show a greater than comparison between two numbers or expressions

Greater than or

equal to ≥

The symbol to show a greater than or equal to comparison between two numbers or

expressions

Less than < The symbol to show a less than comparison between two numbers or expressions

Less than or equal

to ≤

The symbol to show a less than or equal to comparison between two numbers or

expressions

Equal to = The symbol to show two numbers or expressions are equal to each other

MA.6.CE.6.6 The student will find the quotient, given a dividend expressed as a decimal through thousandths

and a divisor expressed as a decimal to thousandths with exactly one non-zero digit (no

calculator)

Quotient The result of dividing two numbers.

Dividend The number being divided.

Divisor The number by which another number is divided.

Page 4: UUnniittUnit Unit BookBBooookkBook ~~~~ Real …tigertweets.weebly.com/uploads/3/2/2/7/32272677/unit_2_algebra...∞ Properties of Real Numbers* Distributive Property Commutative Property

Name: ______Name: ______Name: ______Name: ______________________________________________________________________________________________________________________________________________ DateDateDateDate ________________________________________________________ BlockBlockBlockBlock ________________________________

∞ Mathematics ∞ Virginia Beach City Public SchoolsVirginia Beach City Public SchoolsVirginia Beach City Public SchoolsVirginia Beach City Public Schools ∞

Commutative PropertiesCommutative PropertiesCommutative PropertiesCommutative Properties PropertiesPropertiesPropertiesProperties ExampleExampleExampleExample DefinitionDefinitionDefinitionDefinition AdditionAdditionAdditionAddition 2 + 3 = 3 + 22 + 3 = 3 + 22 + 3 = 3 + 22 + 3 = 3 + 2

MultiplicationMultiplicationMultiplicationMultiplication 2 x 3 = 3 x 22 x 3 = 3 x 22 x 3 = 3 x 22 x 3 = 3 x 2

AssociAssociAssociAssociative Propertiesative Propertiesative Propertiesative Properties PropertiesPropertiesPropertiesProperties ExampleExampleExampleExample DefinitionDefinitionDefinitionDefinition AdditionAdditionAdditionAddition 2 + (3 + 4) = (2 + 3)+ 42 + (3 + 4) = (2 + 3)+ 42 + (3 + 4) = (2 + 3)+ 42 + (3 + 4) = (2 + 3)+ 4

MultiplicationMultiplicationMultiplicationMultiplication 2 x (3 x 4) = (2 x 3) x 42 x (3 x 4) = (2 x 3) x 42 x (3 x 4) = (2 x 3) x 42 x (3 x 4) = (2 x 3) x 4

Inverse PropertiesInverse PropertiesInverse PropertiesInverse Properties PropertiesPropertiesPropertiesProperties ExampleExampleExampleExample DefinitionDefinitionDefinitionDefinition AdditiveAdditiveAdditiveAdditive 2 + 2 + 2 + 2 + ((((----2) = 02) = 02) = 02) = 0

MultiplicativeMultiplicativeMultiplicativeMultiplicative 2 x 2 x 2 x 2 x ½½½½ = 1= 1= 1= 1

Multiplication Multiplication Multiplication Multiplication PropertPropertPropertPropertiesiesiesies PropertiesPropertiesPropertiesProperties ExampleExampleExampleExample DefinitionDefinitionDefinitionDefinition DistributiveDistributiveDistributiveDistributive

2 x (3 + 4) = (2 x 3) + (2 x 4)2 x (3 + 4) = (2 x 3) + (2 x 4)2 x (3 + 4) = (2 x 3) + (2 x 4)2 x (3 + 4) = (2 x 3) + (2 x 4)

Property of Property of Property of Property of Zero Zero Zero Zero (or Zero (or Zero (or Zero (or Zero Product)Product)Product)Product)

0 = 2(0)0 = 2(0)0 = 2(0)0 = 2(0)

Identity Identity Identity Identity PropertiesPropertiesPropertiesProperties PropertiesPropertiesPropertiesProperties ExampleExampleExampleExample DefinitionDefinitionDefinitionDefinition AdditiveAdditiveAdditiveAdditive 2 + 0 = 22 + 0 = 22 + 0 = 22 + 0 = 2

MultiplicativeMultiplicativeMultiplicativeMultiplicative 2 x 1 = 22 x 1 = 22 x 1 = 22 x 1 = 2

PropPropPropPropertyertyertyerty----““““statements that are true for any numberstatements that are true for any numberstatements that are true for any numberstatements that are true for any number””””