uunniittunit unit bookbbooookkbook ~~~~ real...
TRANSCRIPT
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
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)
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.
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””””