# Mathematics

#### Problem Solving Strategies

• Guess & Check
• Organized List
• Tables
• Patterns
• Working Backwards
• Logical Reasoning
• Simpler but Related
• Draw a Picture

#### Number Sense

• Family of Numbers
• Exponents/Scientific Notation
• Divisibility Rules
• Factors, GCF
• Multiples, LCM
• Prime Factorization
• Applications of Percents

#### Integers

• Background information
• Operations
• Coordinate Graphing
• Applications

#### Statistics

• Types of Graphs
• Venn Diagrams
• Mean/Median/Mode
• Rank
• Range

#### Probability

• Fundamental Counting Principle
• Theoretical vs. Experimental
• Compound Events

#### Algebra

• Writing mathematical expressions
• Evaluating expressions
• Equation Solving
• Solving/Graphing Inequalities
• Monomials
• Polynomials
• Functions

#### Measurement

• Customary
• Metrics
• Currency exchange and rate
• Creating a circle graph
• Applications

#### Geometry

• Vocabulary
• Analysis of geometric diagrams (2-Dimensional & 3-Dimensional)
• Circumference
• Area / Surface Area
• Volume
• Pythagorean Theorem
• Graphing Equations
• Applications

#### Unit 1: Number Connections

• Problem Solving
• Four-step method
• Read, plan, solve, look back
• Strategies
• Draw a picture/diagram
• Work backwards
• Solve a simpler problem, then adjust
• Guess and check (1 high, 1 low, 1 right)
• Integers and Absolute Value
• Integers: whole numbers and their opposites
• Absolute Value: the distance a number is from zero on the number line (always positive)
• Operations with Integers
• Addition: – 2 + 3, –8 + –6
• Subtraction: –3 – 5, –7 – (–4)
• Multiplication: (–2)(7), (–8)( –11)
• Division: (–56) (8), (42) (–6), (–36) (–6)
• Powers
• Base, Exponent, Power, Repeated Multiplication, Standard Form
• Order of Operations
• PEMDAS (Please Excuse My Dear Aunt Sally)
• Evaluating Expressions
• Multiplying and Dividing with Exponents
• Properties of Numbers
• Distributive Property
• Associative Property
• Commutative Property
• Percents
• Converting between Fractions, Decimals & Percents
• Problems involving Sales and Discounts (%)
• Problems involving Tips and Commission (%)
• Simple Interest
• I=P*R*T
• Percent of Change
• Percent of Increase (Mark-up)
• Percent of Decrease (Discount)
• Proportions
• Unit Rates

#### Unit 2: Algebra Expressions, Equations & Inequalities

• Algebra Vocabulary
• Variable, coefficient, constant, term, monomial, binomial, trinomial, polynomial
• Combining Like Terms
• Translating Algebraic and Verbal Expressions
• English to Math
• Math to English
• Problem Solving Five-Step Process
• Let statement, Equation, Solve, Answer, Check
• Solving Two-Step Equations
• Add or subtract, then multiply or divide
• Solving Equations with Like Terms
• Combine like terms, then add or subtract, then multiply or divide
• Solving Equations with a Variable of Both Sides
• Eliminate the lesser term (by subtracting), then add or subtract, then multiply or divide
• Solving Equations using the Distributive Property
• Distribute, then combine like terms, then add or subtract, then multiply or divide
• Be careful with negatives!
• Solving and Graphing Inequalities
• Switch the sign if you multiply or divide by a negative number
• Graph solution on number line

#### Unit 3: Algebra:Operations with Polynomials

• Line up like terms
• Do not add the exponents
• Multiplying Monomials
• When multiplying with powers, add the exponents
• Standard Form
• When there is only one variable
• Combine all like terms
• Write in order from highest exponent to lowest exponent
• Multiplying Polynomials
• Using Algebra Tiles
• Table/Box Method
• Distributive Property
• Area and Perimeter
• Label answer with “units” for perimeter
• Label answer with “square units” for area
• Dividing Monomials by Monomials
• When dividing with powers, subtract the exponents
• Dividing Polynomials by Monomials
• Break up into several fractions
• Separate with “+” or “–” where appropriate
• When dividing with powers, subtract the exponents

#### Unit 4: Algebra: Factoring

• Prime, Composite or Neither
• Prime Factorization
• Greatest Common Factor (GCF)
• Factoring using GCF
• GCF(leftovers)
• Factoring “Easy” Trinomials
• Product of 2 binomials
• (x +/- #)(x +/- #)
• Linear:
• Highest exponent of the variable is 1
• Graph is a line
• Highest exponent of the variable is 2 (squared)
• Graph is a parabola (U-shape, smile or frown)

#### Unit 5: Geometry:Angles & The Pythagorean Theorem

• Angle Types
• Acute, obtuse, right, straight
• Parallel Lines Cut by a Transversal
• Angle Pairs
• Adjacent, vertical, complementary, supplementary, corresponding, alternate interior, alternate exterior
• Finding Missing Angle Measures
• Using algebra
• Pythagorean Theorem
• For right triangles only
• a2 + b2 = c2