# Mathematics

## Grade 7

#### 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

## Grade 8

#### 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)

- Four-step method
**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

**Adding and Subtracting 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 vs. Quadratic Equations**- Linear:
- Highest exponent of the variable is 1
- Graph is a line

- Quadratic:
- Highest exponent of the variable is 2 (squared)
- Graph is a parabola (U-shape, smile or frown)

- Linear:

#### 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