Mathematics

Grade 7

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

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

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

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)

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