# Number Theory and Order of Operations

**BIG IDEAS****:**

*(taken from “Big Ideas by Dr. Small”)***:**

- Thinking of numbers as factors or multiples of other numbers provides alternative representations of those numbers.
- Classifying numbers as factors and/or multiples of other numbers, or as primes or composites, provides additional information about those numbers.
- Just as multiplication and division are intrinsically related, so are factors and multiples.
- There is a specific order in which the operations are to be carried out.

**STUDENT LEARNING GOALS:**

**GOAL #1: I can represent numbers as factors and multiples of other numbers.**

- VIDEO: What is a Multiple?
*(Source: Study.com)* - VIDEO: Finding LCM using Multiple Lists
*(Source: Math Wraps)* - QUIZ: Identifying Multiples
*(Source: Nelson Education)*

- VIDEO: Divisibility Tests
*(Source: Khan Academy)* - VIDEO: Recognizing Divisibility (Source: Khan Academy)
- VIDEO: The Why of the 3 Divisibility Rule (Source: Khan Academy)
- PRACTICE: Divisibility Rules
*(Source: MathWarehouse)* - PRACTICE: Using Divisibility Rules (
*Source: IXL Math*)

- VIDEO: Factoring
*(Source: Math Antics)* - VIDEO: Finding Factors of a Number
*(Source: Khan Academy)* - VIDEO: Finding Greatest Common Factor
*(Source: Khan Academy)* - QUIZ: Common Factors and Multiples
*(Source: Nelson Education)* - GAME: Factor Fracture
*(Source: FunBrain)* - GAME: Factors and Multiples Game
*(Source: NRICH)*

**GOAL #2: I can identify numbers as prime or composite.**

- VIDEO: Prime Numbers
*(Source: Khan Academy)* - VIDEO: Recognizing Prime and Composite Numbers
*(Source: Khan Academy)* - VIDEO: Prime Factorization
*(Source: Math Antics)* - QUIZ: Identifying Primes
*(Source: ThatQuiz)* - QUIZ: Identifying Factors, Primes and Composites
*(Source: Nelson Education)* - QUIZ: Identifying Prime and Composite Numbers
*(Source: Nelson Education)* - QUIZ: Prime Factorization
*(Source: Nelson Education)*

**GOAL #3: I know the difference between a perfect square and a square root.**

- VIDEO: What is a Perfect Square?
*(Source: Study.com)* - VIDEO: Intro to Exponents
*(Source: Math Antics)* - VIDEO: Exponents and Roots
*(Source: Math Antics)* - QUIZ: Perfect Squares
*(Source: ThatQuiz)* - QUIZ: Perfect Roots – click on “Roots”
*(Source: ThatQuiz)* - QUIZ: Powers
*(Source: Nelson Education)* - QUIZ: Calculating Powers
*(Source: Nelson Education)* - QUIZ: Square Roots I
*(Source: Nelson Education)* - QUIZ: Square Roots II
*(Source: Nelson Education)*

**GOAL #4: I can use the order of operations to simplify mathematical expressions.**

- VIDEO: Order of Operations
*(Source: Math Antics)* - VIDEO: Order of Operations Rap
*(Source: Flocabulary)* - QUIZ: Order of Operations
*(Source: SoftSchools)* - QUIZ: Order of Operations
*(Source: Nelson Education)* - QUIZ: Order of Operations – Challenging
*(Source: Nelson Education)* - GAME: OrderOps
*(Source: MrNussbaum)* - GAME: Pemdas Blaster
*(Source: MangaHigh)* - PRACTICE: Inserting Brackets
*(Source: Peter Halfpenny Tuition)*

**CURRICULUM EXPECTATIONS:**

- Generate
__multiples__and__factors__, using a variety of tools and strategies (e.g., identify multiples on a hundreds chart; create rectangles on a geoboard) (Sample problem: List all the rectangles that have an area of 36 cm^{2}and have whole-number dimensions.); - Represent perfect
__squares__and square__roots__, using a variety of tools (e.g., geoboards, connecting cubes, grid paper); - Explain the relationship between exponential notation and the measurement of area and volume (Sample problem: Explain why area is expressed in square units [units
^{2}] and volume is expressed in cubic units [units^{3}]; - Solve multi-step problems arising from real-life contexts and involving whole numbers and decimals, using a variety of tools (e.g., concrete materials, drawings, calculators) and strategies (e.g., estimation, algorithms);
- Evaluate expressions that involve whole numbers, including expressions that contain brackets, using
__order of operations__;