Powers and Roots

BIG IDEAS:

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

1. Thinking of numbers as factors or multiples of other numbers provides alternative representations of those numbers.

2. Classifying numbers as factors and/or multiples of other numbers, or as primes or composites, provides additional information about those numbers.

3. Just as multiplication and division are intrinsically related, so are factors and multiples.

4. There is a specific order in which the operations are to be carried out.

STUDENT LEARNING GOALS:

GOAL #1: I can represent powers in exponential form.

• VIDEO: Intro to Exponents (Source: Khan Academy)

• VIDEO: Exponent Example (Source: Khan Academy)

• VIDEO: Patterns in Powers of Ten (Source: Khan Academy)

• VIDEO: Powers of Ten (Source: Khan Academy)

• VIDEO: Multiplying a Decimal by Powers of Ten (Source: Khan Academy)

• VIDEO: Dividing a Decimal by Powers of Ten (Source: Khan Academy)

• VIDEO: Exponent Properties involving Products (Source: Khan Academy)

• VIDEO: Scientific Notation (Source: Khan Academy)

• QUIZ: Powers (Source: Nelson Education)

• QUIZ: Calculating Powers (Source: Nelson Education)

• QUIZ: Expanded Form and Scientific Notation (Source: Nelson Education)

GOAL #2: I can use prime factorization to determine multiples and factors of numbers.

• VIDEO: Divisibility Tests (Source: Khan Academy)

• VIDEO: Factoring (Source: Math Antics)

• VIDEO: Finding Factors of a Number (Source: Khan Academy)

• VIDEO: Prime Numbers (Source: Khan Academy)

• VIDEO: Recognizing Prime and Composite Numbers (Source: Khan Academy)

• VIDEO: Prime Factorization (Source: Math Antics)

• VIDEO: Prime Factorization – exponential notation (Source: Khan Academy)

• QUIZ: Identifying Multiples (Source: Nelson Education)

• QUIZ: Identifying Factors, Primes and Composites (Source: Nelson Education)

• QUIZ: Identifying Prime and Composite Numbers (Source: Nelson Education)

• QUIZ: Prime Factorization (Source: Nelson Education)

• QUIZ: Common Factors and Multiples (Source: Nelson Education)

GOAL #3: I can find common factors and common multiples of two or more numbers.

• VIDEO: Finding LCM using Multiple Lists (Source: Khan Academy)

• VIDEO: Finding LCM using Prime Factorization (Source: Khan Academy)

• VIDEO: Finding LCM using Ladder Method (Source: Khan Academy)

• VIDEO: Finding GCF using Prime Factorization (Source: Khan Academy)

• QUIZ: Common Multiples (Source: Nelson Education)

• QUIZ: Common Factors (Source: Nelson Education)

• COOL LINK: Secret Worlds – The Universe Within (Source: Molecular Expressions)

GOAL #4: I can calculate roots.

• VIDEO: Exponents and Roots (Source: Math Antics)

• QUIZ: Perfect Squares (Source: ThatQuiz)

• QUIZ: Perfect Roots – click on “Roots” (Source: ThatQuiz)

• QUIZ: Square Roots I (Source: Nelson Education)

• QUIZ: Square Roots II (Source: Nelson Education)

GOAL #5: 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:

• Express repeated multiplication using exponential notation

• Represent whole numbers in expanded form using powers of ten

• Determine common factors and common multiples using the prime factorization of numbers

• Solve multi-step problems arising from real-life contexts and involving whole numbers and decimals, using a variety of tools (e.g., graphs, calculators) and strategies (e.g., estimation, algorithms);

• Multiply and divide decimal numbers by various powers of ten

• Estimate, and verify using a calculator, the positive square roots of whole numbers, and distinguish between whole numbers that have whole-number square roots (i.e., perfect square numbers) and those that do not