Integers

BIG IDEAS:

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

1. The negative integers are the “opposites” of the whole numbers. Each integer is the reflection of its opposite across a line that is perpendicular to the number line at 0.

2. In a number of ways, integers are more like whole numbers, than like fractions or decimals.

3. The zero property, that is, (-1) + (+1) = 0, plays an important role in many integer operations.

4. Adding and subtracting integers can be represented by models, such as tiles or on number lines.

STUDENT LEARNING GOALS:

GOAL #1: I can identify and represent integers.

• VIDEO: Identifying Integers (Source: Khan Academy)

• VIDEO: Representing Real-Word Integers (Source: YouTube)

• VIDEO: Absolute Value (Source: Khan Academy)

• VIDEO: Opposite Numbers (Source: Khan Academy)

• VIDEO: Missing Numbers on the Number Line (Source: Khan Academy)

• VIDEO: Negative Numbers (Source: Math Antics)

• VIDEO: Comparing and Ordering Integers (Source: SmithMathAcademy)

• VIDEO: Ordering Negative Numbers (Source: Khan Academy)

• QUIZ: Representing Integers (Source: SoftSchools)

• QUIZ: Comparing Integers (Source: Nelson Education)

• GAME: MathMan (Source: SheppardSoftware)

• GAME: Fruit Shoot (Source: SheppardSoftware)

• GAME: Number Balls (Source: SheppardSoftware)

GOAL #2: I can add and subtract integers

• VIDEO: Adding and Subtracting Integers (Source: Math Antics)

• VIDEO: Adding Integers with the Same Sign (Source: Khan Academy)

• VIDEO: Adding Integers with Different Signs (Source: Khan Academy)

• VIDEO: Adding Integers with Counters (Source: YouTube)

• VIDEO: Adding Integers on the Number Line (Source: Khan Academy)

• VIDEO: Subtracting Negative Numbers (Source: Khan Academy)

• VIDEO: Adding and Subtracting Negative Numbers (Source: Khan Academy)

• VIDEO: Negative Number Word Problems (Source: Khan Academy)

• QUIZ: Adding Integers using the Zero Principle (Source: Nelson Education)

• QUIZ: Adding Integers (Source: Nelson Education)

• QUIZ: Adding Integer Strategies (Source: Nelson Education)

• QUIZ: Using Counters to Subtract Integers (Source: Nelson Education)

• QUIZ: Using Number Lines to Subtract Integers (Source: Nelson Education)

• QUIZ: Relating Integer Subtraction to Addition (Source: Nelson Education)

• QUIZ: Solving Problems by Working Backwards (Source: Nelson Education)

• GAME: Orbit Integers (Source: Arcademics)

• GAME: Spider Match (Source: Arcademics)

GOAL #3: I can multiply and divide integers

• VIDEO: Multiplying Negative Numbers (Source: Khan Academy)

• VIDEO: Why a Negative x Negative = Positive (Source: Khan Academy)

• VIDEO: Dividing Positive and Negative Numbers (Source: Khan Academy)

• VIDEO: Integer Multiplication and Division (Source: Math Antics)

• QUIZ: Multiplying Integers (Source: Nelson Education)

• QUIZ: Dividing Integers (Source: Nelson Education)

• PRACTICE: Integer Division (Source: XP Math)

• PRACTICE: Integer Division (Source: XP Math)

• GAME: Integer Warp (Source: Arcademics)

• GAME: Fruit Shoot (Source: SheppardSoftware)

• GAME: Number Ball Division (Source: SheppardSoftware)

GOAL #4: I can evaluate expressions that involve integers using order of operations

• VIDEO: Order of Operations (Source: Math Antics)

• VIDEO: Order of Operations Rap (Source: Flocabulary)

• VIDEO: Order of Operation WITH negative numbers (Source: Khan Academy)

• 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:

• represent, compare, and order rational numbers

• use estimation when solving problems involving operations with … integers, to help judge the reasonableness of a solution

• represent the multiplication and division of integers, using a variety of tools [e.g., if black counters represent positive amounts and red counters represent negative amounts, you can model 3 x (–2) as three groups of two red counters]

• solve problems involving operations with integers, using a variety of tools (e.g., counters, virtual manipulatives, number lines)

• evaluate expressions that involve integers, including expressions that contain brackets and exponents, using order of operations