The Number System

Grade 6 unit 4: The Number System

STANDARDS:

6.NS.C.6 Understand a rational number as a point on the number line. Extend number line diagrams and coordinate axes familiar from previous grades to represent points on the line and in the plane with negative number coordinates.

• 6.NS.C.6.A Recognize opposite signs of numbers as indicating locations on opposite sides of 0 on the number line; recognize that the opposite of the opposite of a number is the number itself, e.g., -(-3) = 3, and that 0 is its own opposite.
• 6.NS.C.6.B Understand signs of numbers in ordered pairs as indicating locations in quadrants of the coordinate plane; recognize that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes.
• 6.NS.C.6.C Find and position integers and other rational numbers on a horizontal or vertical number line diagram; find and position pairs of integers and other rational numbers on a coordinate plane.

6.NS.C.7 Understand ordering and absolute value of rational numbers.

• NS.C.7.A Interpret statements of inequality as statements about the relative position of two numbers on a number line diagram. For example, interpret -3 > -7 as a statement that -3 is located to the right of -7 on a number line oriented from left to right.
• 6.NS.C.7.B Write, interpret, and explain statements of order for rational numbers in real-world contexts. For example, write -3 oC > -7 oC to express the fact that -3 oC is warmer than -7 oC.
• 6.NS.C.7.C Understand the absolute value of a rational number as its distance from 0 on the number line; interpret absolute value as magnitude for a positive or negative quantity in a real-world situation. For example, for an account balance of -30 dollars, write |-30| = 30 to describe the size of the debt in dollars.
• 6.NS.C.7.D Distinguish comparisons of absolute value from statements about order. For example, recognize that an account balance less than -30 dollars represents a debt greater than 30 dollars.

LESSONS

Topic B: Multi-Digit Decimal Operations - Adding, Subtracting, and Multiplying (6.NS.B.3)

Lesson 9: Sums and Differences of Decimals PRACTICE PROBLEMS

Lesson 10: The Distributive Property and the Products of Decimals

Lesson 11: Fraction Multiplication and the Products of Decimals

Topic A: Relationships of the Operations (6.EE.A.3)

Lesson 1: The Relationship of Addition and Subtraction

Lesson 2: The Relationship of Multiplication and Division

Lesson 3: The Relationship of Multiplication and Addition

Lesson 4: The Relationship of Division and Subtraction

Topic B: Special Notations of Operations (6.EE.A.1, 6.EE.A.2c)

Lesson 5: Exponents

Lesson 6: The Order of Operations

New or Recently Introduced Terms

Absolute Value (The absolute value of a number is the distance between the number and zero on the number line. For example, , , etc.)

Charge (A charge is the amount of money a person must pay, as in a charge to an account, or a fee charged.)

Credit (A credit is a decrease in an expense, as in money credited to an account. For instance, when a deposit is made into a checking account, the money is credited to the account. A credit is the opposite of a debit.)

Debit (A debit is an increase in an expense or money paid out of an account. For instance, using a debit card to make a purchase will result in an expense, and money will be deducted from the related bank account.)

Deposit (A deposit is the act of putting money into a bank account.)

Elevation (Elevation is the height of a person, place, or thing above a certain reference level.)

Integers (The numbers ... , , , , , , , , … are integers on the number line.)

Magnitude (The magnitude is the absolute value of a measurement, given the measurement of a positive or negative quantity.)

Negative Number (A negative number is a number less than zero.)

Opposite (In a position on the other side; for example, negative numbers are the opposite direction from zero as positive numbers.)

Positive Number (A positive number is a number greater than zero.)

Quadrants (The four sections of the coordinate plane formed by the intersection of the axes are called quadrants.)

Rational Number (A rational number is a fraction or the opposite of a fraction on the number line.)

Withdraw (To withdraw is to take away; for example, to take money out of a bank account.)

Withdrawal (A withdrawal is the act of taking money out of a bank account.)