Warm-Up # Hmwk: Close and Check (2,-2) A = 72 sq in $2.12

Real Number System How are numbers classified?

Real Number System A counting number from ONE to infinity Ex. {1, 2, 3, 4, 5, 6, 7, ….} A counting number from ZERO to infinity Ex. { 0, 1, 2, 3, 4, 5, …} A positive number, a negative number, and zero Ex. {…, -4, -3, -2, -1, 0, 1, 2, 3, 4, …} VocabularySection Natural Numbers Whole Numbers Integers

Real Number System VocabularySection Rational

Real Number System VocabularySection Irrational

Real Numbers REAL numbers are all the rational numbers and all the irrational numbers. All the numbers used in everyday life are REAL numbers. Each REAL number corresponds to exactly one point on the number line, and every point on the number line represents exactly one REAL number.

8-31 The REAL Number System Frayer Model Real Numbers All the numbers used in everyday life Includes: Irrational Rational Integers Whole Numbers Natural Numbers

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Warm-Up # Hmwk: Prob Solving WkSh 14 hrs 56 sec 54 n =

9-01 The REAL Number System Frayer Model Real Numbers All the numbers used in everyday life Includes: Irrational Rational Integers Whole Numbers Natural Numbers

9-01 The REAL Number System Rational Natural Whole Integers Irrational

Warm-Up # Hmwk: Order Operations Review Wksh Neither 162, oz ¼

Real Number Skit Narrator Mrs. Rational 1/9 Repeating 3/8 Terminating Pi

Absolute Value & Opposites Learning Target: 1) Using a number line to compare and order Integers. 2) Evaluate absolute values Draw this number line Plot the points 5 and -5 (put a dot on them). 3. How are they alike? 4. How are they different?

Warm-Up # Hmwk: Neither 162, oz ¼

Warm-Up # Hmwk: 10,004, cu ft ½ 50%

Warm-Up # Hmwk: Digits reflection translation cm 1/20 or 5%

Comparing and Ordering Integers 0 is the midpoint on an Integer Number Line 0 is the midpoint on an Integer Number Line The farther LEFT on the NL, the SMALLER THE VALUE of the Integer, regardless of the digits! The farther LEFT on the NL, the SMALLER THE VALUE of the Integer, regardless of the digits! The farther RIGHT on the NL, the LARGER THE VALUE of the Integer, regardless of the digits! The farther RIGHT on the NL, the LARGER THE VALUE of the Integer, regardless of the digits!

˂>=≠~≤≥˂>=≠~≤≥ LESS THAN – makes an ‘L’; arrowhead points to the left – ‘less’; left on number line gets smaller. GREATER THAN – arrowhead points to the right; right on the number line gets bigger. EQUAL TO – has the same exact value. NOT EQUAL TO APPROXIMATELY EQUAL TO – close but not exact LESS THAN OR EQUAL TO – can be one OR the other GREATER THAN OR EQUAL TO – can be one OR the other COMPARISON SYMBOLS

Opposites Integers Two numbers that are equal distance from zero on a number line units Negative integers Positive integers 0 is neither positive or negative. The set of whole numbers and their opposites (… -4, -3, -2, -1, 0, 1, 2, 3, 4…).

Insert an ordering symbol to make each statement true. or = Ordering Integers Example 1) – 3 __ 4 < b p

Whiteboard Practice 2) – 2 __ – 5 > b p 3) – 7 __ 7 <

– 2, 7, – 4, 3, 1, 2 Using a number line put the following integers in order from least to greatest. Example – 2,– 4,73, 1, 2, – 2– 47312

4, – 5, – 4, – 6, 2 Using a number line put the following integers in order from least to greatest. Whiteboard Practice – 5,– 6,4– 4,2, 4– 4– 5– 62

1, 0, 2, – 3, – 2 Using a number line put the following integers in order from least to greatest. Whiteboard Practice – 2,– 3,20,1, – 3– 2120

A negative sign means the opposite of what comes after it. Negative sign Additive Inverse Evaluate each expression. Opposite of what comes next. - (-14) = 14 - (-7) = 7 Additive Inverses ADD together to get zero. Find the additive inverses: 7 + ____ = ____ = 0

3 Graph integer and its opposite (additive inverse) on the number line. Example –, 3 units 3– 3

Name the Additive Inverses of the following: Additive Inverses combine to make ZERO PAIRS! 7 + (-7) = = (-65) = 0

Two changes represented by opposites result in no change.

the distance from zero to the number. (Distance is always positive ) Absolute Value (Distance is like running track; you only run forwards (in a positive way, not the opposite or negative way) Absolute-Value is always positive.

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– 2 Example units = – 2

10 Solve by using an number line to find the absolute value. Whiteboard Practice units = 10

– 16 Solve by using an number line to find the absolute value. Whiteboard Practice units = – 16

Warm-Up # Hmwk: Digits p Four Hundred twenty-seven and sixty-three hundredths YES 10:52 pm

What does l 2 l mean? The symbols l l on either side of a number mean “absolute value.” For example, l 2 l means “the absolute value of 2”. ABSOLUTE VALUE IS ALWAYS POSITIVE! Ex. l - 12 l = l l = 12 spaces 12, because -12 is 12 spaces away from zero 2 spaces 2, because = -2 which is 2 spaces away from zero.

Copy these notes Absolute value is the distance from zero. 5 means the “absolute value of 5” or how many spaces from zero. (5) -5 = 5 -6 > < -60 Absolute Value is always positive! Comparing distance uses absolute value.

The first example means and the second means = │1│. The first is the negative of the A.V. of 15. The second is the A.V. of Explain the difference between… l -2 l + l 3 l and l l - l 15 l and l -15 l

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