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Warm Up Lesson Presentation Problem of the Day Lesson Quizzes
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Warm Up Add or subtract. 1. 16 + 25 2. 84 – 12 3. Graph the even numbers from 1 to 10 on a number line. 41 72 0 1 2 3 4 5 6 7 8 9 10
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Problem of the Day Carlo uses a double-pan balance and three different weights to weigh bird seed. If his weights are 1 lb, 2 lb, and 5 lb, what whole pound amounts is he able to weigh? 1, 2, 3, 4, 5, 6, 7, and 8 lb
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Preview of MA.7.A.3.1 Use and justify the rules for…finding absolute value of integers. Sunshine State Standards
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Vocabulary positive number negative number opposites integer absolute value
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Positive numbers are greater than 0. They may be written with a positive sign (+), but they are usually written without it. Negative numbers are less than 0. They are always written with a negative sign (–).
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Additional Example 1: Identifying Positive and Negative Numbers in the Real World Name a positive or negative number to represent each situation. A. a jet climbing to an altitude of 20,000 feet B. taking $15 out of the bank Positive numbers can represent climbing or rising . +20,000 Negative numbers can represent taking out or withdrawing . – 15
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Additional Example 1: Identifying Positive and Negative Numbers in the Real World Name a positive or negative number to represent each situation. C. 7 degrees below zero Negative numbers can represent values below or less than a certain value. – 7
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Check It Out: Example 1 Name a positive or negative number to represent each situation. A. 300 feet below sea level B. a hiker hiking to an altitude of 4,000 feet Negative numbers can represent values below or less than a certain value. – 300 Positive numbers can represent climbing or rising . +4,000
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Check It Out: Example 1 Name a positive or negative number to represent each situation. C. spending $34 Negative numbers can represent losses or decreases . – 34
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You can graph positive and negative numbers on a number line. On a number line, opposites are the same distance from 0 but on different sides of 0. Integers are the set of all whole numbers and their opposites. Opposites Positive Integers Negative Integers 0 is neither negative nor positive. – 5 – 4 – 3 – 2 – 1 0 +1 +2 +3 +4 +5
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The set of whole numbers includes zero and the counting numbers. {0, 1, 2, 3, 4, …} Remember!
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Additional Example 2: Graphing Integers Graph each integer and its opposite on a number line. A. +2 B. –5 – 2 is the same distance from 0 as +2. +5 is the same distance from 0 as –5. – 5 – 4 – 3 – 2 – 1 0 +1 +2 +3 +4 +5 – 5 – 4 – 3 – 2 – 1 0 +1 +2 +3 +4 +5
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Additional Example 2: Graphing Integers Graph each integer and its opposite on a number line. C. +1 – 1 is the same distance from 0 as +1. – 5 – 4 – 3 – 2 – 1 0 +1 +2 +3 +4 +5
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Check It Out: Example 2 Graph each integer and its opposite on a number line. A. +3 B. –4 – 3 is the same distance from 0 as +3. +4 is the same distance from 0 as –4. – 5 – 4 – 3 – 2 – 1 0 +1 +2 +3 +4 +5 – 5 – 4 – 3 – 2 – 1 0 +1 +2 +3 +4 +5
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Check It Out: Example 2 Graph each integer and its opposite on a number line. C. 0 Zero is its own opposite. – 5 – 4 – 3 – 2 – 1 0 +1 +2 +3 +4 +5
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The absolute value of an integer is its distance from 0 on a number line. The symbol for absolute value is ||. |–3| = 3 |3| = 3 | <--3 units--> | <--3 units--> |
Absolute values are never negative.
Opposite integers have the same absolute value.
|0| = 0
– 5 – 4 – 3 – 2 – 1 0 +1 +2 +3 +4 +5
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Additional Example 3A: Finding Absolute Value Use a number line to find the absolute value of each integer. A. |–2| – 2 is 2 units from 0, so |–2| = 2 2 – 5 – 4 – 3 – 2 – 1 0 +1 +2 +3 +4 +5
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Additional Example 3B: Finding Absolute Value Use a number line to find the absolute value of each integer. B. |8| 8 is 8 units from 0, so |8| = 8 8 – 1 0 1 2 3 4 5 6 7 8 9
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Check It Out: Example 3A Use a number line to find the absolute value of each integer. A. |6| 6 is 6 units from 0, so |6| = 6 6 – 1 0 1 2 3 4 5 6 7 8 9
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Check It Out: Example 3B Use a number line to find the absolute value of each integer. B. |–4| – 4 is 4 units from 0, so |–4| = 4 4 – 5 – 4 – 3 – 2 – 1 0 +1 +2 +3 +4 +5
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Standard Lesson Quiz Lesson Quizzes Lesson Quiz for Student Response Systems
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Lesson Quiz Name a positive or negative number to represent each situation. 1. saving $15 2. 12 feet below sea level 3. What is the opposite of –6? Use a number line to find the absolute value of each integer. 4. |–7| 5. |4| – 12 +15 6 7 4
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1. Identify a positive or negative number to represent the given situation. 10 more students joining music class. A. +10 B. –10 C. D. Lesson Quiz for Student Response Systems
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2. Identify a positive or negative number to represent the given situation. A basement for car parking at 12 feet below the ground level. A. +12 B. –12 C. D. Lesson Quiz for Student Response Systems
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3. What is the opposite of –15? A. +15 B. –15 C. 0 D. Lesson Quiz for Student Response Systems
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4. Gold rate has increased by $3. Identify an integer to represent this situation. A. +3 B. –3 C. 0 D. Lesson Quiz for Student Response Systems
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