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Integer Introduction
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Warm UpWrite each decimal as a fraction.
1.) 1.8 =
2.) 15.25 =
3.) .008 =
4.) .85 =
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Objectives
Student Expectation: We will explore integers on a # line.
Product: I will explore integers on a # line
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Vocabulary
oppositeintegerabsolute value
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Create A Number Line
• Fold Sentence Strip in Half
• Place Zero (0) on sentence strip at fold
• Use a ruler and place marks at each inch.
• # the lines on each side of zero. Should go to 12 and -12.
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Numbers on Number Line• On the LEFT side of zero, start with 1 and
the numbers get larger.
• Label the numbers on the LEFT side of zero with a negative sign (-); these are NEGATIVE NUMBERS and get smaller the farther you go from zero.
• The numbers on the RIGHT side of zero are POSITIVE NUMBERS and get larger the farther you go from zero.
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The opposite of a number is the samedistance from 0 on a number line as theoriginal number, but on the other sideof 0. Zero is its own opposite.
1 2 3 4 5 • •
–5–4–3–2–1 0
–4 and 4 are opposites
–4 4
Negative integers Positive integers
0 is neither positivenor negative
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The integers are the set of whole numbers and their opposites. By using integers, you can express elevations above, below, and at sea level. Sea level has an elevation of 0 feet.
The whole numbers are the counting numbers and zero: 0, 1, 2, 3, . . . .
Remember!
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Graph the integer 7 and its opposite on a number line.
1 2 3 4 5 6 7 –7–6–5–4–3–2–1 0
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Graph the integer 5 and its opposite on a number line.
1 2 3 4 5 6 7 –7 –6–5 –4 –3–2–1 0
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You can compare and order integers by graphing them on a number line. Integers increase in value as you move to the right along a number line. They decrease in value as you move to the left.
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Compare the integers. Use < or >.
4 is farther to the right than -4, so 4 > -4.
1 2 3 4 5 6 7 –7–6–5–4–3–2–1 0
4 -4>
The symbol < means “is less than,” and the symbol > means “is greater than.”
Remember!
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Compare the integers. Use < or >.
-15 -9
-15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1
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Compare the integers. Use < or >.
1 2 3 4 5 6 7 –7–6–5–4–3–2–1 0
6 -6
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Compare the integers. Use < or >.
-4 -11
-15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1
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Use a number line to order the integers from least to greatest.
–3, 6, –5, 2, 0, –8
1 2 3 4 5 6 7 8 –8 –7–6 –5–4 –3 –2 –1 0
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Use a number line to order the integers from least to greatest.
–5, 4, –3, 2, –1, –2
1 2 3 4 5 6 7 8 –8 –7–6–5–4 –3–2 –1 0
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A number’s absolute value is its distance from 0 on a number line.
Since distance can never be negative, absolute values are never negative.
They are always positive or zero.
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Use a number line to find each absolute value.
|8|
1 2 3 4 5 6 7 8 –8 –7–6–5–4 –3–2 –1 0
8 units
8 is 8 units from 0, so |8| = 8.
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The symbol is read as “the absolute value of.” For example -3 is the absolute value of -3.
Reading Math
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Use a number line to find each absolute value.
|–12|
–12 –11 –10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2
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Use a number line to find each absolute value.
|3|
1 2 3 4 5 6 7 8 –8 –7–6–5–4 –3–2 –1 0
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Use a number line to find the absolute value.
|–9|
–12 –11 –10 –9 –8 –7 –6 –5 –4 –3 –2 –1 0 1 2
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Lesson Quiz: Part I
Compare. Use <, >, or =.
1. –32 32
2. 26 |–26|
3. –8 –12
4. Use a number line to order the integers –2, 3, –4, 5, and –1 from least to greatest.
1 2 3 4 5 –5–4 –3 –2–1 0
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Lesson Quiz: Part II
Use a number line to find the absolute value.
5. -3
1 2 3 4 5 –5 –4 –3 –2 –1 0
3 units
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Assignment
Practice 2-1