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2-1 Integers
Pg.76
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Essential Question When would you need to use negative
integers in the real world?
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Definitions integers- the set of whole numbers and
their opposites (positive or negative) opposite- two numbers that are an equal
distance from zero on a number line absolute value- the distance of a
number from zero on a number line; shown by l l
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INTRODUCTION TO INTEGERS Integers are positive and negative numbers.
…, -6, -5, -4, -3, -2, -1, 0, +1, +2, +3, +4, +5, +6, …
Each negative number is paired with a positive number the same distance from 0 on a number line. These numbers are called opposites.
-3 -2 -1 20 1 3
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IntegersNumbers to the left of zero
are less than zero.Numbers to the right of zero are more than zero.
The numbers –1, -2, -3 are called negative integers. The number negative 3 is written –3.
The numbers 1, 2, 3 are called positive integers. The number positive 4 is written +4 or 4.
Zero is neither negative nor positive.
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Negative numbers are used to…
1.2.3.
The answers are on the next 3 slides
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Negative Numbers Are Used to Measure Temperature
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Negative Numbers Are Used to Measure Under Sea Level
0102030
-10-20-30-40-50
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Negative Numbers Are Used to Show Debt
Let’s say your parents bought a car buthad to get a loan from the bank for $5,000.When counting all their money they add in -$5.000 to show they still owe the bank.
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Hint If you don’t see a negative
or positive sign in front of a number it is positive.
9 = 9+
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•The opposite of a number is the same distance from 0 on a number line as the original number, but on the other side of 0. •Zero is its own opposite.
1 2 3 4 5 • •
–5–4–3–2–1 0
–4 and 4 are opposites
–4 4
Opposite Example 1
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Graph the integer 7 and its opposite on a number line.
Opposite Example 2
1 2 3 4 5 6 7 –7–6–5–4–3–2–1 0
7 units 7 units
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1 2 3 4 5 6 7 8 9 -9–8 –7–6–5–4 –3–2 –1 0
1 2 3 4 5 6 7 8 –8 –7–6–5–4 –3–2 –1 0
Graph the integer and its opposite on a number line.
Opposite Examples 3&4
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Absolute Value Video Clip (1:30)
Write down 1 fact from the clip about absolute value.
http://player.discoveryeducation.com/index.cfm?guidAssetId=EE3ED6D0-96E6-4FF7-8D82-3FCD782528EB&blnFromSearch=1&productcode=US
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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.
Absolute Value Example 1
|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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Absolute Value Example 2
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
–12 is 12 units from 0, so |–12| = 12.
12 units
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1 2 3 4 5 6 7 8 –8 –7–6–5–4 –3–2 –1 0
2
1 2 3 4 5 6 7 8 –8 –7–6–5–4 –3–2 –1 0
7
Absolute Value Examples 3 & 4
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•Integers increase in value as you move to the right along a number line.
•They decrease in value as you move to the left.
The symbol < means “is less than,” and the symbol > means “is greater than.”
Remember!
You can compare and order integers by graphing them on a number line.
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Compare the integers. Use < or >.
Comparing Example 1
-4 is farther to the right than -11, so -4 > -11.
-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.
Comparing Example 2
–3, 6, –5, 2, 0, –8
The numbers in order from least to greatest are –8, –5, –3, 0, 2, and 6.
1 2 3 4 5 6 7 8 –8 –7–6 –5–4 –3 –2 –1 0
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-18 -17 -16 -15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 -4
›
‹
Comparing Examples 3&4
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1 2 3 4 5 6 7 8 –8 –7–6–5–4 –3–2 –1 0
Comparing Example 5
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Work Session-Together Showing off Integer WS Meaning of Integer WS
Comparing and Ordering Sort
Number Line WS
Work Session-With your Partner
Work Session- On your own
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Closing When would you use negative numbers in
the real world?
Do the numbers increase or decrease as you move to the left of zero?
< means:
> means:
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Homework
13.3 WS Comparing and Ordering Integers
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Role of IntegersVideo Clip
Write down 3 facts about integers from the clip. 1. 2. 3.
http://player.discoveryeducation.com/index.cfm?guidAssetId=E2DCB058-17F3-41C9-A4C8-B08D1D2AACB8&blnFromSearch=1&productcode=US
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HomeworkWorkbook pg. 13All problems
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Work Session Textbook Pg. 78 16-38 even only GRADED