ABSOLUTE VALUE

​A Number's Distance from 0 on the Number Line.

​

​Absolute Value

Poll

How was your day off?

• What Day OFF?

​Standard: MGSE.6.NS.7c

​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.

​Learning Target

​I can understand the absolute value of a rational number as its distance from 0 on the number line.

I can 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.

​Essential Question

​How can we use absolute value to find horizontal and vertical distances on the number line, coordinate plane or in the real world?

​WHAT IS AN INTEGER?

​An integer is any WHOLE NUMBER (Positive or Negative) and Zero.

Multiple Select

CHOOSE ALL INTEGERS.

• 15

• -2.7

• $$\frac{3}{4}$$  

• -10

​When determining if a number is an integer,

make sure it is in it's simplest form.

​If a number is written as a decimal like 25.00, it is equivalent to 25. That is a whole number

​If an improper fraction can be simplified to a whole number, then it is representing an integer. Example: -15/3 is simplified as -5

Multiple Select

CHOOSE ALL INTEGERS.

• 36.0

• -2.3

• $$\frac{16}{4}$$  

• $$\frac{1}{5}$$  

• 0

Multiple Choice

Students were asked if 20/5 is an integer. Tyrod said YES, Brandon said NO. Who is right?

•  TYROD

• BRANDON

​WHAT ARE OPPOSITES?

​Each integer has an opposite. If the integer is POSITIVE, the opposite is NEGATIVE. If the integer is NEGATIVE, the opposite is POSITIVE.

​EXAMPLES

​5 and -5 are opposites

-32 and 32 are opposites

0 is its own opposite​

Multiple Choice

What is the opposite of 19?

• 19

• -19

Multiple Choice

What is the opposite of -12?

• 12

• -12

Multiple Choice

What is the opposite of 0?

• 0

• None

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​ABSOLUTE VALUE

​Absolute Value means

DISTANCE FROM 0.

​ABSOLUTE VALUE

​The absolute value of 3 and -3 is 3. They are both 3 units aways from 0.

​ABSOLUTE VALUE

​∣ 3 ∣ = 3

​∣ -3 ∣ = 3​

​ABSOLUTE VALUE

​- ∣ 3 ∣ = -3

- ​∣ -3 ∣ = -3

Multiple Choice

What is​ ∣ 10 ∣ ?

• 10

• -10

• 0

Multiple Choice

What is​ ∣ -9 ∣ ?

• 9

• -9

• 0

Multiple Choice

What is​ -∣ -4 ∣ ?

• 4

• -4

• 0

Reorder

Reorder the following in ascending order. (Smallest to Largest)

• | 0 |

• | -1 |

• | 2 |

• | - 45 |

• | -100 |

1

2

3

4

5

• 1
• 2
• 3
• 4
• 5

Match

Match the following

• | 6 |

• | -5 |

• | 32 |

• | 5 |

• | -6 |

6

5

32

5

6

• 6

• 5

• 32

• 5

• 6

Multiple Select

How comfortable do you feel about this assignment?

Absolute Value

​

Multiple Choice

WHICH STATEMENT DESCRIBES THE MODEL?

• |10| = 10
• |-10| = 10
• |-10| = -10
• -|10| = 10

Multiple Choice

The absolute value of 79 is 79.

• False 
• True

Multiple Choice

Compare |-5| to the |-10|

• |-5| > |-10|
• |-5| = |-10|
• |-5| < |-10|

Multiple Choice

What is the absolute value of |-37|.

• 0
• 37
• -37
• 30

Multiple Choice

What is the absolute value of |-26|

• 26
• -26
• -36
• 36

Multiple Choice

What is the reason that absolute value is always written as a positive?

• Absolute value is talking about numbers so it must be positive.
• Absolute value does not always have to be positive.
• Absolute value is like a clock it has only positive numbers.
• Absolute value is talking about distance, distance is always measured by positive numbers.

Multiple Choice

| –3 |

• 3
• -3
• 0.30
• 30

Multiple Choice

Which statement is true?

• The absolute value of 3 is -3
• The opposite of 7 is 7
• The absolute value of 5 is equal to the opposite of 5
• The opposite of -4 is equal to the absolute value of -4

Multiple Choice

|-20|

• 20
• -20

Multiple Choice

Is absolute value always positive?

• yes
• no

Multiple Choice

Which has the same absolute value as -55?

• 0
• -1
• 1
• 55

Absolute Value

​

Multiple Choice

What is the absolute value of 5?

• 5

• -5

Multiple Choice

What is the absolute value of -4?

• 4

• -4

Absolute Value

• A number's distance from 0

• It is always positive!

• Think about it...you can't really be a negative distance from something

Multiple Choice

Which of these is the correct inequality?

• -6 > 5

• -6 < 5

Multiple Choice

Which of these is the correct inequality?

• 9 > -9

• 9 < -9

• 9 = -9

Multiple Select

Select all the correct inequalities.

• -5 > -3

• -5 < - 3

• -3 > -5

• -3 < -5

Multiple Choice

One morning it was -9 in Boston. On the same morning, it was -7 in Framingham. Was it warmer in Framingham or Boston?

• Boston

• Framingham

Comparing Integers

• The farther right --> a number is on the number line, the greater it's value

• Just because a number is closer to 0 does not mean it has greater value

Multiple Choice

What integer represents the description:

A loss of 8 yards

• 8

• -8

Multiple Choice

What integer represents the description:

20 degrees below 0

• 20

• -20

Multiple Choice

What integer represents the description:

A debt of $500

• 500

• -500

Multiple Choice

What integer represents the description:

A profit of $1,000

• 1,000

• -1,000

Opposites and Absolute Value

​

Use your opposite notes to answer the following questions...

Remember to use the dash - to represent a negative number. Do not put a space between the number and the dash

Poll

Which is the correct way to type in a negative number?

• - 4

• 4-

• negative 4

• -4

Fill in the Blanks

What is the opposite of 2?

Fill in the Blanks

What is the opposite of -70?

Fill in the Blanks

Evaluate: - (5)

Fill in the Blanks

Evaluate: - (-9)

Fill in the Blanks

Evaluate: - (- (20)

Fill in the Blanks

Evaluate: - (- (-12)

Use your absolute value notes to solve the following problems..

Fill in the Blanks

$\left|34\right|$  =

Fill in the Blanks

$\left|-8\right|$  =

Fill in the Blanks

$\left|-13\right|$  =

Fill in the Blanks

$\left|65\right|$  =

Fill in the Blanks

$\left|-7\right|\ +\left|-13\right|$  =

Fill in the Blanks

$\left|9\right|\ +\left|-20\right|$  =

Fill in the Blanks

$\left|-150\right|\ -\left|50\right|$  =

Opposites and Absolute Value

Unit 6: Integers

​Opposite Numbers

​*Opposite numbers are numbers that are in the same positions but on opposite sides of zero.

​*Example: The opposite of -4.5 is 4.5

​*Zero is its own opposite.

​*The opposite of the opposite of a number is equal to the original number.

​*Example: The opposite of the opposite of 10 is 10.

​*Parentheses don't change the value of a number.

​Absolute Value

​The absolute value of a number is its distance from zero on the number line.

​*Absolute value is ALWAYS a positive number.

​*Examples:

​|-12| = 12 |32| = 32

Fill in the Blanks

What is the opposite of 37.5?

Fill in the Blanks

What is the opposite of -98?

Fill in the Blanks

What is the value of |20.5|?

Fill in the Blanks

What is the value of |-29.5|?

Multiple Choice

The opposite of 4 is

• positive 4

  and is represented as (4)

• positive 4 and is represented by |-4|

• negative 4 and can be represented by |-4|

• negative 4 and can be represented by (-4)

Multiple Choice

CHOOSE WHICH POINT THAT REPRESENTS THE OPPOSITE OF - 2.

• point A

• point B

• point C

• point D

Multiple Choice

Which value is furthest from 0 on the number line?

• 8

• -9.5

• |9|

• |-8.5|

Multiple Choice

CHOOSE WHICH POINT REPRESENTS THE OPPOSITE OF 2 1/2.

• point A

• point B

• point C

• point D

Multiple Choice

Which one is greater?

1) The opposite of -6

or

2) |5|

• The opposite of -6

• |5|