Integers and Absolute Value

Integers and Absolute Value
Unit 1 Lesson 5
Integers and Absolute Value
Students will be able to:
Understand integers and absolute value
Key Vocabulary:
An integer
Positive number
Negative number
Absolute value
Opposite
Integers and Absolute Value
Integers
β€’ An integer is a positive or negative whole number.
β€’ A positive number is a number greater than zero.
β€’ A negative number is a number less than zero.
Integers and Absolute Value
This number line shows integers.
Negative integers
-6
-5
-4
-3
-2
Positive integers
-1
0
1
2
3
4
5
Zero is neither positive nor negative
6
Integers and Absolute Value
Sample Problem 1: Write an integer to represent each
situation.
a.
𝟐𝟐 𝒇𝒕 below sea level
Integers and Absolute Value
Sample Problem 1: Write an integer to represent each
situation.
a.
𝟐𝟐 𝒇𝒕 below sea level
βˆ’πŸπŸ
Integers and Absolute Value
Sample Problem 1: Write an integer to represent each
situation.
b.
a bonus of $πŸπŸ“πŸŽ
Integers and Absolute Value
Sample Problem 1: Write an integer to represent each
situation.
b.
a bonus of $πŸπŸ“πŸŽ
+πŸπŸ“πŸŽ
Integers and Absolute Value
Sample Problem 1: Write an integer to represent each
situation.
c.
πŸ• points lost
Integers and Absolute Value
Sample Problem 1: Write an integer to represent each
situation.
c.
πŸ• points lost
βˆ’πŸ•
Integers and Absolute Value
Sample Problem 2: Graph each integer or set of integers
on a number line.
a. βˆ’πŸ’
Integers and Absolute Value
Sample Problem 2: Graph each integer or set of integers
on a number line.
a. βˆ’πŸ’
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
Integers and Absolute Value
Sample Problem 2: Graph each integer or set of integers
on a number line.
b.
βˆ’πŸ‘, 𝟎, πŸ‘
Integers and Absolute Value
Sample Problem 2: Graph each integer or set of integers
on a number line.
b.
βˆ’πŸ‘, 𝟎, πŸ‘
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
Integers and Absolute Value
Sample Problem 2: Graph each integer or set of integers
on a number line.
c.
βˆ’πŸ, βˆ’πŸ, πŸ’, πŸ”
Integers and Absolute Value
Sample Problem 2: Graph each integer or set of integers
on a number line.
c.
βˆ’πŸ, βˆ’πŸ, πŸ’, πŸ”
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
Integers and Absolute Value
β€’ Every integer has an opposite integer.
β€’ A number and its opposite are the same
distance from 0.
Integers and Absolute Value
Sample Problem 3: Find the opposite of each integer.
a.
βˆ’πŸ‘πŸ’
Integers and Absolute Value
Sample Problem 3: Find the opposite of each integer.
a.
βˆ’πŸ‘πŸ’
+πŸ‘πŸ’
Integers and Absolute Value
Sample Problem 3: Find the opposite of each integer.
b.
+𝟏𝟎𝟎
Integers and Absolute Value
Sample Problem 3: Find the opposite of each integer.
b.
+𝟏𝟎𝟎
βˆ’πŸπŸŽπŸŽ
Integers and Absolute Value
Sample Problem 3: Find the opposite of each integer.
c.
𝟎
Integers and Absolute Value
Sample Problem 3: Find the opposite of each integer.
c.
𝟎
None opposite
Integers and Absolute Value
Sample Problem 4: Graph each integer and its opposite
on a number line.
a.
βˆ’πŸ”
Integers and Absolute Value
Sample Problem 4: Graph each integer and its opposite
on a number line.
a.
βˆ’πŸ”
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
Integers and Absolute Value
Sample Problem 4: Graph each integer and its opposite
on a number line.
b.
πŸ“
Integers and Absolute Value
Sample Problem 4: Graph each integer and its opposite
on a number line.
b.
πŸ“
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
Integers and Absolute Value
Sample Problem 4: Graph each integer and its opposite
on a number line.
c.
βˆ’πŸ
Integers and Absolute Value
Sample Problem 4: Graph each integer and its opposite
on a number line.
c.
βˆ’πŸ
-6
-5
-4
-3
-2
-1
0
1
2
3
4
5
6
Integers and Absolute Value
Sample Problem 5: Compare the following integers.
Write <, = 𝒐𝒓 >.
a.
𝟏𝟐 _____ βˆ’ πŸπŸπŸ“
Integers and Absolute Value
Sample Problem 5: Compare the following integers.
Write <, = 𝒐𝒓 >.
a.
𝟏𝟐 > βˆ’πŸπŸπŸ“
Integers and Absolute Value
Sample Problem 5: Compare the following integers.
Write <, = 𝒐𝒓 >.
b. πŸπŸ“_______ βˆ’ πŸπŸ“
Integers and Absolute Value
Sample Problem 5: Compare the following integers.
Write <, = 𝒐𝒓 >.
b. πŸπŸ“ > βˆ’πŸπŸ“
Integers and Absolute Value
β€’ The absolute value of a number is the
distance between 0 and the number on a
number line.
β€’ Remember that distance is always a positive
quantity (or zero).
β€’ Two vertical bars are used to represent
absolute value. The symbol for absolute value
of πŸ‘ is πŸ‘ .
Integers and Absolute Value
Sample Problem 6: Find the absolute value of the
following numbers.
a.
βˆ’πŸπŸ‘ =
Integers and Absolute Value
Sample Problem 6: Find the absolute value of the
following numbers.
a.
βˆ’πŸπŸ‘ =
βˆ’πŸπŸ‘ = πŸπŸ‘
Integers and Absolute Value
Sample Problem 6: Find the absolute value of the
following numbers.
b.
+πŸ’πŸ’ =
Integers and Absolute Value
Sample Problem 6: Find the absolute value of the
following numbers.
b.
+πŸ’πŸ’ =
+πŸ’πŸ’ = πŸ’πŸ’
Integers and Absolute Value
Sample Problem 6: Find the absolute value of the
following numbers.
c.
βˆ’πŸ, πŸ—πŸ—πŸ— =
Integers and Absolute Value
Sample Problem 6: Find the absolute value of the
following numbers.
c.
βˆ’πŸ, πŸ—πŸ—πŸ— =
βˆ’πŸ, πŸ—πŸ—πŸ— = 𝟏, πŸ—πŸ—πŸ—
Integers and Absolute Value
Sample Problem 7: Order the values from least to
greatest.
a.
βˆ’πŸπŸ“ , 𝟏𝟏, βˆ’πŸ, βˆ’πŸ’
Integers and Absolute Value
Sample Problem 7: Order the values from least to
greatest.
a.
βˆ’πŸπŸ“ , 𝟏𝟏, βˆ’πŸ, βˆ’πŸ’
βˆ’πŸπŸ“ = πŸπŸ“
βˆ’πŸ’ = πŸ’
πŸπŸ“,
𝟏𝟏,
βˆ’πŸ,
πŸ’
βˆ’πŸ,
πŸ’,
𝟏𝟏,
πŸπŸ“
βˆ’πŸ,
βˆ’πŸ’ ,
𝟏𝟏,
βˆ’πŸπŸ“
Integers and Absolute Value
Sample Problem 7: Order the values from least to
greatest.
b.
πŸ’, +πŸ’πŸ’ , βˆ’πŸ– , βˆ’πŸ, βˆ’πŸ‘πŸ
Integers and Absolute Value
Sample Problem 7: Order the values from least to
greatest.
b.
πŸ’, +πŸ’πŸ’ , βˆ’πŸ– , βˆ’πŸ, βˆ’πŸ‘πŸ
+πŸ’πŸ’ = πŸ’πŸ’
πŸ’,
βˆ’πŸ– = πŸ–
βˆ’πŸ‘πŸ = πŸ‘πŸ
πŸ’πŸ’,
πŸ–,
βˆ’πŸ,
πŸ‘πŸ
βˆ’πŸ,
πŸ’,
πŸ–,
πŸ‘πŸ,
πŸ’πŸ’
βˆ’πŸ,
πŸ’,
βˆ’πŸ– ,
βˆ’πŸ‘πŸ ,
+πŸ’πŸ’
Integers and Absolute Value
Sample Problem 8: Evaluate each of the following
expressions.
a.
βˆ’πŸπŸ‘ + πŸπŸ‘ βˆ’ πŸπŸ’ =
Integers and Absolute Value
Sample Problem 8: Evaluate each of the following
expressions.
a.
βˆ’πŸπŸ‘ + πŸπŸ‘ βˆ’ πŸπŸ’ =
= πŸπŸ‘ + πŸπŸ‘ βˆ’ πŸπŸ’ =
= πŸπŸ” βˆ’ πŸπŸ’ =
= 𝟏𝟐
Integers and Absolute Value
Sample Problem 8: Evaluate each of the following
expressions.
b.
πŸ“πŸ’ βˆ’ +πŸ’πŸ’ βˆ’ βˆ’πŸ– =
Integers and Absolute Value
Sample Problem 8: Evaluate each of the following
expressions.
b.
πŸ“πŸ’ βˆ’ +πŸ’πŸ’ βˆ’ βˆ’πŸ– =
= πŸ“πŸ’ βˆ’ πŸ’πŸ’ βˆ’ πŸ– =
= 𝟏𝟎 βˆ’ πŸ– =
=𝟐
Integers and Absolute Value
Sample Problem 8: Evaluate each of the following
expressions.
c.
πŸπŸπŸ– + βˆ’πŸ— βˆ— 𝟏𝟎 βˆ— βˆ’πŸ’ =
Integers and Absolute Value
Sample Problem 8: Evaluate each of the following
expressions.
c.
πŸπŸπŸ– + βˆ’πŸ— βˆ— 𝟏𝟎 βˆ— βˆ’πŸ’ =
= πŸπŸπŸ– + πŸ— βˆ— 𝟏𝟎 βˆ— πŸ’ =
= πŸπŸπŸ– + πŸ—πŸŽ βˆ— πŸ’ =
= πŸπŸπŸ– + πŸ‘πŸ”πŸŽ =
= πŸ’πŸ–πŸ–