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Integers and Absolute Value - · PDF file Integers and Absolute Value • The absolute value of a number is the distance between 0 and the number on a number line. • Remember that

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  • 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.

    0 1 2 3 4-1-2-3-4 5 6-5-6

    Negative integers Positive integers

    Zero is neither positive nor negative

  • 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’

    0 1 2 3 4-1-2-3-4 5 6-5-6

  • 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‘

    0 1 2 3 4-1-2-3-4 5 6-5-6

  • 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”

    0 1 2 3 4-1-2-3-4 5 6-5-6

  • 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.

    0 1 2 3 4-1-2-3-4 5 6-5-6

    βˆ’πŸ”

  • 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.

    0 1 2 3 4-1-2-3-4 5 6-5-6

    πŸ“

  • 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

    0 1 2 3 4-1-2-3-4 5 6-5-6

  • Integers and Absolute Value

    Sample Problem 5: Compare the following integers. Write .

    a. 𝟏𝟐 _____ βˆ’ πŸπŸπŸ“

  • Integers and Absolute Value

    Sample Problem 5: Compare the following integers. Write .

    a. 𝟏𝟐 > βˆ’πŸπŸπŸ“

  • Integers and Absolute Value

    Sample Problem 5: Compare the following integers. Write .

    b. πŸπŸ“_______ βˆ’ πŸπŸ“

  • Integers and Absolute Value

    Sample Problem 5: Compare the following integers. Write .

    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’ βˆ’πŸ– = πŸ– βˆ’πŸ‘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–