6-1 6th grade math

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6-16th grade math

• Comparing and Ordering
• Positive and Negative Numbers

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Objective

• To compare and order positive and negative
  numbers.
• Why? To understand all types numbers. Negatives
  are to the left of the number line. Zero is in
  the middle. Positives are to the right.

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California State Standards

• NS 1.1 Compare and order positive and
  negative fractions, decimals, and mixed numbers
  and place them on a number line.
• MR 1.1 Analyze problems by identifying
  relationships, distinguishing relevant from
  irrelevant information sequencing and
  prioritizing information, and observing patterns.

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Vocabulary

• Integers
• A set of numbers either positive or negative.
  The term integer is now used instead of the
  term number.
• , -3, -2, -1, 0, 1, 2, 3,
• Negative Numbers
• Integers whose value is less than zero
• -5, -10 , -23 9/11, -456, etc.
• Positive Numbers
• Integers whose value is more than zero. At times
  a positive number may NOT have the sign.
• 2, 63, 77 2/3, etc.
• Absolute Value
• The distance an integer is from zero on a number
  line. It is neither positive nor negative.
• 2 2
• -5 5
• Opposites
• A pair of integers that are the same distance
  from zero
• -2 and 2

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How to Compare and Order Positive and Negative
Numbers

• -5 , 30
• -30 is a negative number and therefore smaller
  than a positive
• -5 lt -30 or -30 gt -5
• -234, 5
• -234 is a negative number and therefore smaller
  than a positive
• -234 lt 5 or 5 gt -234

• Any negative number is less than any positive
  number.
• b) Any positive number is greater than any
  negative number.

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• c) -10, -15
• -15 is farther away from 0
• -10 gt -15 or -15 lt -10
• d) 34, 9 ½
• 9 ½ is closest to 0
• 34 gt 9 ½ or 9 ½ lt 34

• c) If comparing 2 negative numbers, the number
  farther away from 0 is less than the other.
• d) If comparing 2 positive numbers, the number
  closest to 0 is lesser than the other.

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Remember your signs!

• gt means greater than.
• lt means less than.
• c) Eat the bigger number

1. -4 gt -10
2. 9 lt 90

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Placing Integers on a Number Line

• 2, -0.5, 1 ¾, 0, -2 ¼, -3
• Separate the negative integers from the positives
• Remember larger negative integers are farther
  away from 0 and are placed farthest away from 0.
  Count backwards.
• Count forward when placing positive integers.
• Place on a number line, starting with the
  negative integers.

• -0.5, -2 ¼, -3
• 0
• 2, 1 ¾
• 4) -3, -2 ¼, -0.5, 0, 1 ¾, 2

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Try It!

• 3 gt -2
• Why- a positive is always greater than a
  negative.
• 2) -7 lt 0
• Why- zero is always greater than a negative.
• 3) -4 gt -9
• Why- -4 is closer to 0 .
• 4) 8 gt -2
• Why- a positive is always greater than a negative.

• Use lt , gt , or
• 3 -2
• -7 0
• -4 -9
• 8 -2

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Try Some More!

• 5) -12
• 0
• 5, 15
• -12, 0, 5, 15
• 6) -5, -3 ½, -2.25
• 2 ½, 1 ¾
• -5, -3 ½, -2.25, 1 ¾, 2 ½

• Arrange in order least to greatest.
• 5) 0, 5, -12, 15
• 6) -5, 2 ½, -3 ½,-2.25, 1 ¾

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Heres Even More!

• 7) -11
• -11 11
• 11
• 8) -43
• -43 43
• 43
• 9) 18
• 18 18
• -18
• 10) -25
• -25 25
• 25

• Find the absolute value AND the opposite.
• 7) -11
• 8) -43
• 9) 18
• 10) -25

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Objective Review

• To compare and order positive and negative
  numbers.

• Why? Now you can understand all types numbers.
  Negatives are to the left of the number line.
  Zero is in the middle. Positives are to the
  right.

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Independent Practice

• Complete problems 12-25
• Copy original problem first.
• Show all work!

• If time, complete Mixed Review 26-33
• If still more time, work on Accelerated Math.