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INTERESTINGINTERESTING
INTEGERS!INTEGERS!
5
-7
-3
-8
4
What You Will Learn:What You Will Learn:
 Vocabulary related to integers
 Rules for adding and subtracting
integers
 A ...
Part I: Introduction to IntegersPart I: Introduction to Integers
•VocabularyVocabulary
• positive numberpositive number
• ...
 Positive number – a number
greater than (>) zero
0 1 2 3 4 5 6
Vocabulary:
Hint:Hint:
 If you don’t see a negative or
positive sign in front of a number,
the number is positive.
9 is the same as +9
 Negative number – a number less
than (<) zero
0 1 2 3 4 5 6-1-1-2-2-3-3-4-4-5-5-6-6
Vocabulary:
Integer Number LineInteger Number Line
Horizontal
Numbers above or right of 0
are positive
Numbers below or left of 0
are ...
Integer Number LineInteger Number Line
Vertical
Numbers above 0
are positive
ZER
O
Numbers below 0
are negative
Use the number line to compare the
following integers with >, <, or =.
-4 -2 1 -3 -5 0
Hint: On a number line, the number ...
Use the number line to compare
the following integers with >, <,
or =.
Comparing IntegersComparing Integers
Hint: On a num...
Ordering IntegersOrdering Integers
Use the number line to put the following
integers in order from least to greatest.
-4, ...
 Opposite Numbers – numbers
that are the same distance from
zero in the opposite direction
0 1 2 3 4 5 6-1-2-3-4-5-6
Voca...
What is the opposite of each
integer?
+7 -7
+5
-1
+8
+1
5 -8
Vocabulary:
Integers – all the whole numbers
and all of their opposites on the
number line including zero
0 1 2 3 4 5 6-1-...
Now, you’re probably saying,
“That’s interesting and
everything, BUT where are
negative numbers in the real
world??
??
Negative Numbers Are Used to
Measure Temperature
Negative Numbers Are Used to
Measure Under Sea Level
0
10
20
30
-10
-20
-30
-40
-50
Positive and negative numbers
are used when keeping track of
money.
+ Positive +
$$ you earn
- Negative -
$$ you spend
Positive Numbers are Used to Show
Earnings or Assets
When you get paid
(or win the lottery),
you add that $$ to
your accou...
Negative Numbers are Used to Show
What You Owe or Debt
If your mom loaned you $10 for pizza,
Mom,
I. O. U.
$10
The $10 you...
Write an integer to describe the real
world situation:
 Gain 3 pounds:
 Withdraw $15:
 5 feet below sea level:
 Move a...
End - Part I: Introduction to IntegersEnd - Part I: Introduction to Integers
•VocabularyVocabulary
• positive numberpositi...
Part II: Adding IntegersPart II: Adding Integers
Key ConceptsKey Concepts
Integer Addition RulesInteger Addition Rules
Usi...
** Key Concepts **** Key Concepts **
The sum of two positive numbers is always
positive  (+) + (+) = (+)
ex. 5 + 1 = 6
Th...
** Key Concepts **
(+) + (+) = (+) (-) + (-) = (-)
(+) + (-) = sometimes (+)
= sometimes (-)
= sometimes 0
AND
Integer Addition RulesInteger Addition Rules
 Rule #1 – If the signs are the same, add
the numbers and then put the sign ...
SolveSolve the Problemsthe Problems
 -3 + -5 =
 4 + 6 =
 +3 + (+4) =
 -6 + -7 =
 5 + 9 =
 -9 + -9 =
-8
-18
14
-13
7
...
 Rule #2 – If the signs of the addends are
DIFFERENT, start at the location of the
first integer on the number line and:
...
ex. (-6) + 5 = -1Start here at -6
0 1 2 3 4 5 6-1-2-3-4-5-6
then count forward or right 5 spaces
+
Adding Integers Using a...
Solve the ProblemsSolve the Problems
• 8 + 6 =
• (-9) + 5 =
• (–11) + 11 =
• (–8) + 16 =
14
0
8
-4
 Rule #2 – If the signs of the addends are
DIFFERENT, start at the location of the
first integer on the number line and:
...
0 1 2 3 4 5 6-1-2-3-4-5-6
-
ex. +3 + (-5) = -2
Start here at +3
Then count back or left 5 spaces
Adding Integers Using a N...
Solve the ProblemsSolve the Problems
• 2 + (-12) =
• –8 + (-5) =
• 14 + (-7) =
• 15 + (-15) =
-10
7
-13
0
Part III
Part III: Subtracting IntegersPart III: Subtracting Integers
** Key Concept **** Key Concept **
To subtract an integer, ad...
ex. -1 – (-2) is the same as
-1 + (+2) and -1 + 2 = 1
Subtracting a negative number is
the same as adding a positive.
Chan...
-3 – 4 is the same as
-3 + (-4) and -3 + (-4) = -7
More Examples
2 – (-7) is the same as
2 + (+7) and 2 + 7 = 9
KEEP the s...
More Examples
12 – (-8) is the same as
12 + (+8) and 12 + 8 = 20
-3 – (-11) is the same as
-3 + (+11) and -3 + 11 = 8
KEEP...
Problems
to Solve
8 – (-12) is the same as
8 + (+12) and 8 + 12 = 20
22 – (-30) is the same as
22 + (+30) and 22 + 30 = 52...
Problems to Solve
-17– (-3) is the same as
-17 + (+3) and -17 + 3 = -14
-8 – 3 is the same as
-8 + (-3) and -8 + -3 = -11
...
Part IV
How do we know that
“Subtracting a negative number is the
same as adding a positive” is true?
We can use the same method w...
When you subtract a – b it equals c
a – b = c
ex. 5 – 2 = 3
To check if your answer is correct,
add b and c
a = b + c
ex. ...
If a – b = c, and….
2 – (-5) is the same as
2 + (+5), which equals 7,
Then let’s check with the
negative numbers to see if...
Here are some examples:
a – b = c a = b + c
9 – 5 = 4 9 = 5 + 4
a – b = c a = b + c
20 – 3 = 17 20 = 3 + 17
If the method for checking
subtraction works, it should
also work for subtracting
negative numbers.
a – b = c a = b + c
2 – (-5) = 7 2 = -5 + 7
It works!
a – b = c a = b + c
-11 – (-3) = -8 -11 = -3 + -8
YES!
Check Your Answers
1. Solve: 3 – 10 = 7
Check: 3 = 10 + (-7)
2. Solve: 17 – ( 12) = 29
Continued on next slide
Check: 17 =...
Check Your Answers
1. Solve: 20 – ( 5) = 25
Check: 20 = -5 + 25
1. Solve: -7 – ( 2) = -5
Check: -7 = -2 + -5
Review Integers Part V
You have learned many things
about adding and subtracting
positive and negative numbers.
Let’s review!
Definition:
 Absolute Value – the size of a
number with or without the
negative sign.
The absolute value of
9 or of –9 is...
Integer Addition Rules
 Rule #1 – If the signs are the same,
pretend the signs aren’t there. Add the
numbers and then put...
Integer Addition Rules
 Rule #2 – If the signs are different pretend the
signs aren’t there. Subtract the smaller from th...
0 1 2 3 4 5 6-1-2-3-4-5-6
• When the number is positive, count
to the right
• When the number is negative, count
to the le...
Integer Subtraction Rule
Subtracting a negative number is the
same as adding a positive. Change
the signs and add.
2 – (-7...
How do we know that
“Subtracting a negative number
is the same as adding a positive”
is true?
We can use the same
method w...
a – b = c a = b + c
2 – (-5) = 7 2 = -5 + 7
It works!
a – b = c a = b + c
-11 – (-3) = -8 -11 = -3 + -8
YES!
Discuss with a partner ways
that you know that that is
problem is solved correctly.
6 – (-9) = 15
Aren’t integers
interesting?
Independent Practice
Solve The ProblemsSolve The Problems
 3 + -5 =
 -4 + 7 =
 (+3) + (-4) =
 -6 + 7 =
 5 + -9 =
 -9 + 9 =
-25 – 3 = 2
0
...
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Add and subtract pos and neg numbers 4 parts

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Add and subtract pos and neg numbers 4 parts

  1. 1. INTERESTINGINTERESTING INTEGERS!INTEGERS! 5 -7 -3 -8 4
  2. 2. What You Will Learn:What You Will Learn:  Vocabulary related to integers  Rules for adding and subtracting integers  A method for proving that a rule is true Are you ready??Are you ready??
  3. 3. Part I: Introduction to IntegersPart I: Introduction to Integers •VocabularyVocabulary • positive numberpositive number • negative numbernegative number •Horizontal & vertical number linesHorizontal & vertical number lines •Comparing IntegersComparing Integers •Ordering IntegersOrdering Integers •Vocabulary - continuedVocabulary - continued • opposite numberopposite number • integerinteger •Real World Applications & ExamplesReal World Applications & Examples • temperaturetemperature • sea levelsea level • moneymoney
  4. 4.  Positive number – a number greater than (>) zero 0 1 2 3 4 5 6 Vocabulary:
  5. 5. Hint:Hint:  If you don’t see a negative or positive sign in front of a number, the number is positive. 9 is the same as +9
  6. 6.  Negative number – a number less than (<) zero 0 1 2 3 4 5 6-1-1-2-2-3-3-4-4-5-5-6-6 Vocabulary:
  7. 7. Integer Number LineInteger Number Line Horizontal Numbers above or right of 0 are positive Numbers below or left of 0 are negative ZERO
  8. 8. Integer Number LineInteger Number Line Vertical Numbers above 0 are positive ZER O Numbers below 0 are negative
  9. 9. Use the number line to compare the following integers with >, <, or =. -4 -2 1 -3 -5 0 Hint: On a number line, the number to the left is always less than the number to the right. Comparing IntegersComparing Integers < < >
  10. 10. Use the number line to compare the following integers with >, <, or =. Comparing IntegersComparing Integers Hint: On a number line, the number on the top is always greater than the number on the bottom. -3 -5 -5 0 0 -1> > >
  11. 11. Ordering IntegersOrdering Integers Use the number line to put the following integers in order from least to greatest. -4, 3, 0, and -5 -5, -4, 0, 3
  12. 12.  Opposite Numbers – numbers that are the same distance from zero in the opposite direction 0 1 2 3 4 5 6-1-2-3-4-5-6 Vocabulary:
  13. 13. What is the opposite of each integer? +7 -7 +5 -1 +8 +1 5 -8
  14. 14. Vocabulary: Integers – all the whole numbers and all of their opposites on the number line including zero 0 1 2 3 4 5 6-1-2-3-4-5-6 integers
  15. 15. Now, you’re probably saying, “That’s interesting and everything, BUT where are negative numbers in the real world?? ??
  16. 16. Negative Numbers Are Used to Measure Temperature
  17. 17. Negative Numbers Are Used to Measure Under Sea Level 0 10 20 30 -10 -20 -30 -40 -50
  18. 18. Positive and negative numbers are used when keeping track of money. + Positive + $$ you earn - Negative - $$ you spend
  19. 19. Positive Numbers are Used to Show Earnings or Assets When you get paid (or win the lottery), you add that $$ to your account.
  20. 20. Negative Numbers are Used to Show What You Owe or Debt If your mom loaned you $10 for pizza, Mom, I. O. U. $10 The $10 you owe her is described by the integer -10.
  21. 21. Write an integer to describe the real world situation:  Gain 3 pounds:  Withdraw $15:  5 feet below sea level:  Move ahead 4 spaces: 3 or +3 -15 -5 4 or +4
  22. 22. End - Part I: Introduction to IntegersEnd - Part I: Introduction to Integers •VocabularyVocabulary • positive numberpositive number • negative numbernegative number •Horizontal & vertical number linesHorizontal & vertical number lines •Comparing IntegersComparing Integers •Ordering IntegersOrdering Integers •Vocabulary - continuedVocabulary - continued • opposite numberopposite number • integerinteger •Real World Applications & ExamplesReal World Applications & Examples • temperaturetemperature • sea levelsea level • moneymoney
  23. 23. Part II: Adding IntegersPart II: Adding Integers Key ConceptsKey Concepts Integer Addition RulesInteger Addition Rules Using Number LinesUsing Number Lines
  24. 24. ** Key Concepts **** Key Concepts ** The sum of two positive numbers is always positive  (+) + (+) = (+) ex. 5 + 1 = 6 The sum of two negative numbers is always negative  (-) + (-) = (-) ex. -5 + -1 = -6
  25. 25. ** Key Concepts ** (+) + (+) = (+) (-) + (-) = (-) (+) + (-) = sometimes (+) = sometimes (-) = sometimes 0 AND
  26. 26. Integer Addition RulesInteger Addition Rules  Rule #1 – If the signs are the same, add the numbers and then put the sign of the addends in front of your answer. b) -9 + -5 = -14 a) -9 + -5 =
  27. 27. SolveSolve the Problemsthe Problems  -3 + -5 =  4 + 6 =  +3 + (+4) =  -6 + -7 =  5 + 9 =  -9 + -9 = -8 -18 14 -13 7 10
  28. 28.  Rule #2 – If the signs of the addends are DIFFERENT, start at the location of the first integer on the number line and:  a) move RIGHT to add a positive integer Integer Addition RulesInteger Addition Rules -5 + 3 = -2 1 2 3
  29. 29. ex. (-6) + 5 = -1Start here at -6 0 1 2 3 4 5 6-1-2-3-4-5-6 then count forward or right 5 spaces + Adding Integers Using a Number LineAdding Integers Using a Number Line * adding a* adding a positive integer *integer *
  30. 30. Solve the ProblemsSolve the Problems • 8 + 6 = • (-9) + 5 = • (–11) + 11 = • (–8) + 16 = 14 0 8 -4
  31. 31.  Rule #2 – If the signs of the addends are DIFFERENT, start at the location of the first integer on the number line and:  b) move LEFT to add a negative integer Integer Addition RulesInteger Addition Rules 4 + -3 = 1 123
  32. 32. 0 1 2 3 4 5 6-1-2-3-4-5-6 - ex. +3 + (-5) = -2 Start here at +3 Then count back or left 5 spaces Adding Integers Using a Number LineAdding Integers Using a Number Line * adding a* adding a negative integer *integer *
  33. 33. Solve the ProblemsSolve the Problems • 2 + (-12) = • –8 + (-5) = • 14 + (-7) = • 15 + (-15) = -10 7 -13 0
  34. 34. Part III
  35. 35. Part III: Subtracting IntegersPart III: Subtracting Integers ** Key Concept **** Key Concept ** To subtract an integer, add its opposite ex. 5 – 2 = 5 + (-2) = 3 KEEP CHANGE CHANGE
  36. 36. ex. -1 – (-2) is the same as -1 + (+2) and -1 + 2 = 1 Subtracting a negative number is the same as adding a positive. Change the signs and add. Integer Subtraction Rule KEEP CHANGE CHANGE
  37. 37. -3 – 4 is the same as -3 + (-4) and -3 + (-4) = -7 More Examples 2 – (-7) is the same as 2 + (+7) and 2 + 7 = 9 KEEP the sign of the 1st integer the same CHANGE the operation ( + to – or – to +) CHANGE the sign of the 2nd integer
  38. 38. More Examples 12 – (-8) is the same as 12 + (+8) and 12 + 8 = 20 -3 – (-11) is the same as -3 + (+11) and -3 + 11 = 8 KEEP the sign of the 1st integer the same CHANGE the operation ( + to – or – to +) CHANGE the sign of the 2nd integer
  39. 39. Problems to Solve 8 – (-12) is the same as 8 + (+12) and 8 + 12 = 20 22 – (-30) is the same as 22 + (+30) and 22 + 30 = 52 KEEP the sign of the 1st integer the same CHANGE the operation ( + to – or – to +) CHANGE the sign of the 2nd integer
  40. 40. Problems to Solve -17– (-3) is the same as -17 + (+3) and -17 + 3 = -14 -8 – 3 is the same as -8 + (-3) and -8 + -3 = -11 KEEP the sign of the 1st integer the same CHANGE the operation ( + to – or – to +) CHANGE the sign of the 2nd integer
  41. 41. Part IV
  42. 42. How do we know that “Subtracting a negative number is the same as adding a positive” is true? We can use the same method we use to check our answers when we do regular subtraction.
  43. 43. When you subtract a – b it equals c a – b = c ex. 5 – 2 = 3 To check if your answer is correct, add b and c a = b + c ex. 5 = 2 + 3
  44. 44. If a – b = c, and…. 2 – (-5) is the same as 2 + (+5), which equals 7, Then let’s check with the negative numbers to see if it’s true…
  45. 45. Here are some examples: a – b = c a = b + c 9 – 5 = 4 9 = 5 + 4 a – b = c a = b + c 20 – 3 = 17 20 = 3 + 17
  46. 46. If the method for checking subtraction works, it should also work for subtracting negative numbers.
  47. 47. a – b = c a = b + c 2 – (-5) = 7 2 = -5 + 7 It works! a – b = c a = b + c -11 – (-3) = -8 -11 = -3 + -8 YES!
  48. 48. Check Your Answers 1. Solve: 3 – 10 = 7 Check: 3 = 10 + (-7) 2. Solve: 17 – ( 12) = 29 Continued on next slide Check: 17 = -12 + 29
  49. 49. Check Your Answers 1. Solve: 20 – ( 5) = 25 Check: 20 = -5 + 25 1. Solve: -7 – ( 2) = -5 Check: -7 = -2 + -5
  50. 50. Review Integers Part V
  51. 51. You have learned many things about adding and subtracting positive and negative numbers. Let’s review!
  52. 52. Definition:  Absolute Value – the size of a number with or without the negative sign. The absolute value of 9 or of –9 is 9.
  53. 53. Integer Addition Rules  Rule #1 – If the signs are the same, pretend the signs aren’t there. Add the numbers and then put the sign of the addends in front of your answer. 9 + 5 = 14 -9 + -5 = -14
  54. 54. Integer Addition Rules  Rule #2 – If the signs are different pretend the signs aren’t there. Subtract the smaller from the larger one and put the sign of the one with the larger absolute value in front of your answer. -9 + +5 = 9 - 5 = 4 Larger abs. value Answer = - 4
  55. 55. 0 1 2 3 4 5 6-1-2-3-4-5-6 • When the number is positive, count to the right • When the number is negative, count to the left +- Adding Integers Using a Number LineAdding Integers Using a Number Line
  56. 56. Integer Subtraction Rule Subtracting a negative number is the same as adding a positive. Change the signs and add. 2 – (-7) is the same as 2 + (+7) 2 + 7 = 9!
  57. 57. How do we know that “Subtracting a negative number is the same as adding a positive” is true? We can use the same method we use to check our answers when we subtract.
  58. 58. a – b = c a = b + c 2 – (-5) = 7 2 = -5 + 7 It works! a – b = c a = b + c -11 – (-3) = -8 -11 = -3 + -8 YES!
  59. 59. Discuss with a partner ways that you know that that is problem is solved correctly. 6 – (-9) = 15
  60. 60. Aren’t integers interesting?
  61. 61. Independent Practice
  62. 62. Solve The ProblemsSolve The Problems  3 + -5 =  -4 + 7 =  (+3) + (-4) =  -6 + 7 =  5 + -9 =  -9 + 9 = -25 – 3 = 2 0 -4 1 -1 3 9 – 9 = 0 9 – 5 = 4 7 – 6 = 1 4 – 3 = 1 7 – 4 = 3

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