1. 1-1 Adding and Subtracting Whole Numbers

2. Place Values of Whole Numbers

3. Adding Whole Numbers
Set up the problem by writing units under units, tens under tens, and so on.
Add each column separately, beginning at the top of the units column.
If the sum of any column is two or more digits, write the units digit in your answer and carry the remaining digit(s) to the top of the next column to the left.
Add any carried digit(s) above the column with that column.

4. Examples:
#1) #2) #3) #4)

5. #5)

6. Subtracting Whole Numbers
Set up the problem by writing units under units, tens under tens, and so on.
Subtract each column separately, beginning at the bottom of the units column.
If a digit in the number being subtracted is larger than the digit above it, “borrow” 1 from the top digit in the next column to the left, decreasing that digit by one and increasing the digit being subtracted by ten.

7. 4. If there is nothing to borrow in the next left column (column contains a zero), first borrow for that column from its next left column.
5. Check your subtraction by adding your answer to the subtracted number.

8. Examples:
#1) 85-8 #2) #3) #4)

9. Do Now: 9/15/11 Take out HW – Adding and Subtracting Whole Numbers WS
Hand in Class Expectations Form
Hand in Summer Packet
4) Problem of the Day: (Remember to include the date)
a) b)

10. Homework Answers: Adding and Subtracting Whole Numbers CW WS

11. Multiplying Whole Numbers
Set up the problem by writing the larger number (original number) above the smaller number (multiplier), writing units under units, tens under tens, and so on.
If the multiplier contains only one digit, multiply each digit in the original number by it, working from right to left.
If the multiplier contains more than one digit find partial products.
Add the partial products.

12. Examples:
#1) 129 (3) #2) 34 (16) #3) 46 (37) #4) 175(89)

13. #5) 987 (105)

14. Dividing Whole Numbers
Set up the problem by writing the original number (number to be divided) inside a division frame, and by writing the divisor (number you are dividing by) outside the frame.
Determine how many times the divisor will go into the first digit of the original number. If it will not, write a zero in the answer space directly above the first digit, and then determine how many times the divisor will go into the first two numbers of the original number.

15. 3. Multiply the divisor by the answer (digit above frame); write this answer under the digit(s) that divisor went into, and subtract.
4. Bring down the next unused digit from the original number and place it to the right of the subtracted difference (remainder) – even if the remainder is zero.
5. Determine how many times the divisor will go into this new number; write your answer in the answer space above the digit that was brought down.

16. 6. Multiply the divisor by the last digit you wrote in the answer; write this product under the digits that divisor went into and subtract.
7. Continue this process until all numbers in the original number have been used.
8. Write any remaining subtracted differences as a remainder.
9. Check the answer by multiplying your answer times the divisor and adding the remainder to this number.

17. Examples:
#1) #2) 4800 / 80 #3) #4)

18. Word Problems:
#1) A farm produces 864 bushels of corn per square kilometer. The farmer plants 127 km2 of corn. How many bushels of corn will the farm produce?

19. #2) Joan has 688 bananas stored in boxes
#2) Joan has 688 bananas stored in boxes. If the are 86 boxes, how many bananas must go in each box?

20. #3) A bee travels 147 m one way from its hive to the garden
#3) A bee travels 147 m one way from its hive to the garden. If the bee makes 93 round trips between the hive and the garden, how far will it have traveled? Be careful!

21. Today’s Agenda: CW: Basic Operation Review CW WS
Addition, Subtraction, Multiplication, and Division BINGO
HW: Whole Numbers Operations Quiz Review

22. Do Now: 9/19/11
1) Take out HW: Whole Numbers Operations Quiz Review 2) Problem of the Day: (Remember to include the date) a) b) c) 15 (27) d) 216÷ 18

23. Homework Answers: Whole Numbers Operations Quiz Review
#1) 6,126 #2) 1,967 #3) 64,701 #4) 86 #5) 415,741

24. Comparing and Ordering Decimals
When Will I Ever Do That???!!!

25. Why do I have to understand decimals?
This is a good question. We need to understand what the value of each number means in order to understand what we are talking about. Here is an example:
A shirt costs $12.05, but when I wrote the number down I wrote $ What is wrong with this?

26. Why is $12.5 wrong?
$12.5 really is saying $12.50, because when we read how much something costs it always has two places after the decimal point. If we don’t have a number after the first number we must assume it is a zero. However, when we read $12.05, the zero is the place holder so we know it is 5¢ and not 50¢. That is a 45¢ difference. I can get a piece of gum for that amount!

27. McDonald’s Menu…. I’m Lovin It!!
Double Cheeseburger: $ .99
Big Mac Value Meal: $ 4.79
Chicken McNuggetts Meal: $ 3.80
Small Drink: $ .99
McFlurry: $ 1.97
Salad: $ 4.80
2 Cheeseburger Meal: $ 3.70
Ice Cream Cone: $ .87

28. Order Up! Least Expensive to Most Expensive
Ice Cream Cone
Double Cheeseburger:
Small Soft Drink:
McFlurry:
2 Cheeseburger Meal:
Chicken McNuggetts Meal:
Big Mac Value Meal:
Chicken Salad:

29. What Do I Mean Compare Decimals?
When we compare we use terms such as:
Less than <
Greater than >
Equal to =
Comparing decimals is similar to comparing whole numbers.
45<47
150>105
When we compare decimals we use place value or a number line.

30. Place Value

31. Identify the place value of the number
#1) #2) #3) #4)

32. Activity Time!!
Identify the place value that the indicated student represents.

33. Activity Time!! Active Votes – Place Values Log onto your computer.
Choose the answer that corresponds to the question on the board.

34. Compare Sara’s score with Danny’s score. Sara 42.1 Danny 42.5 Ross
Half pipe Results
Compare Sara’s score with Danny’s score.
Line Up Decimal Points
Sara:
Danny:
Start at the left and find the first place where the digits differ. Compare the digits
1<5
42.1<42.5
This means Sara’s score was lower than Danny’s score.
Sara
42.1
Danny
42.5
Ross
42.0
Bethany
40.7
Jacob
46.1

35. Let’s Try Using A Number Line
Sara
42.1
Danny
42.5
Ross
42.0
Bethany
40.7
Jacob
46.1
42.0
42.1
42.5
Numbers to the right are greater than numbers to the left. Since 42.5 is to the right of 42.1 we have:
42.5>42.1

36. Equivalent Decimals
Decimals that name the same number are called equivalent decimals.
0.60 and 0.6
Are these the same???

37. =
0.60
0.6

38. Annexing Zeros
This means placing a zero to the right of the last digit in a decimal.
Although we added a zero, the value of the decimal did not change!!
Annexing or adding zeros is useful when ordering a group of decimals.

39. Ordering Decimals
We can order decimals from least to greatest or we can order from greatest to least.
Let’s try an example:
Order 15, 14.95, 15.8, and from least to greatest

40. One More Example Order these numbers from greatest to least
35.06, 35.7, 35.5,

41. Adding and Subtracting Decimals
Lesson 1-5

42. The Basic Steps: Line up the numbers by the decimal point.
Fill in missing places with zeroes.
Add or subtract.

43. Addition Properties
Commutative Property of Addition: Numbers can be added in any order.
Example: 5+3=3+5
Associative Property of Addition: Numbers can be grouped in any way.
Example: (7+3) + 5 = 7 + (3+5)
Identity Property of Addition: The sum of any number and zero is that number.
Example: = 18

44. Mental Math Addition properties can be used to quickly find sums.
Example: What is ?
We can use an addition property to quickly add this.
First, change the order: ________________ property.
Then, group the first two addends together: ( ) ________________ property
= 112.4
commutative
associative

45. Why Estimate?
Before adding your numbers, use one of the estimating strategies you learned to see what the answer should be close to.
When you add, you can see if your answer is reasonable.

46. Examples:
#1) #2) #3)

47. Subtracting The addition properties do not work for subtraction.
Estimate and subtract to find what the answer is close to.
Subtract to find the real answer.

48. Subtracting Across Zeroes
If you have several zeroes in a row, and you need to borrow, go to the first digit that is not zero, and borrow.
All middle zeroes become 9’s.
The final zero becomes 10.

49. Examples: 15 – 9.372
#1) #2) #3) #4) 5 . 6 2 8

50. Today’s Agenda:
1) Practice 10 WS (Google Document) **Note – Anything you don’t get done is HW***

51. Do Now:
Problem of the Day: 1) 2)

52. 1-4 Multiplying and Dividing Decimals

53. To Multiply Decimals: You do not line up the factors by the decimal.
Instead, place the number with more digits on top.
Line up the other number underneath, at the right.
Multiply
Count the number of decimal places (from the right) in each factor.
Use the total number of decimal places in your two factors to place the decimal in your product.

54. Example 1: 5.63 x 3.7 1

55. Example 2: 0.53 x 2.618

56. Practice: 6.5 x 15.3

57. Multiplying and Dividing Decimals by 10, 100, and 1,000
Lesson 1-8

58. The Basics:
When you multiply by 10, 100, or 1,000, you can move the decimal point to the right.
The number of decimal places you move is the same as the number of zeroes you are multiplying by.
When you divide by 10, 100, or 1,000, you can move the decimal point to the left. Move the decimal point once for each zero you are dividing by.

59. Examples:
#1) x 100 #2) 2, ÷ 1,000 #3) 4.2 ÷ 100 #4) x 1,000

60. Dividing Decimals
Lesson 1-9

61. Terminating and Repeating Decimals
A terminating decimal is a decimal that stops, or terminates.
Examples: 1.25 or 0.892
A repeating decimal is a decimal that has a repeating digit or a repeating group of digits.
Examples: … or …
Repeating decimals usually have a bar across the repeating portion.
2.3

62. Remember the parts of a division problem:

63. Dividing a Decimal by a Whole Number
Place the decimal point in the quotient directly above the decimal point in the dividend.
Divide as you normally would

64. Examples:
#1) 26.4÷4 #2) 85.6 ÷2 #3) ÷ 5

65. Dividing Decimals
If the divisor is not a whole number, move decimal point to right to make it a whole number and move decimal point in dividend the same number of places.

66. Put decimal point directly above decimal point in the dividend.

67. Divide as usual. Keep dividing until the answer terminates or repeats.

68. Check your answer. Multiply quotient by divisor
Check your answer. Multiply quotient by divisor. Does it equal the dividend?

69. Examples:
#1) #2) #3) 16.9÷6.5 #4) ÷3.4

70. Today’s Agenda:
Online Practice: 1) (Practice Questions) - Once you get a score of at least 8, make sure to show your teacher to get credit and then you make play the games below for extra practice. 2) (football, basketball, soccer) 3) (Decimal division football) 4) End of class quiz

71. Today’s Agenda: WS: Algebra A – GCF/LCD Classwork WS
HW: GCF/LCD Homework
LCM and GCF Application Problems:

72. A standard way to simplify mathematical expressions and equations.
Order of Operations
A standard way to simplify mathematical expressions and equations.

73. Purpose Avoids Confusion Gives Consistency For example:
8 + 3 * 4 = 11 * 4 = 44
Or does it equal
8 + 3 * 4 = = 20

74. Order of operations are a set of rules
that mathematicians have agreed to
follow to avoid mass CONFUSION
when simplifying mathematical expressions
or equations. Without these simple, but
important rules, learning mathematics would
be maddening.

75. The Rules Simplify within Grouping Symbols Simplify Exponents
( ), { }, [ ], | |
Simplify Exponents
Raise to Powers
Complete Multiplication and Division from Left to Right
Complete Addition and Subtraction from Left to Right

76. Shortcut for Remembering:

77. Back to Our Example For example: 8 + 3 * 4 = 11 * 4 = 44
8 + 3 * 4 = 11 * 4 = 44
Or does it equal
8 + 3 * 4 = = 20
Using order of operations, we do the
multiplication first. So what’s our
answer? 20

78. Examples:
1) 5 + (12 – 3)
2) 8 – 3 • 2 + 7
3) 39 ÷ (9 + 4)

79. ÷ 2 – 6
15 • 103
36 ÷ (1 + 2)2
7) 3 • 104

80. 14 + 3(7 -2) – 2 • 5
(5 – 1)3 ÷ 4

81. Order of Operations Practice:
#1) 9 - (4)(2)+5 #2) (-3)(6)+(4)(-5)
#3) 9÷(3)(5)+1 #4) –(5–9)(2) + (5)(3)

82. Evaluating Expressions
Substitute the values for the variables
Use the order of operations to simplify.

83. Evaluating Expressions Let:
#1) #2)
#3) #4)

84. Evaluating Expressions Let:
#5) #6) 4x ÷ y(z)
#7) #8)

85. Today’s Agenda:
Online Practice:
HW: Order of Operations (a) Homework WS (odds)
Order of Operations Game

86. Order of Operations Game
Objective: Use the order of operations to create the numbers 1-10.
Rules:
Each of the six numbers that you are given must be used exactly once.
Only one person per team may be at the board at a time.
Once a number has been correctly generated it is no longer available to the other teams.

87. Order of Operations Game
Goal: Create the numbers 1-10 using six random numbers and the order of operations. You must use all six numbers each time. Example: Random numbers: 1, 3, 4, 2, 1, 2

88. Do Now:

89. Activity Time: Divide everybody into groups of 3-4
Divide a piece of paper into 4 parts (addition, subtraction, multiplication, and division)
Take the set of cards that you receive and determine which operation the word on the card implies.
Record the word on your paper (Everybody must have their own copy)

90. Activity Summary
Addition: Subtraction: Multiplication: Division:

91. Problem Solving
Translate the verbal phrase into an algebraic expression:
#1) Nine more than a number
#2) Five less than twice a number
#3) Difference of a number and ten

92. Problem Solving #4) The product of a number and six squared
#5) The quotient of one half and a number

93. Problem Solving
Write an expression/equation and then find the value of the number:
#6) A number is equal to the product of six and negative five.
#7) Twice a number is equal to twelve.
#8) Nine less than the product of ten and a number is eleven.

94. Problem Solving
#9) Eighteen decreased by nine is three times a number.
#10) Three less than twice a number equals half of ten.

95. Today’s Agenda: Partner Worksheets a) Backwards Riddle
b) Verbal Expressions – How does bob marley like his donuts
c) Verbal Expressions – Crossword Puzzle
2) Activity
3) Journal: Make up an algebraic expression that has at least two different operations and then write a sentence describing the expression.

96. Directions for Activity:
Write the equation or inequality on your paper and hold it up before the computer advances to the next slide.
Use n for the variable

97. The difference of eleven and a number is five

98. The difference of eleven and a number is five

99. Twenty less than a number is three

100. Twenty less than a number is three

101. Twelve more than a number is sixteen

102. Twelve more than a number is sixteen

103. The product of four and a number, minus three is seventeen

104. The product of four and a number, minus three is seventeen

105. The quotient of a number and five is greater than two

106. The quotient of a number and five is greater than two
> 2 5

107. Six divided by a number is less than or equal to five

108. Six divided by a number is less than or equal to five6
< 5 n

109. The sum of six and number is at least two

110. The sum of six and number is at least two

111. Six multiplied by a number, take away five is less than seven

112. Six multiplied by a number, take away five is less than seven

113. The sum of six and number all divided by three is two

114. The sum of six and number all divided by three is two
= 2 3

115. Five less than twice a number is seven

116. Five less than twice a number is seven