Lesson 1
Order of Operations
‰ "Operations" means things like add,
subtract, multiply, divide
‰ Student A solved the following
problem:
17 - 7 x 2 = 20. Is he
correct? Why or why not?
Lesson 1
Order of Operations
‰ PEMDAS
‰
You can remember it by saying
"Please Excuse My Dear Aunt Sally".
Lesson 2 & 3
Place Value
Lesson 4
Ordering
‰ The symbols are:
< (less than)
> (greater than)
‰ To compare two whole numbers,
1. Put them in standard form.
2. The one with more digits is greater than the other.
9 Example:
402 has more digits than 42, so
402 > 42
Lesson 4
Ordering
3. If they have the same number of digits,
Compare the most significant digits (the leftmost digit).
The one having the larger significant digit is greater .
If the most significant digits are the same,
Compare the next pair of digits from the left.
Repeat this until the pair of digits is different.
The number with the larger digit is greater
9
Example:
402 and 412 have the same number of digits.
Compare the leftmost digit of each number
Moving to the right, we compare the next two numbers
402 < 412
Lesson 5
Rounding Whole Numbers
‰ Student A has $1200, and Student B has
$2100. Approximately, how many thousands do
they both have?
‰ Rounding makes numbers easier to
work with.
‰ Rounding is useful in making
estimates of sums, differences, etc.
Lesson 5: Rounding Whole Numbers
‰ To round numbers to the nearest ten,
o
Numbers that end in 1 through 4: round down to 0.
o Ex. 43 becomes 40.
Numbers that end in 5 or more: round up to the
next even ten.
o
o Ex. 45 becomes 50.
9 Examples:
Rounding 119 to the nearest ten gives: ?
Rounding 155 to the nearest ten gives: ?
Rounding 102 to the nearest ten gives: ?
Lesson 5
Rounding Whole Numbers
‰
To round numbers to the nearest hundred,
• Numbers that end in 1 through 49: end in 00
o Ex. 243 becomes 200.
• Numbers that end with 50: round up to the next even hundred.
o Ex. 353 becomes 400.
‰
To round a number to any place value
9 Examples:
Rounding 180 to the nearest hundred gives: ??
Round 1,234 to the nearest thousand: ??
Rounding 150,090 to the nearest hundred thousand gives ??
Lesson 6
Adding and Subtracting
Lesson 7
Problem Solving
9 In December, a local burger chain sold
4,354 hamburgers. This was 1,567 fewer
than in November. What was the total
number of hamburgers sold for the two
months?
Lesson 7
Problem Solving
9 What was the total number of hamburgers
sold for the two months?
4,354 Sold in December
+ 1,567 Fewer than in November.
5,921 Sold in November
+ 4,354 Sold in December
10,275 Total number sold
Lesson 8
Multiplying and Dividing Whole
Numbers
Lesson 8: Multiplying and Dividing
Whole Numbers
Lesson 8
Multiplying and Dividing Whole
Numbers
‰ Divisibility by 2
A whole number is divisible by 2 if the rightmost
digit is even:
(either 0, 2, 4, 6, or 8).
9 Examples:
84 is divisible by 2
3336 ?
31 ?
66667?
Lesson 8
Multiplying and Dividing Whole
Numbers
‰ Divisibility by 3
A whole number is divisible by 3 if the sum of all its
digits is divisible by 3.
9 Examples:
177 is divisible by 3: sum = 15
8882151?
sum =?
8882152?
sum =?
Lesson 8
Multiplying and Dividing Whole
Numbers
‰ Divisibility by 4
A whole number is divisible by 4 if the last two digits
are divisible by 4.
9 Examples:
124 is divisible by 4
82151?
88124?
Lesson 8
Multiplying and Dividing Whole
Numbers
‰ Divisibility by 5
A whole number is divisible by 5 if the last digit is 0
or 5.
9 Examples:
125 is divisible by 5
82151?
88120?
Lesson 8
Multiplying and Dividing Whole
Numbers
‰ Divisibility by 6
A whole number is divisible by 6 if it is divisible by
2 and 3
9 Examples:
324 is divisible by 6
315?
120?
Lesson 8
Multiplying and Dividing Whole
Numbers
‰ Divisibility by 8
A whole number is divisible by 8 if the last three
digits are divisible by 8
9 Examples:
128 is divisible by 8
82151?
88160?
Lesson 8
Multiplying and Dividing Whole
Numbers
‰ Divisibility by 9
A whole number is divisible by 9 if the sum of the
digits is divisible by 9
9 Examples:
126 is divisible by 9
82151?
88180?
Lesson 9
Money and Decimals
‰ Everyone who knows how to write dollars and
cents knows how to write decimals.
‰ The dot in $9.50 is a decimal point
‰ The dollars are to the left of the decimal point
‰ The first digit to the right of the decimal point is the dime’s
position
‰ The second digit to the right of the decimal point is the
penny’s position
9Example: To pay $13.09, you need:
… dollars, … dimes, … pennies
Lesson 10
Decimal Place Values
‰ The first place to the right of the decimal point
is called tenth
‰ The second place to the right of the decimal
point is called hundredth
9Example:
In 0.3 we have 3 tenths
In 0.47 we have 47 hundredths