Fifth Grade Math Course I

1
Fifth Grade Math Course I

• Number Theory

2
Agenda

• Discuss Syllabus
• Introductions
• Operations with Whole Numbers
• In class practice exercises

3
Numbers

• Numbers are all around us every day
• Think about your day How many times did you use
  numbers?

4
Whole Numbers

• All whole numbers can be formed using digits
  (0-9)
• Each digit in a number has a place value
• 678, 310, 456, 127
• Large numbers are separated into groups of three
  digits

Hundred-thousands
Hundred-billions
Hundred-millions
Ten-thousands
Ten-billions
Ten-millions
Thousands
Hundreds
Billions
Millions
Tens
Ones
5
Whole Numbers

• 31, 264, 457
• Thirty-one million, two hundred sixty-four
  thousand, four hundred fifty-seven (dont use
  and )
• In the number 325, 467 what does the
• 5 represent?
• 4 represent?
• 2 represent?

6
Addition

• To add whole numbers, you add the digits in the
  ones place, tens place, hundreds place, etc of
  each whole number. The result is called the sum.
• 74 23 ? 544 32 3 ?
• 7 4 5 4 4
• 2 3 3 2
• 9 7 3
• 5 7 9

7
Addition - Carrying

• 47 25 ?
• 47
• 25
• 72

1
Number carried
7 ones 5 ones 12 ones (1 ten and 2 ones). Put
just the 2 in the ones place and carry the 1 ten
to the tens column
1 ten 4 tens 2 tens 7 tens
8
Approach to Word Problems

• READ
• Read the problem slowly and carefully. Determine
  what is being asked for and what are the facts of
  the problem.
• ANALYZE
• Determine what operations are needed to answer
  the question presented in the problem.
• SOLVE
• Do the necessary computation to obtain the answer
  to the given problem.

9
Addition Exercises

• At the bookstore you spend 65 on a math book,
  88 on art books and 19 on supplies.
• What is the total cost before sales tax?
• At a clothing store you spend 69 on a sweatsuit,
  29 for tennis shoes and 3 for socks.
• What is the total bill before sales tax?

10
Multiplication

• Multiplication is repeated addition. The result
  in multiplication is called the product.
• Ex If you knocked down 9 pins in six consecutive
  frames of bowling, how many total pins did you
  knock down?
• 9 9 9 9 9 9 54
• OR
• Six times nine (6 x 9 54)
• factor product

11
Multiplication Exercises

• If parents car needs new tires and one tire
  costs 63, how much would four tires cost?
• If your favorite football team scored 9
  touchdowns (6 points each), 6 field goals (3
  points each) and 7 extra points (1 point each),
  what was the final score in the game?
• If you have three 50 bills, seven 20 bills,
  nine 10 bills, six 5 bills and seventeen 1
  bills, how much cash do you have?

12
Powers (Exponents)

• To express a multiplication problem in which a
  number is repeatedly multiplied by itself, use
  exponents
• Ex 4 x 4 x 4 x 4 x 4 45
• 4 is the base, 5 is the exponent (power)
• 03 0 (0 x 0 x 0 0)
• 80 1

13
Power Exercises

• Identify the base and exponent
• 63 (6 x 6 x 6)
• 74 (7 x 7 x 7 x 7)
• 35 (3 x 3 x 3 x 3 x 3)
• Solve
• 43 ?
• 25 ?
• 80 ?
• 06 ?

14
Square Roots

• Raising a number to the second power (using an
  exponent of 2) is called squaring a number
• 52 5 x 5 25
• The reverse of squaring a number is called taking
  the square root of a number. To find the square
  root of a given number, find a number that, when
  multiplied by itself, results in the given
  number.
• Ex. 49 7

15
Square Root Exercises

• Solve
• 64 ?
• 121 ?
• 0 ?
• 10,000 ?

16
Subtraction

• To subtract whole numbers, place the numbers
  above each other so that the digits with the same
  place values are lined up. The result is called
  the difference.
• Ex 85 43 ?
• 85
• - 43
• 42

17
Subtraction - Borrowing

• Ex 52 -17 you cant subtract a larger number
  (7) from a smaller number (2)
• 52
• - 17
• 35

Borrow 1 ten from the 5 tens, leaving 4 tens
Add the 1 ten borrowed to the 2 ones, to get 12
ones
4 12
Now subtract
12 ones 7 ones 5 ones
4 tens 1 ten 3 tens
18
Subtraction Exercises

• At the start of your vacation, the odometer in
  your mothers car reads 55743. When you and your
  mother return from trip, the odometer reads
  56891. How many miles did she drive on your
  vacation?
• If you earn 750 per week, but have 123 in
  deductions, how much is your take-home pay?

19
Division

• Division is a quick way to do repeated
  subtraction problems
• Ex If you have 28 and you wanted to buy movie
  tickets that cost 7 each, how many tickets could
  you buy?
• 28 21 14 7
• - 7 - 7 - 7 - 7
• 21 14 7 0
• There are four 7s in 28
• We can also say 7 divides into 28 four times and
  write it
• 4 quotient
• divisor 7 28 dividend

20
Division

• You can not divide by 0
• Remainder is the whole number that is left over
  in a division problem whose quotient is not exact
• 26 / 8 ?
• 26 18 10
• -8 -8 -8
• 18 10 2
• 3 8 26
• 24
• 2

remainder
remainder
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Division Exercises

• If you drove 637 miles in 13 hours, how many
  miles did you travel per hour?
• The total amount of an auto loan is 11,376. If
  you pay off the loan with equal monthly payments
  over four years, how much would you pay each
  month?

22
Order of Operations

• We have seen addition, multiplication,
  subtraction, division, exponents, and square
  roots of whole numbers. A combination problem
  would be
• 7 3 x 5 ? 50 or 22?
• Computation in mathematics is done in a
  standardized order.

23
Order of Operations

• Parentheses
• Exponents
• Multiplication
• Division
• Addition
• Subtraction
• Please Excuse My Dear Aunt Sally

From left to right
From left to right
24
Order of Operations Exercises

• (24 4) x 5 ?
• 24 4 x 5 ?
• 24 / 6 x 2 ?
• 16 25 x 32 ?

25
Primes

• A prime number is a whole number greater than one
  that is evenly divisible by only 1 and itself.
• Ex 2, 3, 5, 7, 11, 13, 17, 19, 23,
• A composite number is a whole number greater than
  one that is evenly divisible by other numbers
• Ex 4, 6, 8, 9, 10, 12, 14, 15, 16,

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Divisibility

• In determining if a given number is prime or
  composite, you need to decide if a number besides
  1 and itself divides evenly into the given
  number.
• Divisibility by 2 If a number ends in 0, 2, 4,
  6, or 8, it is an even number. Even numbers are
  divisible by 2
• Divisibility by 3 If the sum of the digits of a
  number is divisible by 3, then the number is
  divisible by 3
• Divisibility by 5 If a number ends in 5 or 0, it
  is divisible by 5
• Divisibility by 10 If a number ends in 0, it is
  divisible by 10
• Divisibility by other numbers

27
Divisibility Exercises

• Is 510 divisible by
• 2?
• 3?
• 5?
• 7?
• 10?

28
Factoring

• Factoring is the process of writing a number as
  the product of other numbers (can use a factor
  tree)
• There are many ways to factor a number
• Ex 12 can be factored in the following ways
• 12 12 x 1 12 1 x 12
• 12 2 x 6 12 6 x 2
• 12 3 x 4 12 4 x 3
• 12 3 x 2 x 2

29
Factor-Trees

• A factor-tree is a diagram that can be used to
  factor whole composite numbers into primes (will
  be useful in fractions)
• Ex 72
• 9 8
• 3 3 2 4
• 2 2
• 72 3 x 3 x 2 x 2 x 2 32 x 23

30
Factoring

• Factor into primes
• 44
• 75
• 100

31
Averages

• To find the average of a list of numbers, add the
  numbers and divide by how many numbers are in the
  list

32
Average Exercises

• If the scores on your last four math tests were
  96, 88, 83 and 93, what is the average of your
  scores?
• 96 88 83 93 360
• 360 / 4 90
• If the Houston Texans scored 24,36,13,10 and 7
  points in their last five games, what is the
  average points per game?
• 24 36 13 10 7 90
• 90 / 5 18

33
Questions

• ?