1. Everyday Math
5th Grade: Unit One

2. Unit One Vocabulary
Rectangular array: an arrangement of objects in rows and columns. Each row has the same number of objects and each column has the same number of objects. Factors – numbers that you multiply together to get a product Factor pair – two numbers that you multiply together to get a product. Product – the answer you get when you multiply factors together Divisibility - A number is divisible by another number if it goes in evenly (no remainder) Composite number – a number that has more than 2 factors Prime number – a number that has exactly 2 factors (1 and itself) Square number – a number that makes a square array (2x2, 4x4, 5x5, etc.) Exponential notation - numbers written with exponents Exponent - a small number written to the right and above the base number to show how many times the base number is multiplied by itself. Square root – when you “unsquare” a square number. (example: The square root of 36 is 6 (6x6 =36)) Prime factorization - writing a number as a product of all prime numbers

3. Divisibility tests 346  715 Χ 450  735  569 Χ 230  455 Χ
Divisible by 2
A number is divisible by 2 if the last digit (number in the one’s place ) is even or 0
(2, 4, 6, 8, 0)
346  Χ
Divisible by 5
A number is divisible by 5 if the last digit is 5 or 0
450   Χ
Divisible by 10
A number is divisible by 10 if the last digit is 0
230  Χ

4. Divisibility tests continued…
Divisible by 3
Add up all the digits in the number. If the sum is divisible by 3, so is the whole number.
 Χ
(2+4+6=12) (4+5+1=10)
12 is divisible by 3, so is is not divisible by 3, neither is 451
Divisible by 4
Look at the last two digits of a number. If the number that the two digits form is divisible by 4, so is the whole number.
2,232  ,311 Χ
32 is divisible by 4, so is 2, is not divisible by 4, neither is 7,311

5. Divisibility tests continued …
Divisible by 6
A number is divisible by 6 only if it is both divisible by 2 and 3.
 Χ
Divisible by both 2 & Divisible by 3, but not 2
Divisible by 9
Add up all the digits in the number. If the sum is divisible by 9, so is the whole number.
846  Χ
(8+4+6=18) (4+5+1=10)
18 is divisible by 9, so is is not divisible by 9, neither is 451

6. Prime numbers – numbers that only have two factors (one and itself.)
Composite numbers – numbers that have more than 2 factors

8. Finding all of the factors for a number:
Step 1: Always begin with the number one.
1 x 24 = 24
Step 2: move on to the number two.
2 x 12 = 24
Step 3: continue on until you start repeating
numbers.
(the next number to check after 4 is doesn’t go into 24 and
so you move on to has already been used so you know
you have found all of your factors.)

11. Prime Factorization: writing a number as a product of all prime factors
Step 1: Divide number into a any factor pair. Step 2: Circle any number that can't be broken down any more (prime). Step 3: Continue to break down numbers until you are left with all prime numbers. Step 4: Connect all prime numbers with x symbols from least to greatest. 3 x 3 x 5 If possible, write your answer in exponential notation 3² x 5 Check: What is 3 x 3 x 5 (or 3² x 5) ?

12. Sources:
-Everdyay Math Student reference book -Some examples taken from: Mr.Wrinkle.net/unit1