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Everyday Math 5th Grade: Unit One

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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

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**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

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**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

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**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

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**Prime numbers – numbers that only have two factors (one and itself.)**

Composite numbers – numbers that have more than 2 factors

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**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.)

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**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) ?

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

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