Multiplication Vocabulary

Clue Words for Multiplication

Factors: the numbers multiplied together to find a product
Product: the answer you get when you multiply
Multiples: the product of a given whole number and another whole number

* the product of
* multiplied by
* times
* of
* double
* triple

Lesson 1
Multiplication Properties (5.NBT.6)

Commutative Property of Multiplication: the order of factors can be changed, but the product will remain the same
   ex. 5x2=10  or  2x5=10 
Associative Property of Multiplication: you can change the grouping of the factors, but the product will remain the same
   ex. (2x3)x4=24  or  2x(3x4)=24
Identity Property of Multiplication: the product of any factor multiplied by 1, will be that factor
   ex. 234x1=234
Zero Property of Multiplication: the product of any factor and zero is zero
   ex. 543x0=0

Lesson 4
Multiplication: Exponents (5.NBT.2)

Exponential Notation: a way of writing repeated multiplication by using a Base number and a Power
   ex. 53 - this is written in exponential notation
Exponent: the number that tells how many times the base is used as a factor
   ex. 53
   - the 3 is the exponent - it sits above the base number
Base: the number that is multiplied
   ex. 53
   - the 5 is the base number
Standard Form: the product, a whole number
   ex. 53=5x5x5= 125
   125 is written in standard form
Expanded Form: writing a multiplication equation
   ex. 53=5x5x5= 125
   5x5x5 is written in expanded form 
Squared: using the power of 2
   ex. 52=5x5= 25
   this numer is spoken as 5 to the second power 
   or 5 squared
Cubed: using the power of 3
   ex. 53=5x5x5= 125
   this numer is spoken as 5 to the third power 
   or 5 cubed
Power: an exponent

Lesson 2
Using Mental Math to Multiply (5.NBT.2)

Factors: the numbers multiplied together to find a product
   ex. 5x11=55...5 and 11 are the factors
Product: the answer you get when you multiply
   ex. 5x11=55...55 is the product
Multiples: the product of a given whole number and another whole number
   ex. Multiples of 2
   2x1=2
   2x2=4
   2x3=6...2, 4, and 6 are the multiples
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Steps to follow when using mental math with multiples of 10, 100, or 1000...
1st - multiply the whole numbers
2nd - add the zeros
   ex. 500x70
   1st - 5x7=35
   2nd - 500 has 2 zeros and 70 has 1 zero, so 
   you need to add 3 zeros to the product of 35
   500x70= 35,000

Lesson 5
Distributive Property (5.NBT.5)

The distributive property is used to simplify complicated multiplication expressions in order to solve the problem mentally.

EXAMPLE
12x302

Step 1: take the larger, or more complicated number and break it into smaller parts (or place values) in order to make them more manageable for mental math

   *320= 300+2, so the problem can be rewitten 

   12 x (300 + 2)  OR  12(300+2)
   * when you write a number directly next to 
   parenthesis that is the same as saying 
   "multiplied by"
   * this is the same as saying 
   12x302= (12x300) and (12x2)

Step 2:  Distribute or share the 12 with each digit within the parenthesis

   *12(300+2) = (12x300) + (12x2)


Step 3: find the product of each set of parenthesis


   *12x300 can be solved by saying
   12x3=36, add the two zeros from the problem 
   and your final product is 12x300=3600
   *12x2=24


Step 4: Add the final products together to get the answer to your original problem
   *12x302= 3600+24 = 3624


When written, this problem will look like this
12 x 302
12(300 + 2)
(12 x 300) + (12 x 2)
3600 + 24
3624

Lesson 3
Estimating Products (5.NBT.5)

Overestimate: both numbers that are used to estimate are greater than the original numbers
   ex. 37 x 23 becomes 40 x 25
   40 is greater than 37 and 25 is greater than 23
   your total estimated product will be more than    your actual product
Underestimate: both numbers that are used to estimate are less than the original numbers
   ex. 33 x 23 becomes 30 x 20
   30 is less than 33 and 20 is less than 23
   your total estimated product will be less than      your actual product


* When estimating you can choose to use rounding rules - 0, 1, 2, 3, 4 leave it alone, don't add any more...5, 6, 7, 8, 9 add one more every time  OR  you can use compatible numbers which make the problem easy to solve using mental math

Lesson 6
Multiplying by 1-Digit Numbers