 # Addition, Subtraction, Multiplication, and Division Strategies

Addition Strategies:

Count All: Count all of the objects in both numbers

Count On: Start with the bigger number and count on

Doubles: Adding a number with itself

Doubles plus One: Use your doubles facts and add 1 extra

"Monkey in the Middle"  or doubles + 2   ex. 3 + 5 (when counting 3, 4, 5) the number in the middle is doubled (4 +4)= 8
(In 4+5 think of 5 as 4+1, so 4+5 is 4 doubled  plus 1)

Add 9: Start by adding 10, then just take 1 away

(For 8+9 start with 8+10  and take away 1 to get 17)

Add 10: To add 10 you are putting 1 in the tens column

(7+10 starts with 0 tens,7 ones; We put 1 in the tens column )

Subtraction Strategies:

Add Up: Use addition to find the difference between numbers

Subtract to 10s: Subtract to get back to the nearest ten, then the rest
(82-5 : 82-2 gets you 80 then -3=77)

Subtract to 100: Subtract to get back to 100, then subtract the rest
(120-50 : 120-20 get you to 100, then -30 = 70)

Multiplication Strategies:
G. E.T. Strategy= G(roups) X  E (number in each group) = T (total)

x 0: The product will always be 0

x 1:
The product is the same as the factor being multiplied by 1

x 2:
Just double the number that is being multiplied by 2 (use your doubles from addition)

x 3:
Doubles plus one group (5x3 = 5x2 plus 5x1.

x 4:
Double Double
(5x4 = 5x2x2. This is 5 doubled  and then double that answer to get 20)

x 5:
Multiply by 10 and then cut it in half or skip count by 5's like on a clock.
(6x5 = Start with 6x10  and then just cut in half to get 30)

x 6:
Multiply by 3 and then just double
(8x6 = Use your previous knowledge [8x3=24] and double the 24 to get 48)

x 7:
Partial products (using 5's) Multiply by 5, Multiply by 2 and combine
(8x7 = 8x5  plus 8x2  ; The final answer is 40+16, or 56)

x 8:
Multiply by 4 and then just double (9x8 = 9x4x2. This is 9x4 doubled : 30 doubled=60 + 6 doubled=12, total is 72)

x 9:
Multiply by 10 then take away a group (look for number patterns)
(9x3= 10x3  take away a group of 3 [30-3] to get 27)

x10:
Product will end with a zero.
(8x10 = 8 groups of 10, or just 8 in the tens place followed by a 0, which is 80)

x11:
For single digits it's just a repeat digit
(9x11=9x1 in the tens column  plus 9x1 in the ones column or 9 shown twice  )

x12:
Multiply by 10, Multiply by 2 and combine (look for a number pattern)
(7x12 = 7x10  plus 7x2  for a total of 84 when you add the 70 and 14)

Divison: (Using the inverse operation is a very efficient method that I would recommend trying first)

÷ 2: Just split the number in half
(18 ÷ 2 is just 18 cut in half, which is 9)

÷ 4: Cut in half twice
(24÷ 2 is just 24 cut in half  then cut that in half to get 6)

÷ 5: Double then divide by 10 or use multiplication
(30÷ 5 is done by doubling the 30  & dividing by 10,which removes the 0 ones  )

÷ 6: Cut in half, then divide by 3
(42÷6 is 42 cut in half  then divide that by 3 to get 7 )

÷ 8: Cut in half three times
(48 ÷ 6 is 48 cut in half  which gets cut in half  and one more time  )

÷10: Remove the 0 that is in the ones column
(90÷10 is done by deleting the 0 in 90 to get 9)