Commutative Property
The Commutative Property lets you add
numbers in any order.
4+2=2+4
5+3+2=5+2+3
The Commutative Property lets you add two decimals in any
order.
$11.45 + ($3.39 + $9.55)= $11.45 + ($9.55 + $3.39)
Switch the order of $3.39 and $9.55
is the same outcome as $9.55 + $3.39
Subtraction is not a commutative property
4.2 – 2.6 is not the same as 2.6 – 4.2
2 – 4 is not the same as 4 – 2
Associative Property
The associative property states that you can
add regardless of how the numbers are
grouped.
By 'grouped' we mean 'how you use parenthesis'. If you are adding it does not
matter where you put the parenthesis.
Compensation
Adjust one or both numbers to make the
calculation easier. Then adjust the difference or
sum to get the final answer.
Subtraction
Addition
Whatever you do to the first number, you have to do the opposite to the answer.
14 – 8 = ?
(-4)
14 – 8 = ?
+4
10 – 8 = 2
18 – 8 = 10
(+4)
(-4)
14 – 8 = 6
14 – 8 = 6
14 + 8 = ?
14 + 8 = ?
(-4)
(+4)
10 + 8 = 18
18 + 8 = 26
(+4)
14 + 8 = 22
(-4)
14 + 8 = 22
Estimate
To give an approximate value rather than
an exact answer.
There is more than one way to estimate a sum or difference.
You can use rounding or compatible numbers by replacing
number with other numbers that are close and easy to
calculate mentally.
628 + 485 = 1,113
628 rounds to 630
And 485 rounds to 490
630 + 490 = 1,120
628 rounds to 600
And 485 rounds to 500
600 + 500 = 1,100
Compatible Numbers
Are numbers that are easy to compute with
mentally.
Compatible numbers are ones that result in multiples of ten
or one hundred when the operations are completed.
25 + 87 + 75 = ?
We call 25 and 75 compatible numbers because their sum is
100. Adding 25 and 75 first allows us to be able to mentally
complete the addition of 25 + 87 + +75 = 87 + 100 = 187
Underestimate
An estimate that is less than the
actual answer.
Overestimate
An estimate that is over the actual
answer.
Inverse Operations
Operations that undo each other: Adding 6
and subtracting 6 are inverse operations.
Reasonableness
Is your answer reasonable? Is your answer
close to the exact/estimated answer?
Use many other techniques for estimating sums and
discovering if your answer is reasonable.
Strip Diagram
Strip Diagram is a tool designed to help
solve math word problems accurately and
efficiently. The model provides an image
that organizes information and simplifies
the problem solving process.
Alicia has $6 more than Bobby. If Bobby has $10, how much
did they have altogether?
Addend
Any numbers that are added together.
Sum
The total amount resulting from the
addition of two or more numbers.
8 + 3 = 11 the “8” and “3” are addends and the “11” is the
sum.
Minuend, Subtrahend, and
Difference
Minuend- The first number in a subtraction. The number
from which the other number will be subtracted.
Subtrahend- The number that is to be subtracted. The
second number in a subtraction.
Difference- The result of subtracting one number from
another. How much one number differs from another.
minuend - subtrahend = difference
Solution
The value of the variable that makes the
equation true.
Addition
Nate has a $5 bill and a $10 bill.
He spends $2.50 for a smoothie
and $2 for a muffin. How much
money does he have left?
How much does Nate have in
total? ($15) How much does he
spend? ($4.50) What is $15 $4.50? (solution)
Multiplication
If you had the equation "x + 6 =
11", you would write "–6" under
either side of the equation, and
then you'd "add down" to get
"x = 5" as the solution.
x + 6 = 11
–6 –6
x
= 5
Evaluate
To find the value of an expression when a
variable is replaced by a number.
Evaluate the cost of each pie if 3 pies cost $6. Answer: $2
each.
Problem:
Jeanne has $17 in her piggy bank. How much money does she need to buy a game that costs $68?
Solution:
Let x represent the amount of money Jeanne needs. Then the following equation can represent this
problem:
17 + x = 68
We can subtract 17 from both sides of the equation to find the value of x.
68 - 17 = x
Answer:
x = 51, so Jeanne needs $51 to buy the game.
In the problem above, x is a variable. The symbols 17 + x = 68 form an algebraic equation.
Equation
An equation says that two things are the
same, using mathematical symbols.
An equal sign (=) is used
Example: 7+2 = 10-1
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2_ addition and subtraction whole numbers and decimals