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Commutative Property of Additon
Changing the order of the addends does not change the sum.
a+b=b+a
Commutative Property of Multiplication
Changing the order of the factors does not change the product.
ab=ba
Associative Property of Addition
Changing the grouping of the addends does not change the sum.
(a+b)+c=a=(b+c)
Identity property of Addition
Adding zero to any number leaves that number unchanged.
a+0=0+a=a
Identity Property of Multiplication
Multiplying any number by 1 leaves that number unchanged.
a x 1= 1 x a=a
Zero Property of Multiplication
Multiplying any number by 0 gives 0.
a x 0=0 x a= 0
Distributive Property of Multiplication over Addition
a(b+c)=ab+ac
Distributive Property of Multiplication over Subtraction
a(b-c)=ab-ac
Look for a pattern
The problems information, predicted work, or possible answers feature some repetition.
Make a table or list
There are several options/ lots of information to keep organized.
Examine a simpler problem
The problem numbers are too big or the situation too complicated.
Write an equation/ use algebra
The answer is an unknown number AND the problem gives enough info to create a relationship.
Write an equation/ use algebra
There is a commonly know formula.
Draw a diagram or picture
The problem contains info that you want/ need to visualize.
Guess and Check
There are a reasonable number of possible option’s.
Guess and Check
The problem give a value or condition to check them against.
Work backwards
Gives clear story or chain of events.
Work backwards
Know the end and need to find out about the beginning.
Use elimination
The problem involves a possibility that can be ruled out.
Use direct arithmetic/ reasoning
Requires straight forward operation.
Use direct arithmetic/ reasoning
Numbers with no additional interpretation.
Break into cases
Problem features totally separate qualities or situations.
Polya’s Four steps
Used for problem solving
Polya’s Four steps
Understand the problem, Devise a plan, Carry it out, Look back
Understand the problem
Vocabulary and Terms
Devise a plan
Something you will try and Looking at characteristics to devise a plan
Carry it out
Writing/ working happens here and Addresses improvements
Look back
Is the answer reasonable and Did we answer + was it what was asked
Repeating Sequence
Repeats the same block of items over and over
Repeating Sequence
123,+,123,+….
Difference Sequence
Describes how the main sequence behaves
Difference Sequence
1,3,5,15,17,51,…
Fibonacci Sequence
Always adds two terms to create the next term
Fibonacci Sequence
1,1,2,3,5,8,13,21,…
Arithmetic Sequence
Always adds the same amount to one term to make the next term
Arithmetic Sequence
13,28,43,58,…
Geometric Sequence
Always multiply by the same amount to turn one term into the next
Geometric Sequence
10,30,90,270,…
How
Describes steps and process
Why
Gives reason
Number sentence
Only uses numbers
Number sentence
2 × 3 + 1= 7
Equation
Has variables to be solved for
Equation
2x + 3 = 9
Expression
Has numbers and variable’s, but no equal sign
Expression
2x + 3
Addends
Sum
Minuend
Subtrahend
Difference
Factors
Product
Dividend
Divisor
Quotient
Identify a sub-goal
Steps that need to be done before anything else
Note 
Flashcard (50)