The ability to solve problems quickly and accurately by knowing which methods to use and how to use them


Getting the correct answer


Selecting a problem-solving method and performing computations without requiring much time to think and process through


How quickly computations are made


Being able to solve problems in more than one way and selecting the most appropriate method


The ability to hypothesize test theories, and draw conclusions

Inductive Reasoning

Conclusions made based on observation

Deductive Reasoning

Conclusions based on logical synthesis of prior knowledge of facts and truths

Adaptive Reasoning

The ability to think logically about relationships between concepts and to adapt when problems and situations change

Concrete Model

Use objects to demonstrate operations (Cubes, Base-Ten Blocks)

Semi-Concrete Model

Use pictures, instead of actual objects, to demonstrate operations

Semi-Abstract Model

Use single symbols (tally marks) to represent numbers of objects while performing operations

Abstract Model

Using numbers only to perform operations


Number lines, bar graphs, pie charts; representations of numerical values

Put-Together Problem

There are 2 oranges and 3 bananas in a fruit bowl. How many pieces of fruit are there all together?

Take Apart Problem

8 students were asked whether they like dogs or cats better. 5 students picked dogs. How many picked cats?


One way to model a multiplication problem visually


A rectangle is divided into unit squares which can be counted to find the area

Measurement Division

Used when students know how many objects are in each group but do not know how many groups there are

Partitive Division

When students know how many groups there need to be, but not how many objects are in each group.


Way to solve problems without visual models


Computational process in which the same steps are repeated until a final answer is found


The ability to instantly see the number of objects in a small set without having to count them

Natural Numbers

The numbers we use to count (1,2,3...)

Whole Numbers

Natural numbers and zero


Whole numbers and their corresponding negatives


Portions of integers expressed with a numerator and a denominator


Portions of integers expressed as numbers following a decimal point

Rational Numbers

All integers and fractions

Irrational Numbers

Numbers that cannot be expressed as fractions, such as infinite, non repeating numbers


Number that raise another number to a power making it multiply itself a certain number of times

Addition Property of Zero

Adding 0 to a number does not change the numbers value

Multiplication Property of Zero

Any number multiplied by 0 equals 0

Additive Inverse

The sum of any number and its additive inverse equals 0. x + -x = 0

Powers of Zero

0 raised to any power equals 0

Division by Zero

Dividing any number by 0 results in a quotient that is undefined

Zero as a Dividend

Dividing 0 by any number results in a quotient of 0

Multiplication Property of One

Multiplication by 1 does not change the value of the number

Multiplication Inverse

The product of any number and its multiplicative inverse is 1

Powers of One

1 raised to any power equals 1

Quotient of One

Any number (other than 0) divided by itself, equals 1

Absolute Value

A numbers distance from 0


Regroup by Carrying


Regroup by Borrowing


Repeated Addition

Commutative Property

The order of the numbers being added or multiplied does not affect the final results

Distributive Property

a (b+c) = ab + ac

Associative Property

If the operations are the same, the terms can be regrouped by moving the parentheses. (a+b) + c = a + (b+c)

Order of Operations



Whole numbers that are multiplied together to get a product.

Prime Factorization

Factoring a number and then factoring its factors until all factors are prime

Greatest Common Factor (GCF)

When comparing 2 numbers, the largest factor they have in common


Multiplying a number by whole numbers

Least Common Multiple (LCM)

When comparing the multiples of two numbers, the smallest multiple that they share

Divisible by 2

All even numbers

Divisible by 3

If all the digits add up to something divisible by 3, then the number is divisible by 3.111: 1 + 1 + 1 = 3

Divisible by 4

If the last two digits of the number are evenly divisible by 4, then the number is divisible by 43480: 80 is divisible by 4

Divisible by 5

If the number ends in 0 or 5

Divisible by 6

If the number is divisible by both 2 and 3, then it is divisible by 6

Divisible by 8

If the last three digits are divisible by 8, then the number is divisible by 8

Divisible by 9

If all of the digits add up to a number divisible by 9234: 2 + 3 + 4 = 9


A letter used to refer to an unknown quantity


Mathematical phrases that can contain numbers, variables, and operations


Two mathematical expressions that are set equal to one another using the equal sign

Reflexive Property

Every number is equal to itself

Symmetric Property

If a number is equal to another number, then the converse is also true

Transitive Property

If number "a" is equal to number "b," and number "b" is equal to number "c," then number "a" is also equal to number "c

Substitution Property

If two numbers are equal to one another, they are interchangeable

Difference of Two Perfect Squares

a^2 - b^2 = (a + b) (a - b)

Quadratic Formula

To solve quadratic equations (ax^2 + bx + c = 0)

Pythagorean Theorem

To find the missing length of a right triangle a^2 + b^2 = c^2

Product Laws of Exponents

(a^n)(a^m) = a^n+m(a^n)(b^n) = (ab)^n

Quotient Laws of Exponents

a^n / a^m = a^n-ma^n / b^n= (a/b)^n

Negative Exponents

b^ -n = 1/b^n

Zero Exponent

b^0 = 10^n = 0

One Rules Exponents

b^1 = b1^n = 1

Midpoint Formula

(X2 - X1/2), (Y2-Y1/2)

Slope Formula

m = (Y2-Y1)/(X2-X1)

Slope Intercept Formula

y = mx + bm=slopeb= y-intercept


Comparison of two expressions Whatever you do to one side, you must do to the other

Multiplying or Dividing Inequalities by a Negative

The sign will become reversed

Scientific Notation

One place value before a decimal point and then the number is written in terms of multiplication by 10 to a power

Expanded Form

Breaking a number apart into an addition expression based on the place value of each digit748 = 700 + 40 + 8

Arithmetic Sequence

The same value is added each time

Geometric Sequence

The same value is multiplied each time

Squares Sequence

Square each number

Cubes Sequence

Cube each number

Fibonacci Sequence

Each number is the sum of the two numbers before it


Algebraic equations that have an input and an output (f(x))

Vertical Line Test

If a vertical line would only pass through the graph once, then it is a function

Add or Subtract Fractions

If there are like denominators, just add the numerator If there are unlike denominators, find the LCM of the denominator and multiply

Multiply Fractions

Multiply across to create a new fraction

Divide Fractions

Keep, Change, Change

Measurement Prefixes

Kilo, Hecto, Deka, Base Unit, Deci, Centi, Milli




Middle of the set when they are arranged in numerical order


The number that appears most frequently


Describes the span between the numbers; subtracts the lowest number from the highest number


How close a measured value is to an actual value


How close measured values are to each other

Complimentary Angle

Angles that add up to 90'

Supplementary Angles

Angles that add up to 180'


2D shape which all sides are straight, non over lapping lines

Acute Triangle

All three angles are less than 90'

Right Triangle

One angle is 90'

Obtuse Triangle

One angle is greater than 180'

Equilateral Triangle

All three sides are equal in length

Isosceles Triangle

2 sides are equal in length

Scalene Triangle

No sides are equal in length

Geometric Nets

2D figures that represent the faces of a 3D shape

Congruent Shapes

Exactly the same shape and size

Similar Shapes

The same shape but different sizes

Area of a Triangle

A = 1/2bh

Area of a Rectangle

A = lw

Area of a Square

A = S^2

Area of a Circle

A = 3.14r^2

Area of a Parallelogram

A = bh