Math
Cube (1000)
Unit (1)
Flat (100)
Rod (10)
Whole Number: An integer which has 1 or more
units and can be positive or negative. A whole number doesn't
contain a fraction.
=1
Fraction: a part or piece of a whole
Factor: numbers multiplied (x) to find a product (=).
Example: Factors of 16 are:
1, 16
2, 8
4, 4
Multiple: The multiples of a whole number
(2,3,4, etc.)
are
found by taking the product (X) of any counting number and that
whole number.
Example 1:
Find the multiples of the whole number 4.
Multiplication:
4x1
4x2
4x3
4x4
4x5
4x6
4x7
4x8
Multiples of 4:
4
8
12
16
20
24
28
32
Standard Form: the number
Example: 1,234
Expanded Form a way to write numbers to show the place
:
value of each digit
Example: 1,000 + 200 + 30 + 4
Word Form: writing out a number using words
Example: one thousand, two hundred, thirty-four
Estimate: make a good guess
Ratio: relation between 2 things.
Shown using a colon
:
Ratio of basketballs to goals is 6 : 2
Prime Number: a number that has only itself
and one as factors.
Examples: 1, 2, 3, 5, 7, 11, 13, 17
Composite: a number with more than 2 factors.
Example: 6 (factors are 1, 6 and 2,3)
Example: 15 (factors are 1, 15 and 3, 5)
Greater than
A comparison between two numbers that shows
the greater amount.
5>4
3,245 > 3,159
Less than
A comparison between two numbers that shows
the smaller amount
23,740 < 24,000
3/10 < 7/10
Equal to:
Having the same value
372,910 = 372,910
½ = 5/10
Round: to find the nearest ten, hundred,
thousand, etc.
Example: Round 372 to the nearest hundred
1. Find the digit in the hundreds place (3)
2. Underline it
3. Move one digit to the right (7)
“1-4 hit the floor” or “5-9 up the line”
4. Since the number is (7) round the (3) to a 4.
5. The answer is 400.
Place: the location of a digit in a
number.
Value: the value of the place of a digit in a
number.
3,425,718
The value of the 4 is: 400,000
The value of the 1 is: 10
Odd Number: a whole number that ends
in 1, 3, 5, 7, or 9 and can’t be divided by 2.
Example: 37 is odd
Even Number: a whole number that ends
in 0,2,4,6, or 8 and can be divided by 2.
Example: 86
Fact Family: Number sentences
that relate addition (+) and subtraction (-)
or multiplication (x) and division ( ).
6+8=14
8+6=14
14-6=8
14-6=8
7x5=35
5x7=35
35
35 5=7
7= 5
Commutative Property (addition and multiplication)
Changing the order of the addends does not change the sum.
3+7=10
7+3=10
Changing the order of numbers we multiply does not change
the product.
4x8=32
8x4=32
Sum-the answer to and addition problem
3+4=7
Difference- the answer to a subtraction problem
8-3=5
Product-the answer to a multiplication problem
Quotient- the answer to a division problem
4x5=20
30
5=6
Square Number: the product of a number
multiplied by itself
6 x 6 = 36
8 x 8 = 64
3x 3 = 9
Pattern: a set of repeated numbers,
shapes, letters…
3, 7, 11, 5, 19
aa b aa b aa b aa b aa b
∆●◊∆●◊∆●◊∆●◊∆●◊∆●◊
Equation: a math sentence stating that two
expressions are equal.
14 + 8 = 22
14 + x =22
X =8
Ordered Pair: relationship between x and y
on a plane (X, Y).
Example: (2,3)
over 2, up 3
Input/ Output table:
Rule: X 4
5
8
2
7
3
20
32
8
28
12
Rule: X 6
5
30
6
36
2
12
4
24
Data Displays: a way to represent facts or
information
Pictograph
Bar Graph
Pie Graph
Line Graph
Line Plot
Tally Table
Shows info
using pictures
Shows info
using bars
(horizontal or
vertical)
Shows info in a
circle divided
into parts
Uses lines to
connect data
A graph
showing the
frequency of
data on a
number line.
Shows data
using tally
marks
Working with Data
Mean (average): found by adding up the data and dividing
by that number.
Example: 2 + 3 + 10 + 5 = 20
20 4= 5
5 is the mean
Median (middle number): found by putting data in order
and locating the middle number. If there are 2-average them.
Example: 1, 4, 3, 6, 9, 2, 4
Put them in order: 1, 2, 3, 4, 4, 6, 9
4,4,6,9
Find the middle number: 1,2,3,
Mode (most often): the number that is seen the most in the
data.
Example: 1, 2, 2, 3, 4, 4, 4, 5, 6, 7
Mode is 4 because that is the number seen the most.
Range (subtract highest and lowest): the difference
between the highest and lowest number in the data.
Example: 1, 2, 2, 3, 4, 4, 4, 5, 6, 7
Subtract highest (7) – lowest (1)
Range is: 7- 1 = 6.
Likelihood and Probability
Impossible: an event will not happen
(The day after Tuesday is Saturday.)
Unlikely: the event probably will not happen
(It will snow in July in Florida.)
Equally likely: the event may or may not happen
(You flip heads if you toss a coin.)
Likely: the event probably will happen
(It will snow in January in Kentucky.)
Certain: the event will definitely happen
(If you add 2 + 2 you will get 4.)
Probability:
Possible total
The probability of spinning an even number (2, 4, 6, 8) is:
4/8 or ½ or 50%
Combinations: to find the total number of
possible combos multiply the number of choices by
each other.
Combinations:
Shirt
Shorts
Blue
Brown
Green
Grey
White






Blue shirt, brown shorts
Blue shirt, grey shorts
Green shirt, brown shorts
Green shirt, grey shorts
White shirt, brown shorts
White shirt, grey shorts
3 x 2 = 6 combinations
Fraction:
Fractions that are equal:
½ = 2/4, 3/6, 4/8
¼ = 2/8, 3/12, 4/16
¾ = 6/8, 9/12, 12/16
To find an equivalent fraction remember that what
you do to the top, you must do to the bottom.
Decimals:
Read as:
seventeen and five hundred, ninety-one thousandths
To measure
Unit of measurement
Length
Inches, feet, yards, miles,
centimeters, meters,
kilometers…
Weight
Grams, ounces, pounds,
tons…
Temperature
Time
Liquid capacity
Degrees (Celsius and
Fahrenheit)
Seconds, minutes, hours,
weeks, months…
Cups, gallons, quarts,
liters…
Tools used
Ruler, yard stick,
measuring tape, odometer
Scale
Thermometer
Clock
Measuring cups, etc.
Commons Conversions:
Length
Weight
Time
Liquid
12 inches (in) = 1 foot (ft)
16 ounces (oz) = 1 pound
(lbs)
60 seconds = 1 minute
2 cups = 1 pint
60 minutes = 1 hour
2 pints = 1 quart
2000 pounds = 1 ton
24 hours = 1 day
4 quarts = 1 gallon
36 inches = 3 feet = 1
yard
5, 280 feet = 1 mile
7 days= 1 week
52 weeks = 1 year
Types of angles:
Right Angle
equal to 90 °
Acute Angle
Less than 90°
Obtuse Angle
More than 90 but less
than 180°
2-D Geometry
Line
a straight
figure that
goes on
forever
Line Segment
Ray
Perpendicular
Lines
Part of a line with
two end points
A line that
extends from
a point
Lines that
cross to form
four right
angles

Parallel Lines
Lines that never
intersect
Intersecting
Lines
Lines that
cross
Measuring Circles:
Diameter: the distance across a circle
Circumference: the distance around a circle measured by the
Diameter (D) x ∏=C
Radius: the distance from the center of a circle to the edge.
The radius x 2 = diameter
Triangles can be
measured in two ways:
1. by their sides
2. by their angles
BY THEIR SIDES
Scalene - no congruent sides.
Isosceles - two congruent sides.
(DF = FE)
Equilateral - three congruent
sides.
BY THEIR ANGLES
Acute - all angles measure less
than 90º.
Right - one angle measures
exactly 90º.
Obtuse - one angle measures
more than 90º.
Parts of a 3-D shape:
Faces
Edges
Vertex
5
9
6
Translations