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Sixth Grade
Math Vocabulary
Algebraic Expression
An expression that is written
using one or more variables
3x
Examples
x – 4y
2a + 5
x2 + x – 6
Bias
A sample that is not representative
of the entire population
Or
A survey that is not fair because of
the population questioned
Example
For a survey about favorite
types of movies of 6th graders:
Asking students attending a
horror movie “what is your
favorite type of movie?”
Composite
A whole number, greater than one,
with more than two whole-number factors
Composite
=
3X91, 21X13
7X39, 1X273
Examples
6 is composite because
6 = 1 X 6 and 6 = 2 X 3
The factors of 6 are 1, 2, 3, 6
3 is NOT composite (it is prime)
because 3 = 1 X 3 and
the only factors of 3 are 1 and 3.
1 is not prime
or composite
Conjecture (with data)
To guess or make a prediction
about future outcomes
based on patterns, logic or survey results
Example:
Add consecutive odd numbers starting with 1:
1+3 =4, 1+3+5=9, 1+3+5+7=16,
A good conjecture would be that
the sums of consecutive odd numbers
starting with 1 are always perfect
squares.
Coordinate Plane
(Ordered Pairs)
A plane formed by a horizontal number line (x-axis) and
a vertical number line (y-axis)
The ordered pairs (x,y)
shown on the coordinate plane
are: A: (4,4)
B: (-3,-3)
C: (3,-6)
D: (-5,2)
The origin is the point (0,0)
Degrees (Angle)
The most common unit of measure for angles
Examples
The angle ABC that is shown below
has a measure of about 40°.
The right angle below
has a measure of 90°.
Equation (Solving)
An equation is a mathematical sentence that
shows that two quantities are equal
X
X=2
To solve an equation,
find a value for the variable
that makes the sentence true
Examples
x+3= 4
Solution:
x=1
2c = 6
c=3
h – 5 = 12
h = 17
Evaluate
To find the value of a numerical expression
Or
In an algebraic expression, to replace the
variable with a number and perform the
operations
2l+2w
Examples
Evaluate:
16 – 2(3+4) =
16 – 2(7) =
16 – 14 = 2
L=5, w=6
2(5)+2(6)
=22
Evaluate if x = 2:
3x + 12 – x + 2
3(2) + 12 – 2 + 2 =
6 + 12 – 2 + 2 =
18 – 2 + 2 =
16 + 2 = 18
Formula
A rule showing the relationship between
certain quantities
w
Examples
l
A = lw
(Area of a rectangle)
P = 2l + 2w (Perimeter of a rectangle)
V = lwh (Volume of a rectangular prism)
h
w
l
Function
A relation or rule that assigns
one and only one output for each input
(Given an input, you get exactly one output)
Examples
Rule: y = x+4,
each output is 4 more than the input
if input=2 then output=6, (2,6)
if input=4 then output=8, (4,8)
3
7
From table:
1 2 3 4
5 6 7 8
input=1 then output=5
input=2 then output=6
input=3 then output=7
input=4 then output=8
n+4
Input/Output: Function machine
Inverse
Operations that undo each other
Examples
Addition and subtraction are inverse operations
(undo adding 3 by subtracting 3)
multiplication and division are inverse operations
(undo multiplying by 2 by dividing by 2)
To solve an equation:
x+3=5
x+3–3=5–3
x=2
Measures of
Central Tendency
A measure used to describe or represent data
The mean, median, and mode
are measures of central tendency
Examples
Given six test scores: 85,87,78,88,88 and 96
Three measures of central tendency are :
Mean = 87, (85+87+78+88+88+96)/6
Median = 87.5, The average of the two middle scores after
putting them in order (78,85,87,88,88,96), (87+88)/2
Mode = 88, The score that appears most often
Odds
Odds in favor: A ratio that compares favorable
outcomes to unfavorable outcomes
Odds against: A ratio that compares unfavorable
outcomes to favorable outcomes
Example
If you roll a six-sided number cube (1-6):
The odds in favor of getting a 3 are 1 to 5
(There is one 3, there are five numbers that are not 3)
This is different than the probability of getting a 3,
which is one out of six or 1/6
Order of Operations
In order to make sure that everyone gets the same answer when
simplifying, there is a set of rules to follow:
1. Do all operations within parentheses (P)
2. Simplify exponents (E)
3. From left to right: do all multiplication and division
(MD)
4. From left to right: do all addition and subtraction (AS)
The acronym for this is PEMDAS
Example:
2 + 3(7 – 4) – 6 + 2 =
2 + 3(3) – 6 + 2 =
2+9–6+2=
11 – 6 + 2 =
5+2= 7
He needed to do the multiplication FIRST
Percent
Per 100 or out of 100
A percent is a ratio that
compares a number to 100
Examples
24
24% 
100
10
 100%
10
8
32

 32%
25 100
17
.17 
 17%
100
Prime
A number greater than one
with exactly two factors, one and itself
Examples
2 is the smallest prime number
(1x2 = 2)
17 is a prime number,
the only factors of 17
are 1 and 17
15 is NOT prime (it is composite)
because the factors of 15
are 1, 3, 5 and 15
Sieve of Eratosthenes
Probability
A ratio that compares
the number of ways a certain event can occur
to the total number of possible outcomes
Examples
If you roll a six-sided number cube (1-6):
The probability of getting a 3 is 1/6
(there is one way to get a 3 out of six possible
outcomes)
The probability of getting an even number
is 3/6 or 1/2
(there are three outcomes that are even: 2,4,6
out of six possible outcomes)
Properties of
shapes and figures
Characteristics or features
that help to recognize and identify them
Examples
Properties of a square: Four sides of equal length
Four right angles
Properties of a trapezoid:
Quadrilateral with
exactly two parallel sides
Properties of a parallelogram: Quadrilateral with
opposite sides congruent,
opposite sides parallel and
opposite angles congruent
Proportion
An equation stating that two ratios
are equal or equivalent
If the cross products of the two ratios are equal,
then the pair forms a proportion
1 4

3 12
Examples
is a proportion because 12 1  3  4
2
7 do not form a proportion
and
5
15 because 15  2  5  7
4 8

5 10
Random
Occurring without any pattern or order
A chance pick from items which each have
an equal likelihood of being chosen
Examples
There are six different colored marbles
in a hat: If you choose one at random,
there is an equal chance that you pick
any one of them
17-34-42-45-50 11
02-08-09-12-19 25
05-18-28-49-55 38
22-32-36-49-55 08
01-08-19-36-42 20
If a list of numbers is random,
the numbers appear without
regard to any order or pattern
and each has an equal possibility
of appearing
Rate of change
A comparison of one quantity to the
unit value of another quantity,
A change in one measure with respect to another,
The slope of a line
Examples
If a car drives 120 miles in 2 hours,
Its rate of change is 60 miles per hour
Students donated money to help hurricane victims.
After 3 days they had collected $48
After 8 days they had collected $128
The rate of change was $80
5 days
or $16 per day
Ratio
A comparison of two numbers or quantities
(usually by division)
Examples
If a class has 14 boys and 12 girls then
The ratio of boys to girls is
14 7

12 6
The ratio of girls to boys is
12 6

14 7
The ratio of boys to total number of students is
The ratio of girls to total number of students is
7
can also be written as 7:6
6
14 7

26 13
12 6

26 13
Reciprocal
The multiplicative inverse of a number
Examples
2
3
The reciprocal of
is
3
2
1
2
2
The reciprocal of
is
2
1
1
The reciprocal of -10 is 
10
Sample
A part of a group or population that is used
to represent the entire population
Examples
Instead of surveying the
entire sixth grade class
about their favorite food,
you only survey 2 sixth grade
classrooms
To find out the favorite type of movie of all
students in your school, you only ask
every tenth student walking down the hall.
Scale Drawing
A drawing used to represent a figure that is too
large or too small to be shown actual size
It maintains the original proportions
Examples
Maps: if a distance of 75 miles
is 1 inch long on a map the
scale would be 1 inch = 75 miles
1 inch = 75 miles
Drawings: if the Eiffel Tower
is 1000 feet tall and the drawing of it
was 10 inches tall, the scale would be
10 inches=1000 feet
or 1 inch= 100 feet.
Simplify
To write an fraction, expression or equation
in its simplest form
Examples
3
33 1
Simplify: 9 = 9  3  3
x+4x=5
x
2x =8 x
=4
Simplify: x + 50 = 60 + 7
x + 50 = 67
x = 17
Simplify: 2x + 5 + 3x – 2
= 5x + 3
Simulation
A model of an experiment
The model is usually used because the actual
experiment would be too difficult
or time consuming to do
Example
Students participate in a
stock market simulation game,
buying stocks with play money
and keeping track of mock portfolios
to make predictions and follow trends
in the real stock market
Statistics
Collecting, organizing, and interpreting data,
especially analyzing characteristics of
populations by sampling
Examples
Statistics can be displayed using graphs,
stem-and-leaf plots, box-and-whisker plots
Statistics of a sample can include the range, mean,
median, mode, upper and lower quartiles
Stem-and-leaf Plot
A graph that uses the digits of each number in
order to show the shape of the data
Examples
The scores on a test were: 83, 79, 84, 86, 84, 99, 98,
87, 98, 78, 96, 92, 90, 100, 84, 85.
The stem-and-leaf plot would look like:
10
0
9
026889
8
3444567
7
89
(The stems represent tens, the leaves represent units)
Tessellation
A repeating pattern of figures that completely
covers a plane
with no gaps and no overlaps
Examples
Hexagons will tessellate and completely cover a plane
MC Escher is a famous artist who
took basic geometric shapes and
used them to make various figures
that would tessellate in a plane
Transformation
A change in the position, shape
or size of a figure
Transformations that change position are
translations, reflections and rotations
Translation
Examples
Rotation
Reflection
Tree Diagram
A branching diagram showing all possible outcomes or
combinations of items or events
Example
Chris has three different colors of shirts
and two different colors of pants
How many different outfits are there?
Tan
Blue
Green
White
Brown
Blue
Green
White
There are 6 different outfits:
Tan/Blue, Tan/Green, Tan/White
Brown/Blue, Brown/Green, Brown/White
Volume
The number of cubic units needed to fill
a given 3-dimensional space
The amount of space occupied by an object
Examples
Some volume formulas:
Cube:
Cylinder:
V  s3
V   r2 h
Rectangular prism:
V  lwh