Sixth Grade Math Vocabulary

Algebraic ExpressionAn expression that is written using one or more variables

Examples3x         x – 4y       2a + 5       x2 + x – 6

2x + x

3x

BiasA sample that is not representative

of the entire populationOr

A survey that is not fair because of the population questioned

ExampleFor a survey about favorite types of movies of 6th graders:

Asking students attending ahorror movie “what is your favorite type of movie?”

Composite

A whole number, greater than one, with more than two whole-number factors

Examples6 is composite because6 = 1 X 6 and 6 = 2 X 3The 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.

=

3X91, 21X137X39, 1X273

Composite

1 is not prime or composite

Conjecture (with data)To guess or make a prediction

about future outcomesbased 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

To solve an equation, find a value for the variable that makes the sentence

true

Examples

x + 3 = 4 2c = 6 h – 5 = 12 Solution: x = 1 c = 3 h = 17

XX=2

Evaluate To find the value of a numerical expression

OrIn an algebraic expression, to replace the variable with a number and perform the

operations

Examples

Evaluate: Evaluate if x = 2:16 – 2(3+4) = 3x + 12 – x + 2

16 – 2(7) = 3(2) + 12 – 2 + 2 = 16 – 14 = 2 6 + 12 – 2 + 2 =

18 – 2 + 2 = 16 + 2 = 18

2l+2wL=5, w=62(5)+2(6) =22

Formula

A rule showing the relationship betweencertain quantities

ExamplesA = lw (Area of a rectangle) P = 2l + 2w (Perimeter of a rectangle)

V = lwh (Volume of a rectangular prism)

l

w

lw

h

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)

From table: input=1 then output=5 input=2 then output=6 input=3 then output=7 input=4 then output=8

1 2 3 4

5 6 7 8n+4

37

Input/Output: Function machine

Inverse

Operations that undo each other

ExamplesAddition 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 – 3x = 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

OddsOdds in favor: A ratio that compares favorable

outcomes to unfavorable outcomesOdds 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

100

24%24

%32100

32

25

8

%17100

1717.

10/10

%

%10010

10

Prime A number greater than one

with exactly two factors, one and itself

Examples2 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

ExamplesIf 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

ExamplesProperties of a square: Four sides of equal length

Four right anglesProperties 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 equivalentIf the cross products of the two ratios are equal,

then the pair forms a proportion

Examples is a proportion because

do not form a proportion because

1 4

3 12

2 7 and

5 1510

8

5

4

43112

75215

Random Occurring without any pattern or order

A chance pick from items which each have an equal likelihood of being chosen

ExamplesThere 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

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

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

Rate of changeA 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

ExamplesIf 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 $48After 8 days they had collected $128

The rate of change was or $16 per day days 5

80$

Ratio A comparison of two numbers or quantities

(usually by division)

ExamplesIf a class has 14 boys and 12 girls then

6

7

12

14The ratio of boys to girls is

7

6

14

12The ratio of girls to boys is

13

7

26

14The ratio of boys to total number of students is

13

6

26

12The ratio of girls to total number of students is

6

7can also be written as 7:6

Reciprocal The multiplicative inverse of a number

Examples

2

3

3

2The reciprocal of is

1

2

22

1The reciprocal of is

10

1The reciprocal of -10 is

Sample A part of a group or population that is used

to represent the entire population

ExamplesInstead 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

ExamplesMaps: if a distance of 75 miles is 1 inch long on a map the scale would be 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.

1 inch = 75 miles

To write an fraction, expression or equation in its simplest form

Examples

Simplify: =

Simplify: x + 50 = 60 + 7 x + 50 = 67

x = 17

Simplify: 2x + 5 + 3x – 2 = 5x + 3

Simplify

9

33

1

39

33

x+4x=5

x

2x =8 x = 4

Simulation A model of an experiment

The model is usually used because the actual experiment would be too difficult

or time consuming to do

ExampleStudents 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

ExamplesThe 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:

(The stems represent tens, the leaves represent units)

10 0

9 0 2 6 8 8 9

8 3 4 4 4 5 6 7

7 8 9

Tessellation A repeating pattern of figures that

completely covers a plane with no gaps and no overlaps

ExamplesHexagons 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 figureTransformations that change position are

translations, reflections and rotations

ExamplesTranslation Reflection

Rotation

Tree Diagram A branching diagram showing all possible

outcomes or combinations of items or events

ExampleChris has three different colors of shirts and two different colors of pantsHow many different outfits are there?

Blue BlueTan Green Brown Green White 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 spaceThe amount of space occupied by an object

Examples

Some volume formulas: Cube: Cylinder: Rectangular prism:

h 2rV

3sV lwhV