Sixth Grade Math Vocabulary. Algebraic Expression An expression that is written using one or more...
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Transcript of Sixth Grade Math Vocabulary. Algebraic Expression An expression that is written using one or more...
![Page 1: Sixth Grade Math Vocabulary. Algebraic Expression An expression that is written using one or more variables Examples 3x x – 4y 2a + 5 x 2 + x – 6 2x +](https://reader036.fdocuments.net/reader036/viewer/2022062407/56649ddd5503460f94ad4dd6/html5/thumbnails/1.jpg)
Sixth Grade Math Vocabulary
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Algebraic ExpressionAn expression that is written using one or more variables
Examples3x x – 4y 2a + 5 x2 + x – 6
2x + x
3x
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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?”
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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
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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.
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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)
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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°.
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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)
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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
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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
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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
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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 $16 per day days 5
80$
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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
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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
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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.
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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
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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
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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
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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
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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
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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
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Transformation A change in the position, shape
or size of a figureTransformations that change position are
translations, reflections and rotations
ExamplesTranslation Reflection
Rotation
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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
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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