Download Mathematics Proficiency Vocabulary

Mathematics Proficiency Vocabulary
A Third- when a whole is cut into three equal parts; a third is one of the three parts
Absolute Value- the absolute value of a number is the number of units it is from zero on the
number line ex. Both 5 and -5 are 5 units from the zero so the absolute value of 5 or -5 is 5
Acute Angle- smaller than a right angle, less than 90 degrees
Adjacent Angles- two angles that have the same vertex and a common side but have no
common interior points ex. The angles marked 1 and 2.
Approximate- to estimate the value of some quantity to a desired degree. To round to the
place value that is specified.
Arc- two points and a continuous part of a circle between points
Area- part of a two-dimensional surface enclosed within a specified boundary or geometric
figure. To measure the inside of a geometric shape using the area formula for said shape. Ex. To
find the area of a square you multiply the length times the width
Associative property- in the operations of addition or multiplication the brackets or parenthesis
may be disregarded. The way the numbers are grouped does not change the sum or product.
Ex. 4+ (5+2) = (4+5) +2
Average- (also known as the mean) - In a collection of data, the sum of all the data divided by
the number of data. Ex. Sum of data 4, 6, 2, 7, 3 and 8=30 divide by number of data which is 6.
30÷6=5. The average or mean is 5.
Bar Graph- a graph consisting of a series of vertical or horizontal bars representing data. This
type of graph is used to show comparison of two or more types of data.
Bisect- to divide into two congruent parts. To cut something into two equal parts.
Box and Whisker Plot- A diagram that divides a ser of data into four parts using the median and
quartiles.
Ex.
Capacity- measuring the ounces, cups, pints, quarts and gallons in standard measurement or
millimeters, liters, and kiloliters in the metric measurement. Usually measuring a liquid.
Chord- a segment that joins two points on a circle
Circle- a curved line with every point on the line being an equal distance from the center point.
A circle has 360 degrees. Ex. 50% of a circle is 180 degrees.
Circle Graph- also called pie graphs are used to show how parts relate to the whole and to each
other
Circumference- the distance around a circle
Commutative property- in the operations of addition or multiplication the order of the
numbers does not change the product or sum.
Ex. 4+5=5+4
Complement or complementary angle- two angles the sum of whose measure is 90 degrees.
Ex. 40° angle has a complementary angle of 50°, since 40+50=90
Composite Numbers- a whole number greater than one with more than two factors. Ex. The
number 4 is a composite number since 1, 2 and 4 are all factors
Congruent- figures that have the same size and shape
Data or Information- numerical information that is gathered for statistical purposes
Decimal- counted in groups of ten using the number ten as a base and counted or ordered in
units of ten. Ex. In .0 the zero is in the tenths place and .02 the two is in the hundredths place.
When asked to change a decimal to a percent or fraction use the following examples: .8 is
written as 8 over 10 the reduced and .35 is written as 35 over 100 and then reduced (for every
decimal place a zero is added in the denominator of the fraction). To change a decimal to a
percent, multiple the decimal by 100, .38 becomes 38%
Degrees- a unit for measuring angles
Dependent Event- the outcome of a dependent even is affected by the outcome of another
event.
Diameter- a line segment that passes through the center of a circle and has both endpoints on
the circle
Distributive property- if one factor is a sum, multiplying before adding does not change the
product
ex. 3(4+5) = (3×4) + (3×5)
Domain- the x value in an ordered pair also known as the output
Double- to multiply by two or to add the same number twice
Ex. To double 35 means to multiple 35 by 2, which equals 70
Equation- a number sentence with an equal sign
Ex. 9+x=15
Equivalent- having the same solution set
Ex. 2+x=6 and 5+x=9: x=4 for each equation so they have equivalent answers
Estimate- To give an approximate rather than an exact answer. To round to the place value
that is specified.
Expression- a mathematical phrase made up of a variable or combination of variables
and/or numbers and operations.
Ex. 5n, 4x-7, (5×2)
Exterior Angle- 1. An angle on the outside of a polygon, formed between a side and an
extension of an adjacent side.
2. An angle formed by a line crossing any of the four angles formed on the outside of lines
that are crossed be a third. (a transversal)
Ex.
Factors- Numbers that are multiplied to obtain a product. A number that goes into a
number evenly is a factor of that number.
Ex. 3×8=24, therefore 3 and 8 are factors of 24
Fraction- A number that is not a whole number such as ½. A fraction is also a division
statement; the numerator (top) is divided by the denominator (bottom).
Ex. Fraction to decimal; divide the numerator by the denominator and the answer is now in
decimal form. Fraction to percent; First divide the numerator be the denominator and then
multiply by 100.
Frequency- Also known as frequency table or frequency distribution
1. A table of tally marks used to record and display how often events occur
2. How often something happens
Greatest Common Factor- (GCF) The greatest number that is a factor of each of two or more
numbers. The largest number that divides into the other numbers evenly.
Ex. The GCF of 24 and 30 is 6, since it is the largest number that is a factor of both 24 and
30
Half- To divide something into two equal pieces
Ex. A question asks you to cut the bill in half, the total was $24.58. $24.58÷2= $12.29
Histogram- used to demonstrate frequency distribution
Hypotenuse- In a right triangle, the side opposite the right angle. The side of a right triangle
designated as side C, the longest side of a right triangle.
Inclusive- Including the specified limits indicated in the range
Ex. From 10 to 20 inclusive means, all numbers from 10 to 20 including both 10 and 20 as
well
Identity Property- 1. Identity property of addition A+0=A
2. Identity property of multiplication A×1=A
Independent Event- The outcome of an independent event is not affected by the outcome of
another event
Inequality- A mathematical sentence that uses one of the symbols <, ≤, >, ≥ or g
Ex. 3x<24, 2x+5 g 7
Integers- The numbers…-3, -2, -1, 0, 1, 2, 3,… Both positive and negative whole numbers.
Interest (simple or compound) - the charge for borrowing monkey or the amount paid for
the use of money
Formula (simple) - I=prt
Interior Angle- 1. An angle inside a polygon is formed between two adjacent sides of the
polygon and lying in its interior.
2. Angle within intersecting line, any of four angles formed in the area between two parallel
lines by a third line that intersects them (a transversal)
Ex.
Least Common Denominator: LCD- the least common multiple of the denominators of two
or more fractions. The smallest number that the denominators of the fractions multiply
into evenly.
Ex. The LCD of 2/3 and 4/5 is 15 because that is the first number both 3 and 5 multiply into
evenly
Line Graph- A graph on which lines connect dots to show values. This type of graph is used
to compare data.
Linear Equation- A function is linear if it can be defined by f(x)=ax+b an equation whose
graph is a line.
Linear Function- a function is linear if it can be defined by f(x)=mx+b where m and b are
real numbers
Linear Relation- The use of a linear equation to show the relationship between domain and
range.
Ex. Miles driven and gallons of gasoline have a linear relationship. The more miles you go
the more gasoline you use.
Mean- Also known as the average. In a collection of data, the sum of all the data divided by
the number of data.
Ex. Sum of data 4, 6, 2, 7, 3 and 8 = 30 divide by number of data which is 6. So the mean = 5
Measure of a central angle- An angle that has its vertex at the center of a circle.
Ex. A pizza is cut into 12 pieces; what is the measure of the central angle? The question is
asking you to divide the circle into 12 equal parts or 360÷12=30 degrees for each angle.
Measure of an angle- the degree of an angle, whether it is a straight line, circle, square or
triangle. A straight line is 180 degrees, a circle has 360 degrees and a triangle has 180
degrees.
Ex. The question is usually asking for a missing angle’s measurement. If a right triangle has
one angle that is 50 degrees what are the other two angles? Answer; 90 degrees because it
is a right triangle
Measure of Central Tendency- The mean, median and mode or averages are known as
measures of central tendency. The one that best describes the average can be the mean, the
median or the mode depending on the data given.
Ex. In the following set of data 2, 5, 7, 9, 11, 14, 45 which best describes the measure of
central tendency, the mean is 13 the median is 9 and there is no mode. The best answer is
median since it represents the average of the 6 smallest numbers and 45 cause the mean to
be larger than all but 2 numbers from the set of data.
Median- The middle value of a set of data in numerical order. If there are two middle =
values, the median is the mean of those values.
Ex. 12, 4, 9, 7, 8 and 5 first put the data in numerical order 4, 5, 7, 8, 9, 12 then find the
middle value, which are 7 and 8. The mean of 7 and 8 is 7+8=15. 15÷2=7.5 so the median
is 7.5.
Metric Measurements
Liquid Measurements
1000 Milliliters=1 Liter
1000 Liters=1 Kiloliter
Milliliter=Eyedropper
Liter= a Pepsi bottle (the slam size)
Kiloliter=a bathtub full of water
Length Measurements
10 millimeters=1 centimeter
100 centimeters=1 meter
1000 meters=kilometer
millimeter=Thickness of a penny
centimeter= the diameter of a penny
meter= about 1 yard
kilometer= less than a mile
Weight Measurements
1000 milligrams=1 gram
1000 grams=1 kilogram
Milligram=a grain of sand
Gram=a paper clip
Kilogram= a book
Mode- The number or numbers that occur most often in a collection of data. There an be
non, 1 or many modes in a set of data
Multiple- And number of polynomial that is the product of a given number or polynomial
and an integral multiplier
Ex. 8 is a multiple of 2 and 4 or x2 – y2 is a multiple of x+y
Obtain- to get to the answer
Obtuse angle- an angle with a measure greater than 90 degrees but less than 180 degrees
Odds- Favorable/unfavorable outcome (what you want to happen/what you don’t want to
happen). Odds and probability are similar but not exactly the same.
Ex. What are the odds of getting heads when you flip a coin?
Answer: There is one head and one tail on a coin so the odds of getting heads are 1 to 1.
One chance to get heads and one chance that you won’t so the odds are even.
Operation- any procedure such as addition, subtraction, multiplication, or division.
Parallel lines- lines in the same plane that never intersect
Parallelogram- A quadrilateral with opposite sides parallel. Each pair of opposite sides and
angles is congruent.
Percent- Used to express a portion of 100. Changing percent to decimal or fraction
Ex. Percent to decimal: to change a percent to a decimal divide by 100 or move the decimal
place two places to the left, 4% becomes .04. To change percent to fraction; the percent
becomes the numerator of the fraction and the denominator becomes 100, 35% becomes
35 over 100 now reduce.
Percent of increase or decrease: (profit or loss) - How much something has increased or
decreased in percentage. Formula: Difference divided by original.
Ex. A chair costs $50 to make and they sold it for $80 what is the profit? 80-50=30 that is
the difference and 30 over 50 (original price) is 3/5 or 60% increase.
Perimeter- The distance around a polygon. When finding a perimeter of a shape you add all
the sides together
Perpendicular lines- two lines that intersect to form a right angle
Pictograph- a chart with pictures or symbols representing values
Polygon- a closed plane figure made up of line segments. Three or more line segments;
triangle, square, rectangle, parallelogram, rhombus etc are all polygons
Portion- a part of a whole
Power- an expression in the form of xn
Prime Numbers- A whole number greater than 1 with only two factors- itself and 1
Ex. 2, 3, 5, 7, 11. The number 2 is the only even prime number and neither 1 nor 0 is prime
Probability- The ratio of favorable outcomes to possible outcomes of an experiment.
Ex. What is the probability of getting heads when you flip a coin? There are two sides and
only one is heads so the probability is 1 out of 2 or 50%
Experimental Probability- what happens when you actually experiment
Theoretical probability- what is supposed to happen
Product- the answer in a multiplication problem
Proportion- a sentence in a multiplication problem
Ex. 3/6=8/16
Pythagorean Theorem- A proved geometric proposition stating that the square of the
longest side (hypotenuse) of a right triangle is equal to the sum of the squares of the other
two sides. A2+B2=C2
Quadratic Equation- An equation containing one or more terms raised to the power of two
Ex. x2+2x-5=3
Quadratic Formula- a formula used to solve quadratic equations
Quotient- the answer in a division problem
Radius- a line segment with one endpoint at the center of a circle and the other endpoint on the
circle (half the diameter)
Ratio- a comparison of two numbers by division
Ex. 2/3, 2:3, or 2 to 3 are different ways to write a ratio
Rational Numbers- Any number that can be expressed as a ratio a/b, of two integers, a and b, of
which b may not be zero.
Ex. 3 may be written as 3/1 and .5=1/2 so 3 and .5 are both rational numbers
Range- The difference between the largest and smallest number in a set of data. Occasionally
range is lumped in with mean, median and mode in a question regarding the measure of central
tendency, but since the range in the following set of data 2, 5, 7, 9, 11, 14, 45 is (45-2=43) this
would not be called an ave3rage of the set of data.
Rectangular solid- a three dimensional rectangle
Reflection- the mirror image of a figure about the line of symmetry in a plane
Right angle- An angle that measures 90 degrees. The angle is usually marked with a box like
figure
Ex.
Rotation- A transformation obtained by rotating a figure through a given angle about a point
Round- to estimate or give an approximate rather than an exact answer, to round to the place
value that is specified
Sample, Sample Size or Sample Space- all the possible results, or outcomes for an experiment
Scatter Plot- two sets of data plotted as ordered pairs in a coordinate system
Ex.
Shared among- to divide up into equal parts
Ex. a bill was shared among you and three others, the bill totaled $36.12, 36.12÷4= $9.03
Similar- figures that are the same shape but not necessarily the same size
Simplify- to reduce an expression to its simplest form
Ex. 5/10 = 1/2, 3x + 5x + 7 = 8x + 7 or 3(2x+7) = 6x + 21
Simulate- Usually means to experiment to produce results
Ex. tossing a dice or flipping a coin a certain amount of times to find the probability of a
particular outcome
Split- usually means to cut into two equal parts
Square-(power and shape)-power- something to the second power, ex. 22 = 4. Shape- a
rectangle with all four sides congruent, has 360 degrees
Slope- y = mx+b. The b tells you where the line crosses the y-axis and the m tells you the
steepness and direction of a slope. (hint) the m tells you if the slope is climbing or descending
form left to right. A negative slope goes downward as you read left to right and a positive slope
goes upward from left to right.
Ex. y = ½x + 3, the 3 is b which tells you that the line crosses at positive 3 on the y-axis and the
½ is m which is positive so it goes up one unit for every two units it moves to the right
Standard Measurements
Length
12 inches = 1 foot
3 feet = 1 yard
1,760 yards = 1 mile
Weight
16 ounces = 1 pound
2000 pounds = 1 ton
Capacity
8 ounces = 1 cup
2 cups = 1 pint
2 pints = 1 quart
4 quarts = 1 gallon
Statistics- the science of collection, organizing and analyzing data
Straight angle- an angle that measures 180 degrees
Sum- the answer in addition
Supplement or supplementary angle- two angles the sum of whose measure is 180 degrees
Ex. 120 degree angle has a supplementary angle of 60 degrees, since 120 + 60 = 180
Surface Area- the area of part of a surface. Usually the outside areas added together to find the
total surface area
Symmetry- the property of being the same on both sides of a central dividing line
Ex. a butterfly or a square cut exactly in half would be symmetrical, some letters of the alphabet
have symmetry depending on where the dividing line is, A, B, E, M and W are just a few
Total- the sum of several amounts added together
Transformation- a mapping that establishes a one to one correspondence between points in the
plane. Also known a movements of geometric figures
Translation- a change in position resulting from a slide without any turn
Transversal- a line that intersects two coplanar lines in two different points
Triangles
Right triangle- a triangle having one right angle
Scalene triangle- a triangle that has no sides congruent
Isosceles triangle- a triangle with at least 2 sides congruent
Equilateral triangle- a triangle with all 3 sides congruent
Acute triangle- a triangle with all acute angles, all angles less then 90 degrees
Obtuse triangle- a triangle with one obtuse angle, one angle greater then 90 degrees
Trig Functions
Cosine- side opposite angle/hypotenuse
Sine- side adjacent angle/hypotenuse
Tangent- side opposite angle/side adjacent angle
Twice- to multiply by two
Undefined- without fixed limits for which no definite limits have been decided. A number
cannot be divided by zero. The answer is called undefined
Ex. 3/0 is undefined or 3 ÷ (x + 1) is undefined when x = -1
Vertical Angles- two nonadjacent angles formed by a pair of intersecting lines
Ex. the angles marked 1 and 4 are vertical angles and the angles marked 2 and 3 are vertical
angles
Volume- the number of cubic units needed to fill a space figure. Volume is the capacity a three
dimensional figure can hold in all directions
Ex. if you filled the entire classroom full of jello from the floor to the ceiling this would be
volume
Whole numbers- another term for natural numbers, usually including zero. Usually known as
positive integers
Typical Polygons
Pentagon- a 5 sided figure with 540 degrees
Hexagon- a 6 sided figure with 720 degrees
Quadrilateral- a 4 sided figure with 360 degrees
Triangle- a 3 sided figure with 180 degrees
Octagon- an 8 sided figure with 1080 degrees