our math glossary

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PreProposal Letter Our symbols 1 1

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Math Glossary

A Acute A positive angle measuring less than 90 degrees.

Adjacent Two angles that share both a side and a vertex.

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Angles The union of two rays with a common endpoint, called the vertex.

acute angle right angle

obtuse angle Two angles that share both a side and a vertex.

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Arc A portion (part) of the circumference of a circle.

Area Area is the inside of a figure and you either count up the squares or multiply the length and width.

If the length is 5 and the width is 2. A = 10 sq Associative Property of Addition (a + b) + c = a + (b + c) Example: 3 + 4 + 5 can be done either of the following two ways a) (3 + 4) + 5 b) 3 + (4 + 5) Associative Property of Multiplication (a x b) x c = a x (b x c) Example: 3 x 4 x 5 can be done either of the following two ways

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a) (3 x 4) x 5 b) 3 x (4 x 5) Average A number that represents the characteristics of a data set. Example: A data set of the numbers 12, 17, 23, 29, and 34 1) Add all the numbers in the data set together 12 17 2) Take the sum of all the numbers and divide it by how many 23 numbers there are in the data set - for this example 29 there are five numbers +34 115 ÷ 5 = 23 _____ 115 3) Thus the average for this data set is 23 4) Remember that the average will always be a number between the smallest number (in this case the number 12 is smallest) and the largest number (in this case the number 34) - notice that our average 23 is between these two numbers. B B Base The bottom of a plane figure or three-dimensional figure.

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B C Chord A line segment that connects two points on a curve (not through the center).

Circumference The distance around a circle.

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Common Multiple A multiple of two or more numbers. Commutative Property of Addition a + b = b + a Example: 3 + 4 = 4 + 3 Commutative Property of Multiplication a x b = b x a Example: 3 x 4 = 4 x 3 Complementary Angles Two angles whose sum is 90 degrees. = angle, thus ABC is an angle that has points A, B, and C on it. Example: FAB or FAD (same angle) is 45° and CAB is 90° then CAF is also 45° which makes FAB and CAF complimentary angles since they add to 90°

Composite Number A natural number that is not prime. Which is any number that has factors of more than one and itself. Such as 4 which has factors of (1, 2, 4) - 1x4 and 2x2. Cone A three-dimensional figure with one vertex and a circular base.

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Congruent Figures or angles that have the same size and shape.

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Coordinate Plane The plane determined by a horizontal number line, called the x-axis, and a vertical number line, called the y-axis, intersecting at a point called the origin. Each point in the coordinate plane can be specified by an ordered pair of numbers.

Cross Product A product found by multiplying the numerator of one fraction by the denominator of another fraction and the denominator of the first fraction by the numerator of the second. Cube A solid figure with six square faces.

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Cylinder A three-dimensional figure having two parallel bases that are congruent circles.

B D Data Information that is gathered. Decimal Number The numbers in the base 10 number system, having one or more places to the right of a decimal point. Example: 12.38 Decimals: Compare or Order - (make sure the decimals are in the same place by making equivalencies)

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.9 .09 will become .90 > .09 as you make the decimals into the same place 3.80 3.8 will become 3.80 = 3.80 12.09 12.9 will become 12.09< 12.90 1.2 , 1.02, 11.2 , 12, 12.1 will become 1.20, 1.02, 11.20, 12.00, 12.10 When ordered least to greatest it will be 1.02, 1.20, 11.20, 12.00, 12.10 Decimals: Converting to a Fraction and Percent - (the denominator must be 100 and you do this by making an equivalent fraction) .4 = 4/10 = 40/100 = 40% .25 = 25/100 = 25% Decimals: Counting - (make sure you are in the same place as requested) count by tenths .8, .9 ,1.0. 1.1 etc.... count by hundredths .98, .99, 1.00, 1.01 etc.... .9 would need to be changed to .90 before you could count by hundredths Decimals: Equivalent (zeros to the right of decimal) 0.7 = 0.70 1.9 = 1.90 13.503 = 13.503 (can't remove zero when trapped by digit to right) Decimals: Place Value 1,234.56789 1 = thousands 2 = hundreds 3 = tens 4 = ones 5 = tenths 6 = hundredths 7 = thousandths 8 = ten thousandths 9 = hundred thousandths

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Decimals: Rounding - (is usually to the nearest whole number unless indicated otherwise) 1.25 = 1 3.09 = 3 1.9 = 2 Degree A unit of measure of an angle.

Denominator The bottom part of a fraction.

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Diameter The line segment joining two points on a circle and passing through the center of the circle.

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Difference The result of subtracting two numbers.

Digit The ten symbols, 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. The number 215 has three digits: 2, 1, and 5. Distributive Property of Multiplication Example: 34 x 56 1) way 1:( 30 + 4 ) x ( 50 + 6 ) (30 x 50) + (30 x 6) + (4 x 50) + (4 x 6)

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2) way 2: (30 + 4) x 56 (30 x 56) + (4 x 56) 3) way 3: 34 x (50 + 6) (34 x 50) + (34 x 6) 4) way 4: (40-6 ) x 56 (40 x 56) - (6 x 56) Dividend In a ÷ b = c, a is the dividend. In the

problem the 56 is the dividend. Division DMSB or dad, mother, sister, brother, is an acronym we use to help us divide. It stands for divide, multiply, subtract and bring down. Does McDonalds Serve Cheese Burgers Daily in another acronym. Does = Divide, McDonalds = Multiply, Serve = Subtract, Cheese = Check (check to make sure subtraction answer is lower than number dividing by), Burgers Daily = Bring Down. Divisor In a ÷ b = c, b is the divisor. In the

problem the 8 is the divisor. B E Equation A mathematical statement that says that two expressions have the same value; any number sentence with an =. Examples: 3 + 4 = 7, 5 x 8 = 40, a - b = c Evaluate To substitute number values into an expression. If a = 4, b = 2, substitute the numbers for the letters in the expression. a + b = c, 4 + 2 = 6 so c = 6

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Even Number A natural number that is divisible by 2. Exponent (see also power) A number that indicates the operation of repeated multiplication.

B F Face A flat surface of a three-dimensional figure.

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Factor One of two or more expressions that are multiplied together to get a product.

Factoring To break a number into its factors.

Formula A equation that states a rule or a fact.

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Fraction A number used to name a part of a group or a whole. The number below the bar is the denominator, and the number above the bar is the numerator.

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Fractions: Addition & Subtraction of Fractions with Like Denominators - Add the numerators and keep the denominators the same. 4/5 + 1/5 = 5/5 = 1 1 2/5 + 2/5 = 1 4/5 3 2/4 - 1/4 = 31/4 Fractions: Adding & Subtraction of Fractions with Unlike Denominators - Must first find common denominator before adding or subtracting - The following is an example - the numbers would change depending on the problem.

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Fractions: Close to 0, 1/2, 1 or more than 1 - close to zero if numerator and denominator are far apart 2/20 - close to one if numerator and denominator are close to together 19/20 - exactly one if numerator and denominator are the same 7/7 - over one if the numerator is biggier than the denominator 5/4 Fractions: Comparing & Ordering unit fractions have same numerator 1/20 1/5 1/25 1/8 In this case the bigger the denominator the smaller the piece 1/25 1/20 1/8 1/5 = least to greatest same denominator fractions 3/6 2/6 1/6 5/6 In this case the bigger the numerator the bigger the piece 1/6 2/6 3/6 5/6 when comparing fractions use cross multiplication 4 8 12 < 9 multiply 4 x 9 = 36 and 12 x 8 = 96 so 8/9 is bigger Fractions: Equivalent Fractions that reduce to the same number. 10/15 = 2/3 Fractions: Numerator = number above the fraction bar

(division bar) (the 3 in this fraction) Fractions: Fraction of a Whole whole number times numerator divided by denominator 4/5 of 20 = 4 x 20 = 80 80 divided by 5 = 16

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1.2 = 1 2/10 = one and two tenths 13.09 = 13 9/100 = 13 and 9 hundredths 0.54 = 53/100 = fifty three hundredths Fractions: Whole Set and in Word Problems

- (a b a) what fraction is vowels? = 2/3 - If I have 6 cookies and 9 people, how much will each person get of the cookies? = 6/9 Frequency The number of times a particular item appears in a data set. B G Graph A type of drawing used to represent data.

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Verticle Bar Horizontal Bar Line Circle or Pie Pictograph Graph Graph Graph Graph Greatest Common Factor (GCF) The largest number that divides two or more numbers evenly. Example: The GCF of 12 and 15 is 3 because it is the largest number that both can be divided by B H Horizontal A line with zero slope.

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B I Improper Fraction A fraction with a numerator that is greater than the denominator.

Inequality A mathematical expression which shows that two quantities are not equal. Integers The set of numbers containing zero, the natural numbers, and all the negatives of the natural numbers. Intersecting Lines Lines that have one and only one point in common.

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Inverse Opposite. -5 is the additive inverse of 5, because their sum is zero. 1/3 is the multiplicative inverse of 3, because their product is 1. Inverse operations Two operations that have the opposite effect, such as addition and subtraction. B J B K B L Least Common Denominator (LCD) The smallest multiple of the denominators of two or more fractions.

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Least Common Multiple (LCM) The smallest nonzero number that is a multiple of two or more numbers

Like Fractions (common denominator) Fractions that have the same denominator.

Line A straight set of points that extends into infinity in both directions.

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Line of Symmetry Line that divides a geometric figure into two congruent

portions. Lines

parallel lines

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perpendicular lines

intersecting lines

line segment has two points

line has two arrows

ray has one arrow Logic The study of sound reasoning. Lowest Terms Simplest form; when the GCF of the numerator and the denominator of a fraction is 1. B M Mean (see Average) Median Example: Data Set: 1,4,7,2,8,2,7,9,7

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1) place in order from least to greatest 1,2,2,4,7,7,7,8,9 2) Median = the number in the middle (when there is an equal number of numbers in the data set the two middle numbers are averaged to find the median (see average) Minuend The number to be subtracted from.

Mixed Number A number written as a whole number and a fraction.

Mode Example: Data Set: 1,4,7,2,8,2,7,9,7 1) place in order from least to greatest 1,2,2,4,7,7,7,8,9 2) Mode= the number that is written down the most often (there can be more than one mode in a data set) Multiple A multiple of a number is the product of that number and any other whole number. Zero is a multiple of every number. B N Natural Numbers The counting numbers.

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Negative Number A real number that is less than zero. Number Line A line on which every point represents a real number.

Numerator The top part of a fraction.

B O Obtuse Angle An angle that is greater than 90 degrees

Obtuse Triangle A triangle with an obtuse angle.

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Octagon A polygon with 8 sides.

Odd Number A whole number that is not divisible by 2. Operation Addition, subtraction, multiplication, and division are the basic arithmetic operations. Opposites Two numbers that lie the same distance from 0 on the number line but in opposite directions. Example: 8 and -8 also -3/4 and 3/4 Order of Operations PEMDAS is an acronym that shows what to do first in an equation: p stands for parenthesis, m for multiplication, d for division, a for addition, and s for subtraction. You solve a problem using this order. The multiplication and division are reversable - do whichever comes first, also the addition and subtraction are also reversable - do whichever comes first.

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example: 32 ÷ (4 + 4) x 2 You would do addition first to get 8 because it is in the parenthesis, then the division to get 4, and then finally the multiplication to get 8. Ordered Pair Set of two numbers in which the order has an agreed-upon meaning, such as the Cartesian coordinates (x, y), where the first coordinate represents the horizontal position, and the second coordinate represents the vertical position. Outcome In probability, a possible result of an experiment. B P Parallel Two lines are parallel if they are in the same plane and never intersect.

Parallelogram A quadrilateral with opposite sides parallel.

Pentagon A five-sided polygon.

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Percent A fraction, or ratio, in which the denominator is assumed to be 100. The symbol % is used for percent. Example: 34% = 34 parts of 100 Perimeter The perimeter is the outside of a figure and you add up all the sides.

If the length is 5 and the width is 2. P = 14 Perpendicular Two lines are perpendicular if the angle between them is 90 degrees.

Pi

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The ratio of the circumference of a circle to its diameter.

Place Value expanded form = 300,000 + 20,000 + 3,000 + 400 + 60 + 9 written form = three hundred twenty three thousand four hundred sixty nine 3,456,789 value of 3 = 3,000,000 place value of 3 = million Plane A flat surface that stretches into infinity. Point A location in a plane or in space, having no dimensions. Polygons - are many sided figures

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*triangle is a three sided figure *quadrilaterial is a four sided figure *pentagon is a five sided figure*hexagon is a six sided figure*heptagon is a seven sided figure *octagon is a eight sided figure *nonagon is a nine sided figure *decagon is a ten sided figure Polyhedron A three-dimensional solid that is bounded by plane polygons.

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Positive Number A real number greater than zero. Power (also see exponent) A number that indicates the operation of repeated multiplication.

Prime Number A number whose only factors are itself and 1. Such as 3 - 1x3, 5 - 1x5, 7 - 1x7, 11 - 1x11, and 13 1x13, ect. Probability

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For an experiment, the total number of successful events divided by the total number of possible events. a,4,a,b,3,4,6,7 Probability of pulling out an "a" from above list is 2/8 and unlikely Probability of pulling out a "number" from the above list is 5/8 and likely The words we use are impossible, unlikely, maybe, likely, and certain. Product The result of two numbers being multiplied together.

Proper Fraction A fraction whose numerator is less than its denominator.

Pyramid A three-dimensional figure that has a polygon for its

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base and whose faces are triangles having a common vertex. Or meeting point.

B Q Quadrant One of the quarters of the plane of the Cartesian coordinate system (coordinate grid)

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Quadrilaterals - are four sided figures

trapezoid has one set of parallel lines

parallelogram has two sets of parallel sides rectangle has two sets of parallel and equal sides with right angles

rhombus has all sides equal

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Quotient The answer to a division problem.

B R Radius The distance from the center to a point on a circle; the line segment from the center to a point on a circle.

Range Example: Data Set: 1,4,7,2,8,2,7,9,7 1) place in order from least to greatest 1,2,2,4,7,7,7,8,9 2) Range = highest number minus lowest number 9-1 = 8

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Rate A ratio that compares different kinds of units. Example: 10 km per 2 hours or 5 km per hour - comparing km to hours Ratios girls 13 boys 15 (written 3 ways for each) ratio of girls to boys is 13 to 15 or 13/15 or 13:15 ratio of girls to total is 13 to 28 or 13/28 or 13:28 Ray part of a line, with one endpoint, and extending to infinity in one direction.

Reciprocal The number which, when multiplied times a particular fraction, gives a result of 1. Example: 3/4 x 4/3 = 12/12 which equals 1 Rectangle A quadrilateral with four 90-degree angles.

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regular rectangle square which is a special rectangle Reflection A transformation resulting from a flip.

Right angle An angle that is exactly 90 degrees

Rhombus A parallelogram with four equal sides.

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Right Angle An angle whose measure is 90 degrees.

Right Triangle A triangle that contains a right angle.

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Rotation A transformation in which a figure is rotated through a given angle, about a point.

B S Scale Drawing A drawing that is a reduction or an enlargement of the original. Scalene Triangle A triangle with three unequal sides.

Scientific Notation A method for writing extremely large or small numbers compactly in which the number is shown as the product of two factors.

Shapes: Analyzing

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Students will need to be able to analyzse a figure to see if it has certain

characteristics. For example: a trapezoid has parallel lines and in this case obtuse and acute angles. Students will need to be able to analyse a figure to see what other shapes can be found in the figure. For example: a trapezoid could be made up of three triangles or a rectangle with two triangle. Shapes: Congruency & Similarity Congruent is the same size and shape Similar is the same shape Shapes: Nets There may be more than one net for each figure.

cube

cone

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cyclinder C Shapes: Plotting Students will ned to be able to plot a geometry figure or line on a coordinate grid. The trapezoid is at points (2,1) and (4,1) and (5, 4) and (1, 4).

Similar Two polygons are similar if their corresponding sides are proportional.

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Simplifying Reducing to lowest terms.

Solution The value of a variable that makes an equation true. Example: 4a - 3 = 21 solving for the variable a gets the solution a = 6

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Square Root The square root of x is the number that, when multiplied by itself, gives the number, x.

Statistics The science of collecting, organizing, and analyzing data. Stem and Leaf Plot A technique for organizing data for comparison.

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Straight Angle An angle that measures 180 degrees.

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Subtrahend The number to number to be subtracted.

Supplementary Angles Two angles are supplementary if their sum is 180 degrees.

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Surface Area For a three-dimensional figure, the sum of the areas of all the faces.

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B T Transformation A change in the position, shape, or size of a geometric figure.

Translation A transformation, or change in position, resulting from a slide with no turn.

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Trapezoid A quadrilateral that has exactly two sides parallel.

Tree Diagrams I have three flavors of ice cream: vanilla, chocolate, and praline. I have two types of cones: sugar and plain. I have two toppings: nuts and fruit. How many combinations can I make? 3 x 2 x 2 = 12 combinations 1) vanilla: sugar: nuts 2) vanilla: sugar: fruit 3) vanilla: plain: nuts 4) vanilla: plain: fruit 5) chocolate: sugar: nuts

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6) chocolate: sugar: fruit 7) chocolate: plain: nuts 8) chocolate: plain: fruit 9) praline: sugar: nuts 10) praline: sugar: fruit 11) praline: plain: nuts 12) praline: plain: fruit

Triangles three sided figures 1) Triangles based on their angles: -acute triangle has all acute

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angles -obtuse triangle has one obtuse

angle -right triangle has one right

angle 2) Triangles based on their sides: -isosceles triangle has two sides the same

length -equalateral triangle has all sides the same

length -scalene triangle has no sides the same

length B U

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Unit Price Price per unit of measure. B V Variable A letter used to represent a number value in an expression or an equation. Examples: r - 3 = 12, 4b = 16, 8 + s = 24, 40 ÷ y = 5, 3r + 4 = 22 Vertex The point on an angle where the two sides intersect.

Vertex Edge Graphing

vertex = a point on a graph ( blue ) edge = a line segment or curve connecting two vertices ( black lines )

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path = a connected sequence of edges that starts at a vertex and ends at a vertex circuit = a path that begins and ends at the same vertex

graph coloring = assigning colors to the vertices of a graph so that adjacent vertices are assigned different colorsdegree of vertex = the number of edges that come off of a vertex.

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Example: If 1 is green then 5 and 2 can not be green, but 4 should be green. If 5 is yellow than 6 and three should be yellow. 2 must be a new color. In other words you want to try to color with the fewest colors without having the same color next to each other.This is called chromatic coloring.

cycle graph = a graph where the vertices can be arranged in a circle so that each vertex is adjacent to the vertices that come before and after it disconnected graph = a graph that contains two or more vertices that are not connected The following are some applied problems using the concept of wieghted vertex edge graphs. a)

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b)

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C for more information on Vertex Edge Graphing Vertical Angles A pair of opposite angles that is formed by intersecting lines.

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Volume A measurement of space, or capacity.

B W Whole Numbers The set of numbers that includes zero and all of the natural numbers. Word Problems: Key words that signal x, ÷ , + and - product x increase or decrease by - quotient / how many more - area x difference - total x or + er word like taller or smaller -

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times x sum + split evenly / perimeter + share evenly / B X X-Axis The horizontal axis in a Cartesian coordinate plane.

X-Axis B Y Y-Axis The vertical axis in a Cartesian coordinate system. Y-Axis

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B Z Zero Property of Multiplication The product of zero and any number is zero. Example: 3,458 x 0 = 0 B

Algebra Symbols List of mathematical algebra symbols and signs.

Algebra math symbols table

Symbol Symbol Name Meaning / definition Example

x x variable unknown value to find when 2x = 4, then x = 2

≡ equivalence identical to

≜ equal by definition equal by definition

:= equal by definition equal by definition

~ approximately equal weak approximation 11 ~ 10

≈ approximately equal approximation sin(0.01) ≈ 0.01

∝ proportional to proportional to f(x) ∝ g(x)

∞ lemniscate infinity symbol

≪ much less than much less than 1 ≪ 1000000

≫ much greater than much greater than 1000000 ≫ 1

( ) parentheses calculate expression inside first 2 * (3+5) = 16

[ ] brackets calculate expression inside first [(1+2)*(1+5)] = 18

{ } braces set

⌊x⌋ floor brackets rounds number to lower integer ⌊4.3⌋=€4

⌈x⌉ ceiling brackets rounds number to upper integer ⌈4.3⌉=€5

x! exclamation mark factorial 4! = 1*2*3*4 = 24

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| x | single vertical bar absolute value | -5 | = 5

f (x) function of x maps values of x to f(x) f (x) = 3x+5

(f ∘g) function composition (f ∘g) (x) = f (g(x)) f (x)=3x, g(x)=x-1 ⇒(f ∘g)(x)=3(x-1)

(a,b) open interval (a,b) ≜ {x | a < x < b} x ∈ (2,6)

[a,b] closed interval [a,b] ≜ {x | a ≤ x ≤ b} x ∈ [2,6]

∆ delta change / difference ∆t = t1 - t0

∆ discriminant Δ = b2 - 4ac

∑ sigma summation - sum of all values in range of series ∑ xi= x1+x2+...+xn

∑∑ sigma double summation

∏ capital pi product - product of all values in range of series ∏ xi=x1·x2·...·xn

e e constant / Euler's number e = 2.718281828... e = lim (1+1/x)x , x→∞

γ Euler-Mascheroni constant γ = 0.527721566...

φ golden ratio golden ratio constant

π pi constant π = 3.141592654... is the ratio between the circumference and diameter of a circle

c = π·d = 2·π·r

Linear Algebra Symbols

Symbol Symbol Name Meaning / definition Example

· dot scalar product a · b × cross vector product a × b

A⊗B tensor product tensor product of A and B A ⊗ B

inner product

[ ] brackets matrix of numbers

( ) parentheses matrix of numbers

| A | determinant determinant of matrix A det(A) determinant determinant of matrix A || x || double vertical bars norm

A T transpose matrix transpose (AT)ij = (A)ji

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A † Hermitian matrix matrix conjugate transpose (A†)ij = (A)ji

A * Hermitian matrix matrix conjugate transpose (A*)ij = (A)ji A -1 inverse matrix A A-1 = I

rank(A) matrix rank rank of matrix A rank(A) = 3

dim(U) dimension dimension of matrix A rank(U) = 3 Nets A net in geometry is a flat shape that can be folded to make a three-‐dimensional shape. Nets can be used to construct prisms or pyramids using paper or cardboard. You can create your own net by unfolding a cereal box and then folding it up to make the box again. Triangular Prism Cube

Square Prism Rectangular Prism

Pentagonal Prism Hexagonal Prism

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Some nets of common pyramids

A net is the plan of a solid as displayed in only two dimensions. Nets can be used to construct pyramids using folder paper or cardboard. Triangular Pyramid Square Pyramid

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Rectangular Pyramid

Pentagonal Pyramid

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our math glossary

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