Number Sense Number Families MATH DICTIONARY Counting (Natural) Numbers The numbers we say when we count Example: {1, 2, 3, 4 } Whole Numbers The counting numbers plus zero Example: {0, 1, 2, 3, 4 } Positive Numbers All numbers greater than zero. Example: {1, 2, 3, 4, } All numbers to the right of zero Negative Numbers All numbers less than zero. Example: { -4, -3, -2, -1} All numbers to the left of zero Integers The whole numbers and their opposites. Example: { -2, -1, 0, 1, 2 } Rational Numbers All numbers that can be written as a fraction (or ratio) of two integers. Prime Numbers Numbers that have exactly two factors, one and itself Example: {2, 3, 5, 7, 11, 13, 17 } Composite Numbers Numbers that has three or more factors Example: {4, 6, 8, 9, 10 } Factor A whole number that divides another whole number with no remainder Operations Addend a number added to one or more other numbers to find a sum Sum the answer to an addition problem. Difference the answer to a subtraction problem Product the answer to a multiplication problem 1
Factor one of two or more numbers that are to be multiplied Quotient the answer to a division problem Dividend the number to be divided Example: 10, the dividend is 10 2 Divisor the number by which another number is divided. Divisible a number is divisible by a second number if it can be divided by that number with no remainder. Order of Operations a rule telling in what order a series of operations should be done. Example: The order of operations is: 1. do all operations within parenthesis or other grouping symbols such as brackets or braces 2. evaluate any term with exponents or roots 3. multiply and/or divide in order from left to right 4. add and/or subtract in order from left to right General Terms Simplify Solve to make less complex Solve to find the answer or a solution Repeating Decimal a decimal number that repeats a digit or a pattern of digits forever. Repetend the repeating digit or pattern of digits of a repeating decimal often indicated by a bar over them. Reciprocal two numbers are reciprocals if their product is 1. Example: The numbers 5 and 5 1 are reciprocals because 1 5 = 1. Dividing by a number is the same as multiplying 5 by the reciprocal of that number. 2 4 is the same as because 2 and 2 1 are reciprocals. The reciprocal of a 1 4, 2 fraction is obtained by interchanging the numerator and the denominator. To find the reciprocal of a mixed number, change it into an improper fraction and then invert it. 2
Algorithm a particular process for solving a certain type of problem. Example: the long division algorithm or multiple digit multiplication algorithms etc. Formula a rule showing relationships among quantities. Formulas usually contain variables. Example: A= L x W Variable a symbol usually a letter that represents a number. A variable s value may vary. Fraction a part of a whole or the indicated division of two numbers, by a division bar, such as 5 4 is the same as 4 5 Proper fraction a fraction whose numerator is less than the denominator Improper fraction a fraction whose denominator is less than the numerator Exponents A number telling how many times the base is being multiplied by itself. Example: 8 3 8 8 8, where 3 is the exponent and 8 is the base. 83 is read 8 to the third power or 8 cubed. 82 is read 8 to he second power or 8 squared. 85 is read 8 to the fifth power. Base (1) the bottom number when a number is written with an exponent (2) a designated side of a polygon (3) a designated face of a solid Sequence a list of numbers that follow a pattern Terms in sequence each number in a sequence is a term Positions in sequence refers to the position each term holds in a sequence (First, second, third, fourth ). This has nothing to do with the value of the term. Ex. In this sequence 2, 4, 6, 8, 10, the term 6 holds the third position in the sequence Measures of Central Tendency Data a group of numbers used for calculations Mean the sum of a group of numbers divided by the number of numbers in the group; also called the average. 3
Median The middle number when a set of numbers is arranged in order from least to greatest or greatest to least Mode the number in a set of numbers that appears most often Range the difference between the largest (greatest) and the smallest (least) numbers in a set of numbers Stem & leaf - displays a group of numbers in order. A leaf is a number s last digit on the right. A stem represents the digits to the left of the leaf. Box and whisker a graph showing how a data set is distributed compared to a number line Probability used to describe how likely an event will happen. It can be calculated using the number of ways an event can occur divided by the total number of possible outcomes. Compound Probability the probability of independent events occurring in a specified order is the product of the probabilities of each event Geometry Angle - a figure formed by 2 rays that have a common endpoint called a vertex Example: 1 is made up of GP and GS with common endpoint G Vertex (of an angle) the common endpoint of the rays forming the angle Example: See figure for angle Vertices the plural of vertex Acute angle an angle that measures less than 90º 4
Obtuse angle an angle that measures more than 90º and less than 180º Straight angle an angle that measures 180º Right angle an angle that measures 90º Complementary angles two angles are complementary if the sum of their measures equal 90º Supplementary angles two angles are supplementary if the sum of their measures is 180º Measurement Area the number of square units inside a closed figure need to cover the surface of the figure Square units - To measure area we use units that take up area. We include the word square or the exponent 2 when we designate units of area. Perimeter the distance around the outside of a shape Volume the number of cubic units that fills the interior of a shape 5
Cubic units to measure volume, we use units that take up space. The units that we use to measure volume are cubes of certain sizes. Cube a solid with six square faces Face a flat surface on a three dimensional figure. Pi (π) the number of diameters equal to the circumference of a circle Diameter the distance across the circle through its center Radius the distance from the center of the circle to a point on the circle. The radius is half of the diameter. Example: Circumference the distance around a circle Chord a line segment that has both endpoints on the circumference of a circle Example: CB is a chord of circle O. Arc a part of a circle; the length of an arc is known as its arc length Semi-circle is exactly half of a circle 6
Similar Figures they have the exact same shape which means their corresponding angles are congruent, but not necessarily the same size. Their corresponding sides must be proportional Congruent figures figures that have the same size and shape Corresponding angles the matching angles (same position) of similar or congruent figures Corresponding sides the matching sides (same position) of similar or congruent figures Proportional corresponding in size. The corresponding sides must have equivalent ratios Solids Cone A solid figure with a circular base connected to a vertex Sphere a round solid figure in which all points on the surface are at an equal distance from the center Prism a solid figure with two parallel bases which are congruent polygons Rectangular Prism a solid figure with parallel bases that are rectangles Triangular Prism a solid figure with parallel bases that are triangles 7
Pyramid three dimensional figures with only one base. The base is a polygon and the other faces are triangles. A pyramid is named for the shape of its base Net a pattern that can be folded to cover a solid figure Ex. Nets for a cube Cylinder a three dimensional figure with two circular, parallel, and congruent bases Cube a rectangular prism whose faces are squares Polygons A closed multi-sided two-dimensional figure that is made up of three or more line segments Regular Polygon any polygon whose sides are all the same length Triangle three sided polygon with a base and a height where the height is perpendicular to the base. base height Base a designated side of a triangle Height (altitude) perpendicular distance from the base to the opposite vertex (does not have to be a side of the triangle) Isosceles triangle triangle that has two sides of equal length Scalene triangle a triangle that has no sides of equal length Equilateral triangle a triangle that has three sides of equal length 8
Acute triangle a triangle where all of its angles measureless than 90º Obtuse triangle a triangle that has one angle that is greater then 90º Right triangle a triangle with one right (90º) angle Example: ABC is a right triangle because B is a right angle. Quadrilateral a four sided polygon Parallelogram a four sided polygon with two pairs of equal and parallel sides Example: KV is parallel to AD and AK is parallel to DV so KVDA is a parallelogram height base Trapezoid a four sided polygon with one pair of parallel side height bases Rhombus a parallelogram with four equal sides Trapezium a four sided polygon with no parallel sides Pentagon a five sided polygon Hexagon a six sided polygon Octagon an eight sided polygon 9
Plane a flat two-dimensional surface General Terms Intersecting a point at which two or more lines cross Ray a part of a line. It has one endpoint and it extends indefinitely in one direction Line a straight collection of points that extends without end in both directions Line segment part of a line with two endpoints Parallel lines that never meet and are in the plane Perpendicular two intersecting lines forming right angles Coordinate Geometry Coordinate Plane formed by a horizontal number line called the x-axis and the vertical number line called the y- axis X-axis horizontal line on coordinate plane Y-axis vertical line on coordinate plane Quadrant The x-axis and the y-axis divide the coordinate plane into four regions, called quadrants Ordered pairs/coordinates a pair of numbers that describe the location of a point on a coordinate plane The first value is the x-coordinate, and the second value is the 10
y-coordinate. The numbers are enclosed in parenthesis and separated by a comma. Example: (2,-1) is an ordered pair. The x-coordinate is -2; the y-coordinate is 1 Origin the point of intersection of the x and y-axes on a coordinate plane Example: The ordered pair that describes the origin is (0,0) Grid a network of horizontal and perpendicular lines Transformation movements of figures on a plane. A transformation can be a translation, reflection or rotation Translation a transformation that slides a figure without affecting its size or shape Reflection a transformation that flips a figure over a line without affecting Symmetry a figure is symmetrical when one side of the figure is the mirror image of the other side Example: The left and right sides of the mask are mirror images of each other Rotation turns a figure about a fixed point, called the center of rotation Dilation a transformation that results from the reduction or enlargement of an image. 11
Proportionality Ratio a comparison of two numbers written s a fraction but can be written with a colon or with the word to. Ex: A B A : B A to B Equivalent Ratio two fractions representing the same number such as 2 1 and 16 8 Proportion an equation made up of two equivalent ratios such as 1 4 3 12 Proportional being in proportion Rate is a ratio that compares two quantities measured in miles boys different units, such as or hour girls Unit Rate a rate that has a denominator of one Unit Cost or Unit Price a unit rate giving the cost of one item Scale (in drawings & maps) an enlarged or reduced drawing of an object that is proportional to the original object Scale Factor the ratio used to enlarge or reduce similar figures General Terms Justify to prove to be right or reasonable Appropriate suitable (ok) for the occasion Reasonable logical; does it make sense Solution an answer to a problem Solve find the answer Simplify solve to make less complex Consecutive following in regular order Unique being the only one of its kind 12