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TExES EC-6 Mathematics
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This flashcard set was created by Dr. Jerry Whitworth at Texas Woman's University to assist students in reviewing math content for the EC-6 Generalist TExES exam.
Terms in this set (110)
Reliability
refers to the consistency of a measure. A test is considered reliable if we get the same result repeatedly. For example, if a person is administered the same test repeatedly his/her results on the test should be approximately the same each time, if the test is reliable.
Irrational Number
A number whose decimal form is nonterminating and nonrepeating. Irrational numbers can't be expressed as fractions.
Geometry
A branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space. Considered to have its formal beginning in about 300 BC, when the Greek mathematician Euclid gathered what was known at the time, added original work of his own, and arranged 465 propositions into 13 books, called 'Elements'.
Mathematical Proofs
A proof is a rhetorical device for convincing someone else that a mathematical statement is true or valid.
Geoboards
a mathematical manipulative used to explore basic concepts in plane geometry such as perimeter, area and the characteristics of triangles and other polygons. It consists of a physical board with a certain number of nails half driven in, around which are wrapped rubber bands.
Protractor
A square, circular or semicircular tool, typically in transparent perspex, for measuring angles. The units of measurement utilized are usually degrees
Manipulatives
An object which is designed so that a learner can perceive some mathematical concept by manipulating it. The use of manipulatives provides a way for children to learn concepts in a developmentally appropriate, hands-on and an experiencing way. Mathematical manipulatives are used in the first step of teaching mathematical concepts, that of concrete representation.
Place Value
In our decimal number system, the value of a digit depends on its place, or position, in the number. Each place has a value of 10 times the place to its right.
Symmetry
To discover what symmetry is, take a piece of paper, fold it, and cut out a shape along the fold. Unfold the shape that you cut out. This figure is symmetric. That means it is exactly the same on both sides of the crease. The simplest symmetry is Reflection Symmetry (sometimes called Line Symmetry or Mirror Symmetry). It is easy to recognise, because one half is the reflection of the other half.
Least Common Multiple
he multiples of a number are what you get when you multiply it by other numbers. When you list the multiples of two (or more) numbers, and find the same value in both lists, then that is a common multiple of those numbers. The "Least Common Multiple" is simply the smallest of the common multiples.
Estimating
Finding a number that is close enough to the right answer. You are not trying to get the exact right answer. What you want is something that is close enough. Also, involves the concept of predicting, or making an educated guess
Deductive Reasoning
Deductive reasoning is one of the two basic forms of valid reasoning. It begins with a general hypothesis or known fact and creates a specific conclusion from that generalization. The basic idea of deductive reasoning is that if something is true of a class of things in general, this truth applies to all members of that class.
Inductive Reasoning
A method of drawing a probable conclusion from an emerging configuration of data. It occurs by analyzing observations and discovering common patterns. When patterns repeat for an extended period of time, an analyst can logically predict that those patterns will continue to repeat.
Quadrilaterals
Means "four sides. "Any four-sided shape is a Quadrilateral. But the sides have to be straight, and it has to be 2-dimensional.
Function
A relation that uniquely associates members of one set with members of another set. There will always be three main parts: The input, The relationship, The output. For instance, 4(input) X 2(function) = 8(output)
Congruent Triangles
If two triangles are congruent they will have exactly the same three sides and exactly the same three angles. The equal sides and angles may not be in the same position (if there is a turn or a flip), but they will be there.
Complementary Angles
Two Angles that add up to 90 degrees (a Right Angle). They don't have to be next to each other, just so long as the total is 90 degrees.
Interior Angles
An angle inside a shape. When you add up the Interior Angle and Exterior Angle you get a straight line, 180°. The sum of the measures of the interior angles of a triangle is 180 degrees. All the interior angles of a square are right angles -- that means that they are all 90 degrees.
Isoceles Triangle
Has at least two sides that are exactly the same length. This forces two of their angles to also be acute angles of exactly the same size.
Equilateral Triangle
A triangle with all three sides the same length. All equilateral triangles are also isoceles triangles. All three internal angles are also congruent to each other and are each 60°.
Equivalent Fractions
Fractions that may look different, but are equal to each other. Two equivalent fractions may have a different numerator and a different denominator. For instance, The fractions 2/3 and 4/6 are equivalent. (A fraction is also equivalent to itself. In this case, the numerator and denominator would be the same.)
Pi
A name given to the ratio of the circumference of a circle to the diameter. That means, for any circle, you can divide the circumference (the distance around the circle) by the diameter and always get exactly the same number. It doesn't matter how big or small the circle is, Pi remains the same. While Pi has a decimal that never ends, it is usually estimated as 3.14.
Radius
The distance from the center of a circle to the edge of the circle. It is also half the diameter of a circle.
Diameter
The distance across a circle through its center point. It is twice the radius of the circle.
Prime Number
A number that can be divided evenly only by 1 or itself. And it must be a whole number greater than 1.
Significant Number (or Figures)
The digits in a value that are known with some degree of confidence. As the number of these increases, the more certain the measurement. They are especially important in rounding.
Probability
The measure of how likely an event is. It is usually determined by dividing the number of ways something can happen by the total number of outcomes.
Perimeter
The distance around a two-dimensional shape, such as a triangle or rectangle.
Girth
The distance around something; the circumference.
Mass
A measure of how much matter is in an object. Commonly measured by how much something weighs. But weight can change depending on where you are (such as on the moon) while this stays the same.
Prime Factorization
Finding which prime numbers multiply together to make the original number.
Associative Property
The change in grouping of three or more addends or factors does not change their sum or product. holds good for both addition and multiplication, but not for subtraction and division.
Addition: (2 + 3) + 5 = 2 + (3 + 5)
Multiplication: (4 X 5) X 10 = 4 X (5 X 10)
Distributive Property
States that the product of a number and a sum is equal to the sum of the individual products of addends and the number.
That is: a(b + c) = ab + ac.
Commutative Property
States that changing the order of addends does not change the sum.
That is, a + b = b + a.
Commutative Property of Multiplication: It states that changing the order of factors does not change the product.
That is, a × b = b × a.
Additive Inverse
The opposite of the number. A number and its opposite add up to give zero. They are called inverse additives of each other.
Greatest Common Factor (GFC)
The greatest number that is a factor of each of two or more given numbers.
Examples:
The greatest common factor of 24 and 15 is 3.
The greatest common factor of 40, 50, and 25 is 5.
Supplementary Angles
Supplementary angles are two angles that add up to give a straight angle, 180°.
Expression
A mathematical phrase that combines numbers and/or variables using mathematical operations. An expression is a representation of a value; for example, variables and/or numerals that appear alone or in combination with operators are expressions.
Examples:
5 + 6 - (3 + 2)/18
a + b - c
Zero - Product Property
States that if the product of two factors is zero, then at least one of the factors must be zero
Ordered Pair
A pair of numbers used to locate a point on a coordinate plane is called an ordered pair.
An ordered pair is written in the form (x, y) where x is the x-coordinate and y is the y-coordinate.
Area
The amount of space inside the boundary of a flat (2-dimensional) object such as a triangle, rectangle or circle. Different objects have different formulas to determine area. For a rectangle it is length X width. Area of a triangle is 1/2 of the base times the height. The area would be expressed as a square (10 square feet, etc.)
Volume
The amount of 3-dimensional space an object occupies. For a rectangle the formula would be length times width time depth or height. Since there are three dimensions it is expressed as cubics (9 cubic inches).
Absolute Value
The absolute value of a real number is equal to the numeric value of the number without regard to its sign (e.g -3 is 3) Absolute value is often thought of as the distance a number is from zero on the number line
Acute Angle
An angle that measures greater that 0 degrees and less than 90 degrees
Acute triangle
A triangle that contains acute angles (<0 and > 90 degrees
Addend
A number that is added. in 5 + 8 = 13, the addends are 5 and 8
Adjacent angles
Two angles with a common vertex, a common ray, and not common interior points
Algorithm
A step by step procedure or formula for solving a problem
Array
A systematic arrangement of objects or numbers, generally in rows and columns
Average
A number obtained by dividing the sum of tow or more addends by the number of addends (2+4+6 = 12/3 = 4
Bisect
To divide into two congruent parts
Circle Graph
A round graph that uses different-sized wedges to show how portions of a set of data compare with the whole set.
Circumference
The distance around a circle (C). C=pi times the diameter or d X pi. Or, 2radius X pi. (Pi - 3.14).
Common Denominator
A common multiple of two or more denominators for 1/6 and 5/8, it is 24.
Common Factor
A number that is a factor of two or more numbers. A common factor of 9 and 6 is 3.
Common multiple
A number that is a multiple of two or more numbers. A common multiple of 2 and 3 is 6.
Complementary angle
Two angles whose sum is equal to 90 degrees.
Composite number
A whole number greater than 1 that is not a prime number (e.g 4, 6, 9, 10, 12 etc).
Congruent angles
Two angles that have the same degree of measurement.
Coordinate system
A graph with a horizontal number line (x-axis) and a vertical number line (y-axis) that are perpendicular to each other. The point of intersection is called the origin and labeled 0 on the graph. An ordered pair (x,y) is used to name a point on a coordinate system.
Denominator
he bottom number of a fraction, telling in how many parts the whole is divided. in 1/3 the 3 is the denominator.
Diagonal
In a polygon, a segment that connects one vertex to another vertex but is not a side of the polygon.
Dividend
A number that is divided by another number. For example, in 36/4 = 9, 36 is the dividend.
Divisor
A number that divides another number. In the example 36/4 = 9, the 4 is the divisor.
Endpoint
The point at the end of a line segment
Expanded form
Expressing a number as factors [325 = (3x100) + (2x10) + (5x1)]
Exponent
A number that tells how many times the base is to be used as a factor or to be multiplied by itself. in 2 to the 3rd power, 2 is the base and 3 is the exponent meaning 2x2x2
Face
A flat surface of a solid figure
Fact Families
The related number sentences for addition and subtraction or multiplication and division that contains all the same numbers (e.g. 2+3 =5; 3+2 =5; 5-3 =2; and 5-2 =3)
Factor
A number to be multiplied or a number that divides evenly into a given second number is a factor of that number. In 2x3 =6, 2 and 3 are factors of 6
Factor tree
A diagram showing how a composite number breaks down into its prime factors.
Histogram
A graph showing the results of tabulating the number of items found in defined categories and shown using vertical bars; often referred to as a bar chart.
Integers
The whole numbers and their negatives (e.g. -2, -1, 0, 1, 2).
Inverse operations
Operations that are the opposite of each other and cancel each other out. Addition and subtractions are inverse operations, as are multiplication and division
Iteration
A computational process in which a cycle of actions or operations is repeated, generally to get closer to a final answer.
line graph
A graph in which a line shows changes in data, often over time
Line of Symmetry
f you can reflect (or flip) a figure over a line and the figure appears unchanged, then the figure has reflection symmetry or line symmetry. The line that you reflect over is called the line of symmetry. A line of symmetry divides a figure into two mirror-image halves. The dashed lines below are lines of symmetry.
Line segment
Part of a line with two endpoints.
Mean
The average of a set of numbers; the sum of the numbers divided by how many number there are; 2 + 5 +5 =12, then 12/3 = an average/mean of 4
Median
The middle number of a set of numbers after they have been placed in numerical order. In the set [2,3,4], 3 is the median. If there are an even number of numbers, the median is the average of the two middle numbers.
Minuend
...
Mode
The number that occurs the most frequently in a set of data. In the set [2,4,4,3,5] 4 is the mode.
Multiplicand/multiplier
A number that is multiplied by another number. In 7 x 4 =28 the multiplicand is 7 and the multiplier is 4.
Obtuse angle
An angle that measures greater than 90 degrees and less than 180 degrees.
Order of operations
When there is more than one operation and parentheses are used, first do what is inside the parentheses, then the exponents. Next, multiply or divide from left to right. Then add of subtract from left to right (PEMDAS of Please Excuse My Dear Aunt Sally).
Ordered pair
A number pair, such as (2,3), in which the 2 (x-axis) is the first number and the 3 (y-axis) is the second number.
Parallel lines
Lines in the same plane that do not intersect.
Parallelogram
A quadrilateral (any four-sided polygon) with opposite sides parallel and congruent.
Perimeter
The sum of the lengths of the sides of a polygon (p = 2l x 2w where l =length and w = width).
Perpendicular lines
Lines that intersect at right angles.
Pictograph
A visual representation used to make comparisons. A key always appears at the bottom of a pictograph or picture graph showing how many each object represents
Polygon
A simple closed figure with any number of sides (square, triangle, hexagon etc.).
Polyhedron
A geometric figure solid with flat faces and straight edges.
Power (of a number)
A number found by multiplying the number by itself one or more times.
Probability
Probability (or likelihood) is a measure or estimation of how likely it is that something will happen or that a statement is true. Probabilities are given a value between 0 (0% chance or will not happen) and 1 (100% chance or will happen). The higher the degree of probability, the more likely the event is to happen, or, in a longer series of samples, the greater the number of times such event is expected to happen.
Pythagorean Theorem
In any right triangle, the are of the square whose side in the the hypotenuse (longest side and opposite from the right angle) is equal to the sum of the areas of the squares whose sides are the two legs (the sides that meet at the right angle). Where c is the length of the hypotenuse and a and b are the lengths of the two sides, this may be expressed as a squared + b squared = c squared.
Range
The difference between the highest and lowest values in a data set.
Ratio
A comparison of two or more values( 1/2, 4/6 or 1:2, 4:6) or ( 1 is to 2; 4 is to 6).
Reciprocals
Reciprocals are two numbers which multiply together and make 1. They are also called multiplicative inverses of each other. For example:
3 and 1/3 are reciprocals because 3 × 1/3 = 1
5/6 and 6/5 are reciprocals because 5/6 × 6/5 = 1
-0.2 and -5 are reciprocals because -0.2 × -5 = 1
Rhombus
A parallelogram with four congruent sides.
Rounding
Expressing a number to the nearest thousandth, hundredth, tenth, one, ten, hundred, thousand, and so on as directed.
Scalene Triangle
A triangle where all three sides are different in length.
Scatterplot
A graph showing paired data values. A scatter plot can suggest various kinds of correlations between variables with a certain confidence interval
Tessellation
ometimes referred to as tiling of the plane. A tessellation is a collection of plane figures that fills the plane with no overlaps or gaps. Tiles on a kitchen floor can be thought of as a simple form of tessellation.
Translation
The image of a figure that has been "slid" to a new position without flipping of turning.
Trapezoid
A quadrilateral with one pair of parallel sides. These sides are called the upper and lower bases.
Vertex
The common endpoints of two rays that form an angle, or the point of intersection of two sides of a polygon of polyhedron
Set
A well-defined collection of objects or numbers.
Rational number
Any number that can be expressed as a fraction a/b where a and b are integers and b does not equal 0, such as 3, 3/1, 1/4, .34 and 56 percent.
Frequency
The number of times a score appears in a list of data.
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