(291) EC-6 Math Content :)

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'.

Common Denominator

A common multiple of two or more denominators for 1/6 and 5/8, it is 24.

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).

Iteration

A computational process in which a cycle of actions or operations is repeated, generally to get closer to a final answer.

Factor tree

A diagram showing how a composite number breaks down into its prime factors.

Face

A flat surface of a solid figure

Polyhedron

A geometric figure solid with flat faces and straight edges.

line graph

A graph in which a line shows changes in data, often over time

Scatterplot

A graph showing paired data values. A scatter plot can suggest various kinds of correlations between variables with a certain confidence interval

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.

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.

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

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.

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.

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.

Power (of a number)

A number found by multiplying the number by itself one or more times.

Average

A number obtained by dividing the sum of tow or more addends by the number of addends (2+4+6 = 12/3 = 4

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.

Prime Number

A number that can be divided evenly only by 1 or itself. And it must be a whole number greater than 1.

Divisor

A number that divides another number. In the example 36/4 = 9, the 4 is the divisor.

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.

Addend

A number that is added. in 5 + 8 = 13, the addends are 5 and 8

Dividend

A number that is divided by another number. For example, in 36/4 = 9, 36 is the dividend.

Multiplicand/multiplier

A number that is multiplied by another number. In 7 x 4 =28 the multiplicand is 7 and the multiplier is 4.

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

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

Irrational Number

A number whose decimal form is nonterminating and nonrepeating. Irrational numbers can't be expressed as fractions.

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.

Rhombus

A parallelogram with four congruent sides.

Mathematical Proofs

A proof is a rhetorical device for convincing someone else that a mathematical statement is true or valid.

Parallelogram

A quadrilateral (any four-sided polygon) with opposite sides parallel and congruent.

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)

Circle Graph

A round graph that uses different-sized wedges to show how portions of a set of data compare with the whole set.

Polygon

A simple closed figure with any number of sides (square, triangle, hexagon etc.).

Protractor

A square, circular or semicircular tool, typically in transparent perspex, for measuring angles. The units of measurement utilized are usually degrees

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

Acute triangle

A triangle that contains acute angles (<0 and > 90 degrees

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°.

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

Composite number

A whole number greater than 1 that is not a prime number (e.g 4, 6, 9, 10, 12 etc).

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.

Obtuse angle

An angle that measures greater than 90 degrees and less than 180 degrees.

Acute Angle

An angle that measures greater that 0 degrees and less than 90 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.

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.

Expanded form

Expressing a number as factors [325 = (3x100) + (2x10) + (5x1)]

Rounding

Expressing a number to the nearest thousandth, hundredth, tenth, one, ten, hundred, thousand, and so on as directed.

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

Prime Factorization

Finding which prime numbers multiply together to make the original number.

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.)

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.

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.

Diagonal

In a polygon, a segment that connects one vertex to another vertex but is not a side of the polygon.

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.

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.

Parallel lines

Lines in the same plane that do not intersect.

Perpendicular lines

Lines that intersect at right angles.

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.

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

Line segment

Part of a line with two endpoints.

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.

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

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.

Zero - Product Property

States that if the product of two factors is zero, then at least one of the factors must be zero

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.

Supplementary Angles

Supplementary angles are two angles that add up to give a straight angle, 180°.

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

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).

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.)

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

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)

Range

The difference between the highest and lowest values in a data set.

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.

Diameter

The distance across a circle through its center point. It is twice the radius of the circle.

Circumference

The distance around a circle (C). C=pi times the diameter or d X pi. Or, 2radius X pi. (Pi - 3.14).

Girth

The distance around something; the circumference.

Radius

The distance from the center of a circle to the edge of the circle. It is also half the diameter of a circle.

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.

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.

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.

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.

Endpoint

The point at the end of a line segment

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)

Perimeter

The sum of the lengths of the sides of a polygon (p = 2l x 2w where l =length and w = width).

Integers

The whole numbers and their negatives (e.g. -2, -1, 0, 1, 2).

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.

Bisect

To divide into two congruent parts

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.

Congruent angles

Two angles that have the same degree of measurement.

Complementary angle

Two angles whose sum is equal to 90 degrees.

Adjacent angles

Two angles with a common vertex, a common ray, and not common interior points

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).

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.

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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.

Denominator

he bottom number of a fraction, telling in how many parts the whole is divided. in 1/3 the 3 is the denominator.

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.

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.