WGU - Math of Elementary Educators III - Set 1

Circle Graph

used to represent categorical data, used to show the division of a whole into parts

Histograms and bar graphs

distinguishing feature between histograms and bar graphs is that there is no ordering that has to be done among the bars of the bar graph, where as there is an order for a histogram. used to compare numbers of data items grouped in numerical intervals, order of the data matters for histograms and doesnt matter for bar graphs

ASA Postulate

If two angles and the included side of one triangle are equal to two angles and the included side of another triangle then the triangles are congruent

SAS Postulate

If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.

Positive association in scatterplots

if the trend line slopes up from left to right, there is a positive association between the data on the horizontal axis and the data on the vertical axis. An increase in the value of the variable on the horizontal axis would predict an increase in the value of the variable on the vertical axis

translation

is a motion of a plane that moves every point of the plane a specified distance in a specified direction along a straight line (x+a, y+b)

Statistics

once referred to numerical information about state or political territories; much of statistics involves making sense of data

Pictographs

represent tallies of categories; using a symbol or icon to represent a quantity of items.

Circumference

the distance around a circle; to carry the distance around a circle, C=2(pi)r R=radius (pi)=3.14; C=2PiR=piD

Computing means

the number commonly used to characterize a set of data is the arithmetic mean. x=a+b+c+d+e/5

Data Analysis

usually refers to a more informal approach to statistics. It is a relatively new term in math.

Statistics misleading on advertising

1. the questions being asked, 2. the number of people being surveyed, 3. the number of people who responded, 4. how the people who participated in the survey were chosen, 5. the number and type of pain relievers tested, 6. how the answers were interpreted.

Statistics misused with graphs

1. title, 2. labels on both axes of a line or bar chart and on all sections of a pie chart, 3. source of the data, 4. key to a pictograph, 5. uniform size of symbols in a pictograph, 6. scale: does it start with zero? if not, is there a break shown? 7. scale: are the numbers equally spaced?

Dihedral angle

Formed by the union of two half-planes and the common line defining the half-planes; is measured by any of the associated planar angles

Triangle

Containing one right angle is a right triangle

Categorical data

Data that consists of names, labels, or other nonnumerical values

skew lines

Lines that do not intersect and are not coplanar

Triangle Inequality Theorem

The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

Computing Medians

The value exactly in the middle of an ordered set of numbers is the median. To find the median for a set of n numbers, 1. Arrange the numbers in order from least to greatest. 2. a. If n is odd, the median is the middle number. b. If n is even, the median is the mean of the two middle numbers.

Numerical data

data collected on numerical variables

straight angle

measures exactly 180 degrees

right angle

measures exactly 90 degrees

obtuse angle

measures greater than 90 degrees and less than 180 degrees

Acute angle

measures less then 90 degrees

No association of scatterplots

If the points do not approximately fall about any line, we say there is no association. No prediction of one variable can be made based on the value of the other.

Negative association of Scatterplots

If the trend line slopes down from left to right, there is a negative association between the data on the horizontal axis and the data on the vertical axis. An increase in the value of the variable on the horizontal axis would predict a decrease in the value of the variable on the vertical axis.

SSS Postulate

If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.

AAS postulate

If two angles and a non-included side of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent.

Line graph

A graph that uses line segments to show changes that occur over time

Trend Line

A line that closely fits the data points in the scatter plot.

rhombus

A parallelogram with four congruent sides; with two adjacent sides congruent

parallelogram

A quadrilateral with two pairs of parallel sides are opposite

Isometry

A transformation in which the preimage and image are congruent

right triangle

A triangle that has a 90 degree angle.

obtuse triangle

A triangle with one angle that is greater than 90 degrees.

equilateral triangle

A triangle with three congruent sides

transformation

any function from a plane to itself that is a one to one correspondence

Find the mean, median and mode 60 60 70 95 95 100

Mean - 80 Median - 82.5 Mode - 60 and 95

Stem and Leaf Plots

Similar to the dot plot, but the number line is usually vertical and digits instead of x's. Advantages: created by hand, no not become unmanageable, no data values lost. Disadvantages: we lose information, we know a data value but we cannot tell which one it is. used to show the relationship between two variables

HL

The hypotenuse leg theorem states that any two right triangles that have a congruent hypotenuse and a corresponding, congruent leg are congruent triangles.

Statistics misuse including mean, median and mode

The important thing to watch for when a mean is reported is disparate cases in the reference group. If the sample is small, then a few extremely high or low scores can have a great influence on the mean.

Finding Modes

The mode of a set of data is the number that appears most frequently, if there is one, but the mode does not have to be in anyway a measure of cental tendency. A mode is frequently reported with categorical data.

Dot Plots

a graph where dots that represent the value of data are plotted above a number line, uses x's

Scatterplots

a graphed cluster of dots, each of which represents the values of two variables. The slope of the points suggests the direction of the relationship between the two variables. The amount of scatter suggests the strength of the correlation (little scatter indicates high correlation).

Theorems about points, lines and planes

a line and a point not on the line determine a plane, two parallel lines determine a plane, two intersecting lines determine a plane

line perpendicular to a plane

a line that intersects the plane in a point and is perpendicular to every line in the plane that intersects it

rectangle

a parallelogram with a right angle

Arc length

a portion of the circumference of a circle, measured in degrees (it's length is measured in linear units)

trapezoid

a quadrilateral with at least one pair of parallel sides

kite

a quadrilateral with two adjacent sides congruent and the other two sides also congruent

square

a rectangle with four congruent sides; two adjacent sides congruent

isosceles trapezoid

a trapezoid with congruent base angles

isosceles triangle

a triangle with at least two congruent sides

scalene triangle

a triangle with no congruent sides

acute triangle

a triangle with three acute angles