TExES Generalist EC-6 Math

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area of a parallelogram
a=lxh
achieved by multiplying the length of the figure by the width of the figure.
area of a circle
a=pie (3.14) x r squared
area is achieved by squaring the radius and multiplying it by 3.14.
Ex: if radius is 6, then 6 squared (6x6) = 36.
36 x 3.14 = 113
area=113
volume of a rectangular solid
v=lxwxh
volume is achieved by multiplyng the length of figure by the width of figure, then multiplying that by the height.
sum of measures of 3 angles of triangles
180 degrees
pythagorean theory
theory stating that in any right triangle with legs (shorter sides) a and b, and hypotenuse (longest side) c, the sum of the suares of the sides will be equal to the square of the hypotenuse:
(a squared + b squared = c squared)
side a = 3 (leg, short side)
side b = 4 (leg, short side)
side c = 5 (hypotenuse/longest side)
3 squared = 9 4 squared = 16
3 squared + 4 squared = 9 + 16
9 + 16 = 25
5 squared = 25
25 = 25
figure with 4 lines of symmetry
square
figure with 2 lines of symmetry
rectangle
figure with infinite number of lines of symmetry
circle
tesselation
pattern formed by the repetition of a single unit or shape that, when repeated, fills the plane with no gaps and no overlaps.
time conversions
1 year = 365 days
1 year = 12 months
1 year = 52 weeks
1 week = 7 days
1 day = 24 hours
1 hour = 60 minutes
1 minute = 60 seconds
celsius
temperature scale used in countries throughout the world.
Its especially used in scientific experimentation.
farenheit
temperature scale that is used in the united states.
temperature water boils
212 degrees farenheight or 100 degrees celsius.
temperature water freezes
32 degrees farenheit or 0 degrees celsius.
translation
also called a slide.
In geometry, this simply means moving.
The direction and distance of each move is known as a transformation that moves a geometric figure by sliding.
rotation
also called a turn.
In geometry this is known as a transformation that mean to turn the shape around.
Each turn has a center and an angle for movement around a given number of degrees.
reflection
also called a flip.
Known as a transformation that means to make the figure/object appear to be backwards or flipped.
It produces a mirror image of a geometric figure.
scientific notation
Form of writing a number based on powers of the base number 10.
Ex: 123,000,000,000
1.23 x 10 to the 11th power (meaning 10 x itself 11 times)
the first number 1.23 is called the "coefficient". It must be greater than or equal to 1 and less than 10.
The second number is called the "base" . It must always be 10 in scientific notation. The base number 10 is always written in exponent form. In the number 1.23 x 10 to the 11th power, the number 11 is referred to as the exponent or power of ten.
To write a number in scientific notation:
1. Put the decimal after the first digit and drop the zeroes.
In the number 123,000,000,000 the coefficient will be 1.23
*the decimal will go after the 1 and get rid of all the zeroes in the number. Keep all numbers besides zeroes as part of the coefficient.
2. To find the exponent count the number of places from the decimal to the end of the number. All the numbers after the decimal are included in this counting, regardless if they're zeroes or other numbers.
In 123,000,000,000 there are 11 places.
1.23,000,000,000
12 345 678 91011
therefore we write 123,000,000,000 as:
1.23 x 10 to the 11th power.
linear measurements: standard & metric
standard (customary) units of length includ inches, feet, yards, and miles.

Metric units of length include millimeters, centimeters, meters, and kilometers. The centimeter is the basic metric unit of length, at least for short distances. There are about 2.5 centimeters to 1 inch. The kilometer is a metric unit of length used for longer distances. It takes more than 1.5 kilometers to make a mile.
measurement of mass: standard & metric
standard (customary) units of weight include ounces, pounds, and tons.

Metric units of weight include grams and kilograms. The gram is the basic metric unit of mass. A large paper clip weighs about 1 gram. It takes about 28 grams to make 1 ounce.
volume measurements: standard & metric
standard (customary) units of capacity include teaspoons, tablespoons, cups, pints, quarts and gallons.

Metric units of capacity include milliliters and liters. The liter is the basic metric unit of volume. A liter is slightly larger than a quart, so it takes mmore than 4 liters to make a gallon.
linear measurement conversion chart
standard:
12 inches = i foot
3 feet = 1 yard
1,760 yards = 1 mile
5,280 feet = 1 mile

metric:
10 millimeters = 1 centimeter
100 centimeters = 1 meter
1000 meters = 1 kilometer
capacity & volume measurement conversion chart
standard:
1 gallon = 4 quarts
1 gallon = 128 fluid ounces
1 quart = 2 pints
1 pint = 2 cups
1 pint = 16 fluid ounces
1 cup = 8 fluid ounces

metric:
1 liter = 1000 milliliters
1 liter = 1.0556 quarts
mass & weight measurement conversion chart
standard:
1 ton = 2000 pounds
1 pound = 16 ounces

metric:
1 kilogram = 1000 grams
1 gram = 1000 milligrams
deductive reasoning
reasoning from the general to the specific.
inductive reasoning
reasoning that involves examining particular instances to come to some general assumptions.
It is informal and intuitive.
similar
figures having the exact same shapes, even if they do not have the same size.
proportional
corresponding angles of similar figures that have the same measure, and the lengths of corresponding sides.
congruent
figures that have the same size and same shape.
parallel lines
lines that do not intersect.
perpendicular lines
lines crossing at right angles.
range
the difference between the greatest and the lest numbers in the data set.
Subtract the two numbers to find the difference.
mean
the average of the data values in a set of numbers.
To find, add all of the data values and then divide this sum by the number of values in the set.
median
the middle value of all the numbers in a set.
To find the middle value, list the numbers in order from least to greatest. Cross out one value on each end of the list until you reach the middle.
If there are 2 values in the middle, find the number halfway between the 2 values by adding them together and dividing their sum by 2.
mode
the value (or values) that appear in a set of data more frequently than any other values.
If all of the values in a set of data appear the same number of times, the set does not have a mode.
probability
a way of describing how likely it is a particular outcome will occur.
Using a fraction: the numerator of the fraction is the number of favorable outcomes for the experiment.
The denominator of the fraction is the number of all the possible outcomes for the experiment.

Probability= number of favorable outcomes
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total number of possible outcomes
sample space
set of all possible outcomes of an experiment.
permutations
all possible arrangements of a given number of items in which the order of the items makes a difference.
Ex: the different ways a set of 4 books can be placed on a bookshelf.
line plot
represents a set of data by showing how often a piece of data appears in a set.