391 EC-6 Mathematics (902)

obtuse angle

An angle that measures more than 90 degrees but less than 180 degrees

front-end estimation

a rounding technique of replacing the numbers in mathematical problems with approximate numbers. To use it, round all your numbers to the place value on the far left of your number. That way, all of your numbers will be some non-zero digit followed by all zeros.

equiangular triangle

all sides are equal

Translation

also called a slide simply means moving

isoceles

having two equal sides and two equal angles

Axion

mathematical rule

K-2nd

understand the principles and patterns of the number system and the symbol used to represent numbers

grades 1 and 2

use quantitative reasoning and basic algorithms for addition and subtraction

to simplify the fraction

use the Greatest Common Factor (GCF)

Adding and subtracting fractions with the same denominator

when adding or subfraction with same denominator just add or sub the numerator across and keep the denominator

Interger

whole numbers positive or negative including 0 but they do not include decimals or fractions

adding and subtracting decimals

-Line up the decimal points and then add or subtract in the same manner you would add or subtract regular numbers -Adding in zeros can make the problem easier to work with -Whole numbers can have decimal points to their right

Araba contributions

-quadratic equation -perfected geometric algebra Used Greek geometry and improved the development of the field Founded the non-Euclidian geometry and made advances to trigonometry -greatest contribution-numeric system which resulted in the spread of the cumulative knowledge of mathematics to the world most historians agree that the Arabs used information from the Hindus to develop our modern numeric system, which includes the zero

Area of a triangle

A=1/2bh ex.

Area of a parallelogram

A=bh (base x height)

Area of a rectangle

A=lw

Area of a square

A=s² ex. a square has a side of 5ft which will be A=(5FT)^2=25FT^2

Area of a circle

A=πr²

multiplying exponential terms

Constant terms are multiplied, but the exponents of the terms with the same variable bases are added together ex. 4w^2 multiplied by 8w^3= 32w^5

Pythagorean Theorem

a²+b²=c² where the right triangle with legs (shorter sides) a and b, and hypotenuse (the longest leg) c, the sum of the squares of the legs will be equal to the square of the hypotenuse (a^2+b^2=c^)

Archimedes

calculated the distance of the planets from the Earth and constructed a spherical planetarium imitating the Sun, Moon

percentage of a known quantity

change the percentage to a common fraction or a decimal fraction and multiply the fraction times the quantity ex. to find 25% of 360 books, change 25% to 0.25 and multiply times 360 or 0.25*360=90books

grade 3

continues through elementary school to improve their basic knowledge of the number system and the abstraction of mathematic reasoning and begin with algebraic, geometric, and spatial reasoning

parallel lines

coplanar lines that do not intersect

improper fractions to mixed number

divide the numerator by the denominator

Percent to Decimal

divide the percent by 100 OR just move decimal to the left 2 places the ex. 25% 25/100=0.25

Fraction to Percent

divide the top number by the bottom number. then multiply the result by 100, and add the "%" sign.

decimal infinitely

endlessly is indicated by a bar over the repeating number

Distributive Property

everything in parentheses needs to be multiplied by the number on the outside a(b+c)=a*(b+c) ex.8(5+2)=8*7=56 or a(b+c)=(a*c)+(a*c) ex.(8*5)+(8*2)=56

linear function

ex. y=4x is linear because it can e written as y=mxtb

dividing algebraic terms

exponents are subtracted ex.2x^7/5x^3= 2x^4/5

Adding fraction with different denominators

find a common denominator for both,the lowest common denominator for ex. 1/2 and 2/3 the least is 6 because 2 times 3=6 and 3 times 2= 6 after finding the common denominator then cross multiply 1/2*6= 6/12=3/6 and 2/3*6=12/18=4/6 then add the fraction 3/6+4/6=7/6

simplification of Fractions

find the number that can be divided evenly into the numerator and the denominator ex. 2/4 the number 2 can be divided evenly into 2 and 4 the results 1/2

multiplying mixed fractions

first, make the fraction improper then proceed with multiplying the numerators together and denominators together

Grade 3

have difficult with word problems and problem-solving activities that require them to identify the appropriate mathematical process. Understanding questions involving multiple steps and decide in on appropriate answer

grades 3-12

heavily emphasized in preparation for the TEKES word problems and mathematical reasoning

greeks

historians believe that the formal study of mathematics began with Anthenian Greek school of Thales and Pythagoras Thales and Pythagoras founders of Greek mathematics Pythagoras- Pythagorean theorem Ptolemy- founded the University at Alexandria in Egypt which became central to learning for the Western world Greek also discovered rational numebrs and irrational numbers numbers

Multiplying Decimals

ignor decimal points and multiply the two numbers, then count the digits to the right of the decimal points in the original numbers and place the decimal so there are the same number of digits to the right of the decimal

proportional resoning

important in preparing students for algebra students in 5th grade begin to use a ratio chart to solve proportion problems

Upper elementary

involving deductive and deductive reasoning

mathematical reasoning

k-12th involves logical reasoning requires some level of cognitive maturity and the ability to think abstractly

early grades-3

logical thinking many opportunities to explore, manipulate and experience concrete objects

mixed numbers to improper fractions

multiply the denominator by the whole number then add the results to the numerator to obtain the new numerator and keep the denominator the same

Coefficient

number in front of a variable ex. 4a

Composite numbers are

numbers that have more than two factors and greater than zero ex. 9 is a composite number because it has three factors 1,3,9

Egyptians

numbers using hieroglyphs to represent the numbers 1,10,100,1000,

Prime numbers are

numbers who have 1 and itself as factors

additon and subtracting algebraic terms

only like terms can be added or subtracted to produce simpler expressions ex. 2x^3 and 3x^3 can be added together to get 5x^3 because they are like terms (same exponent)

Associative Property of Addition and Multiplication

order of the addends or factors will not change the sum or the product ex. (a*b)*c=a*(b*c)

percent to fraction

put the percent over 100 and simplify as neccessary

deductive reasoning

reasoning in which a conclusion is reached by stating a general principle and then applying that principle to a specific case (The sun rises every morning; therefore, the sun will rise on Tuesday morning.) ex. its raining so I need to take my umbrella to school. ex. The sum of the measures of the three angles of any triangle is 180, The sum of the measures of K AND L IS 120 therefore the measure of the j is 60

expanded notation

shows place value by multiplying each digit in a number by the appropriate power of 10 ex. 523=5*10^2+2 times 10+3 times 1

negative exponent

take the reciprocal and change the exponent to positive

range

the difference between the highest and lowest

Irrational Number

the irrational numbers are all the real numbers that are not rational numbers. That is, irrational numbers cannot be expressed as the ratio of two integers ex. √2 or pi

circumference

the perimeter of a circle formula

By first grade

the principle of conservation is generally acquired

real numbers

the set of all rational, irrational numbers, positive, negative, or zero also includes decimal and infinite decimal sequences such as the pie symbol

y=mx+b

the slope-intercept form of an equation of a line (m=slope) and (b=y-intercept) changing m makes line steeper, changing b moves the line up or down

acute triangle

A triangle with 3 acute angles

scalene triangle

A triangle with no equal sides

expanded form

A way to write numbers that shows the place value of each digit.

inductive reasoning

A type of logic in which generalizations are based on a large number of specific observations. ex. "If I do my homework all this week, i think my mother will take me to the concert on Saturday."

Euclid

Father of geometry

adding and subtracting mixed numbers

2 5/10 + 1 4/10 = 3 9/10 7 9/12 - 5 4/12 = 2 5/12 If necessary, change the top mixed number by borrowing from the whole number part: ex. 5 2/7 - 3 4/7 = 4 2/7 + 7/7 - 3 4/7 = 4 9/7 - 3 4/7 = 1 5/7

First eight prime numbers

2, 3, 5, 7, 11, 13, 17, 19

traingles

3 sided

quadrilateral

4 sided polygon

pentagons

5 sided polygons

hexagon

6 sided polygon

octagons

8 sides

right angle

90 degree angle

polygon

A closed figure formed by three or more line segments

diameter of a circle

A line that passes through the center of the circle, connecting any two points

scientific notation

A mathematical method of writing numbers using powers of ten.

Rational number

A number that can be written as a ratio, fraction, or decimal ex. 3/5 or 0.6

rotation

also called a turn, rotates or turns the shape around. Each rotation has a center and a angle for movement of a given number of degrees

Natural Numbers

Counting numbers: 1, 2, 3, ...... also include the infinity symbol but does not include 0, negative, fractions or decimal #'s

acute angle

an angle that measures less than 90 degrees

congruent angles

angles that have the same measure

Van Hiele Theory

Describes the levels of thinking associated with the learning of geometry, as well as being a general theory of mathematics education. 1988 - Fuys, Gedds, and Tischler 0 - Visualization mental pic teacher provides lots of good physical or nonphysical examples lEARNER can select a specific shape, sort, and match, and point out shapes 1 - Analysis-being to talk and notice the properties of the shapes ; predict shapes final form after seeing part of it list several attributes of each shape 2 - Informal Deduction-stop relying on visuals and use relationships to conclude focus on the first two level for K-8 3 - Formal Deduction-high school level such theorems 4 - Rigor- level college

Rounding

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

Dividing Decimals

Move the decimal to the right in the divisor, making it a whole number. Move the decimal the same number of places in the dividend and bring to the top in the quotient, then divide normally. (Example: 34/2.5 is 340.0/25.)

Perimeter of a triangle

P = a + b + c ex. the perimeter of a triangle is given 3 inch, 4 inch, 5 inches= 12inches

Perimeter of a rectangle

P=2l+2w or P=2(l+w)

perimeter of a square

P=4s (s=side)

Orders of Operations

PEMDAS

absolute value

The distance a number is from zero on a number line. ALWAYS POSITIVE

radius

The distance from the center of a circle to any point on the circle

greatest common factor

The largest factor that two or more numbers have in common or the highest number that divides exactly into two or more numbers

Commutative Property

The property that says that two or more numbers can be added or multiplied in any order without changing the result.

Dividing Fractions

To divide fractions, invert the second one and multiply

Multiplying Fractions

To multiply fractions, multiply the numerators and multiply the denominators then simplify the product

supplementary angles

Two angles whose sum is 180 degrees

complementary angles

Two angles whose sum is 90 degrees

perpendicular lines

Two lines that intersect to form right angles

Steps Solving Problem

Understanding the problem, Planning a solution strategy, Carrying out the solution, Evaluating checking your answer

nonlinear function

a function whose graph is not a line or part of a line ex. y=x^2+x-2 cannot be written as y=mx+b another ex. y=7/x ( x does not repeat in a function ex. (10,2) (7,2) (10,8) is not a function because x is repeating with the number 10 and there should only be one x input another example, to see if a graph is a function do the vertical line test and it should only cross one point

common multiple

a number that is a multiple of two or more numbers

reflection

also called a flip to reflect an object or to make the figure/object appear to be backward or flipped. It produces the mirror image of a geometric figure