Critical Thinking
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| Inductive Reasoning |
Developing generalizations based on observation of a limited number of related events or experiences
Based on observation
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| Deductive Reasoning | Arriving at specific conclusions based on general principals, observations, or experiences.
Based on previous experience or truth.
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| Problem Solving | The ability to apply and adapt a variety of mathematical strategies to solve problems.
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| Relative magnitude | Size relationship b/t numbers; is the number smaller, larger, close or the same?
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| Natural numbers ( Counting Numbers) | 1,2,3,4,5,6,7....
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| Whole Numbers | All the Counting numbers and 0 ex: 0,1,2,3,4,5,6,7....
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| Integers | All the natural and whole numbers including the negatives of those numbers ex: -7,-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7....
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| Rational Numbers | All integers are rational numbers, also fractional numbers or fractions, any integer over any integer ex: 1/2, 1/4, 4/1, 7/8...
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| Prime Number | An integer other than 0 and 1 that has only 2 factors; itself and 1; a number that is divisible only by itself ex: 3,5,7,11,13,17...
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| Even numbers | An integer divisible by 2: 2n.
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| Odd Numbers | An integer that is not divisible by 2: 2n - 1.
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| Complex Numbers | The numbers with "I" in them: 6 - 2i.
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| Addition | Carrying (regrouping)
Sum
More than
In addition to
Exceeds
Increased by
Altogether
Sum
And
Extra
Combined
Total of
Count up
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| Subtraction | Borrowing (regrouping)
Less than/ fewer than
Decreased by
Diminished
Take away
Difference
Deduct
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| Subtrahend | Number subtracted from another
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| Minuend | Number to be subtracted from
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| Difference | Answer
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| Multiplication | Multiplicant
Mutiplier
Product
Times
Twice
Of
Multiplied by
Increased by
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| Multiplicant | Number to be multiplied. (Top number)
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| Multiplier | Number being multiplied by. (Bottom number)
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| Product | Answer
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| Division | Quotient
Remainder
Separated
Distribute
Per
Out of
Percent
Ratio of
Divisor
Dividend
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| Divisor | How hany times to divide
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| Dividend | The number being divided.
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| Quotient | Answer
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| Arithmetic Sequence | Add the same value each time; add 3 each time ex: 1,4,7,10,13,16,19
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| Geometric Sequence | Multiply the same value each time; multiply by 2 each time ex: 2,4,8,16,32,63,128
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| Fibonacci numbers | The next number is found by adding the two numbers before it. Ex: 0,1,1,2,3,5,8,13,21,34...
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| Equivalence | Being equal in value or amount
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| 1/5 | A.). 2/10
B.). 1/2
C.) 4/16
D.). 5/7
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| Equivalent Fractions | Found by multiplying the numerator and denominator by the same number
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| Equivalent Decimal | Found by dividing the numerator by the denominator of the equivalent decimals
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| Equivalent percents | Found by moving the decimal point over to the right to create a whole number of the Equivalent Decimal given ex: 0.25 = 25%
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| Factor | Prime or composite number that is multiplied to get a product.
The breakdown of a larger number.
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| Factoring | The process of taking a number apart and expressing it as the product of its factors.
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| 2 | A factor of all even numbers
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| 10 | A factor of all numbers ending in 0
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| 5 | A factor of all numbers ending in 0 and 5
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| 3 | Is a factor of that number if it is a factor of the sum of it's individual digits found within the number ex: 65,331 6 +5+3+3+1=18
3 is a factor of 18
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| 9 | Is a factor of that number if it is a factor of the sum of it's individual digits found within the number ex: 89,172 8+9+1+7+2= 27. 3 x 9 = 27
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| 11 | Is a factor of a three digit number if ithe middle digit is the sum of the two outside digits. Ex: 682 6+2=8
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| Multiples | Found by multiplying a whole number by a whole number
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| Lowest common Multiple | A number that is a multiple of 2 numbers being compared as is the lowest of all the multiples.
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| Ratio | A comparison between two numbers.
:
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5 dogs to 3 cats
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| Proportion | 2 ratios with an equal sign b/t them; 2 ratios that are equal to one another.
5/3=10/6 or 2:3=4:6.
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| The ratio of apples to oranges in a grocery store is 6/7, and there are 246 apples. How many oranges are there? | A.). 900
B.). 621
C.). 287
D.). 21
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| Percent | Per one hundred
Fifty percent
50%
0.50
50/100
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| What percentage of 105 is 36.75 | Set up the cross multiplation fractions
X/ 100 = 36.75/105
Cross multiply
105x = 3675
Divide by 105 to get x by itself
X= 35%
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| Equals | Is
Are
Was
Were
Will be
Gives
yields
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| 18 is what % of 20? | Divide the number you have by the number possible and multiply by 100 to find a percent.
A.). 45
B.). 56
C.). 60
D.). 90
18/20= 0.9x 100= 90%
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| A pair of shoes is on a 20% off sale rack. The sale price is $60. What is the original price. | A.). $75
B.). $62
C.). $72
D.). $74
X equals the original price
X-(0.20)x=60
Add x to both sides to isolate the variable
60/0.8= 75
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| Associative Property | Numbers can be grouped or regrouped in an operation in any manner w/o changing the answer; doesn't matter the order or how the numbers are combined the answer will always be the same. Addition and multiplication are both associative
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| Associative Property of addition | A + (B+C)= ( A+B) + C
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| Associative Property of addition | 3 + (4+6) = (3+4) + 6
(10). (7)
3+. (10). +6
13. 13
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| Associative Property of multiplication | A x (B x C) = ( A x B) x C
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| Associative Property of multiplication | 3 x ( 4 x 6 )= ( 3 x 4) x 6
(24). (12)
3x (24). X. 6
(72) (72)
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| Commutative Property | Numbers in an operation can change order w/o changing the answer; doesn't matter the order of the numbers the answer will always be the same. Addition and multiplication are both commutative
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| Commutative Property of addition | A + B = B + A
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| Commutative Property of addition | 60 + 15 = 15. +. 60
75. =. 75
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| Commutative Property of multiplication | A X. B =. B. X. A
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| Commutative Property of multiplication | 10. X. 5. =. 5. X. 10
50. =. 50
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| Distributive Property | One operation may change to another. This property is used to make equations simplier by breaking them apart. Can be used when multiplying with parenthesis.
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| Distributive Property | A (B + C) =. AB. +. AC
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| Distributive Property | 4 (3+2). =. 4(3). +. 4(2)
4. (5). =. 12. +. 8
20. =. 20
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| Transitive Property | If X is related to Y and Y is related to Z then X is related to Z.
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| Transitive Property | 5 > 4 and 4 > 3 then 5 > 3
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| Additive Inverse | The opposite of the number, the number when added to (n) the result is 0
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| Additive Inverse | The additive inverse of 2 is:
A.). 0
B.). -2
C.). 4
D.). -4
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| Multiplicative Inverse | The reciprocal, the number when multiplied by (n) the result in the product of 1.
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| Powers of zero | Anything to the zero power will create an answer of 0.
1' = 0
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| Multiplicative Inverse yields one | Any number multiplied by its inverse gives an answer of one. Ex: x * 1/x = 1
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| Absoloute value | Never negative
Ex: 3. =. 3
-6. =. 6
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| Negative Exponents | Any number to a negative exponent is the same as one over that number with a positive exponent.
Ex: 6 -2 = 1/6 2
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| Parallell lines | Non- vertical lines in a plane with the same slope.
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| Perpendicular lines | 2 lines in a plane with the product of the slopes equaling -1.
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| Pythagorean Theorem | Used to explain the lengths of a rt. triangle. The 2 legs ( a + b ) squared equal the length of the hypotenuse (c) given any two values of the 3, the 3rd value can always be found.
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| Pythagorean Theorem | A2 + B2 = C2
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| Slope | Given 2 point. (x1,y1), (x2,y2):
To find the slope (m) use m= y2-y1/ x2-x1.
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| Edges | sides or arches of a 1- dimensional figure
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| Vertices | The end points or edges of the figure which is 0 dimensional
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| Angles | When 2 sides meet at a vertex measured in degrees
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| 2 dimensional figures | Equilateral triangle
Rhombus
Square
Isosceles triangle
Rectangle
Trapezoid
Right triangle
Kite
Chevron
Scalene triangle
Ellipse
Circle
Parallelogram
Ellipse
Circle
Parallelogram
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| Polygons | 2 dimensional figures in which:
All edges are segments
Every vertex is the endpoint of 2 or more edges
No 2 sides cross each other
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| 10 | Decagon
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| 11 | Undecagon
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| 12 | Dodecagon
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| Three-dimensional figures include the following | Sphere
ellipsoid
ovoid
cone
cylinder
prism
pyramid
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| polyhedrons | are three-dimensional figures and shapes in which:
all faces are plane regions
every edge is the edge of two faces
every vertex is the vertex of three or more faces
no two faces cross each other
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| 4 | tetrahedron
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| 6 | cube
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| 8 | octahedron
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| 12 | dodecahedron
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| 18 | icosahedron
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| transformation | changes the position of the shape upon a coordinate plane resulting in the same value and magnitude. The shape moves from one place(coordinate)to another.
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| rotation (turn) | the shape is turned on 360° axis
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| reflection (flip) | the shape is a mirror image
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| translation (slide) | the shape moves by sliding into another area in the plane
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| King Henry's Dad Mark, Larry, Gary, Drinks Chocolate Milk. | Kilo
Hecto
deka
m l g
deci
centi
milli
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| 1 foot | 12 inches
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| 1 yard | 36 inches
3 feet
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| one-mile | 5280 feet
1760 yards
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| 1 pound | 16 ounces
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| 1 ton | 2000 pounds
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| 1 cup | 8 fluid ounces
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| 1 pint | 2 cups
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| one quart | 4 cups
two pints
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| 1 gallon | 4 quarts
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| perimeter rectangle | 2l + 2w
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| area of a rectangle | l x w
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| perimeter of the triangle | a + b+ c
s1 +s2+ s3
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| area of a triangle | 1/2 bh
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| Pythagorean theory | all angles equal 180°
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| perimeter of the square | 4s
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| area of the square | s2
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| perimeter circle | 2(3.14)r 3.14d
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| area of the circle | (3.14)r2
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| volume | measured in cubes and is the amount of cubes that is required to fill the object completely.
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| cube | A3
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| rectangular prism | length times width times height
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| prism | based times height
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| pyramid | 1/3 base time height
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| cylinder | 3.14 r2h
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| cone | 1/3 3.14 r2h
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| sphere | 4/3 3.14 r2
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| rate | rate= distance/time
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| angles | consistent two rays that share the same endpoint (vertex). The two rays are the sides of the angle.
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| acute angle | any angle that is less than 90° but greater than 0°
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| obtuse angle | any angle is greater than 90° but less than 180°
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| right angle | any angle measuring exactly 90° two lines that meet at a right angle are said to be perpendicular
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| complementary angles | when two angles are measured the sum of their degrees is equal to 90°
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| supplementary angles | when two angles are measured the sum of their degrees is equal to 180°
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| favorable outcome | what someone wants to happen
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| total outcome | all the things that could happen
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| probability | the measure of the likelihood that an event will occur.
Fractions
ratios
decimals
percentages
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| probability | to get the probability of an event count the number of times the event can acquire and divide that number by the possible number of outcome
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| probability | what is the probability of rolling at three on a standard six sided die
there are six possible outcomes
there is only one favorable,
therefore the probability of rolling up three is 1:6, 1/6, or 1 to 6 or .6 0r 16.7%
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| event | this set of outcomes found with in a probability it is the occurrence ( one or more outcomes) of the probability
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| combination | a selection of numbers or objects which order is not important and there is no repetition
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| permutation | an arrangement of numbers or objects in which order is important and there is no repetition. If factorial is a number that is successfully multiplied down to the number one denoted by!
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