1
Q
Relatively Prime
*Test [If they have no shared factors (besides 1)]
A
Two numbers; If they have no shared factors besides 1. To determine if two numbers are relatively prime, find the prime factors of each and compare.
Ex: If they have no common factors they are relatively prime. The # 34 and 15 are relatively prime because 34= 2x17 and 15= 5x3, so there a no factors in common.
2
Q
Fraction Decomposition
A
Which means to break down a faction. (In fraction composition/decomposition, the denominator is the same. The numerators will add up(composition) or break apart (decomposition) to the same total.)
3
Q
Prime Factorization
A
For each unique factor, identify which number has the most occurrence’s. Ignore the other instances of that factor. Multiply the remaining values together to calculate the least common multiple.
Ex: What is the least common multiple of 6&8? Since 6&8 are small values, use method 1:
Multiples of 6: 6 12 18 24 30 36
Multiples of 8: 8 16 24 32 40 48
The first multiple that the two numbers have in common is 24. The LCM 6&8 is 24/.
4
Q
(LCM) Least Common Multiple
A
Smallest # that 2 values will divide into evenly
5
Q
(GCF) Greatest Common Factor
A
Is the largest factor shared by two or more numbers. Sometimes called the greatest common divisor (GCD).
-To find the greatest common factor , find the prime factorization of the numbers in question and circle all factors that are shared. If more than one factor is shared, multiply the factors together.
-Ex: What is the greatest common factor of 12 and 15?
12: 2x2x3
15: 3x5
-The only value is common for the two lists is 3. The greatest common factor is 3.
6
Q
Prime Factors
A
Factor that is also prime. Ex: 2 x 3=6
7
Q
Rectangular Arrays
A
Tools for introducing and identifying factors
8
Q
Composite #
A
Natural # that do have # and divide evenly into them. Ex: 1,2,4
9
Q
Prime Numbers
A
greater than 1 that one divisible only by 1 and themselves. Ex: 2,3,5,7,11,13,17,23,29,31
a natural number greater than 1 that has exactly two distinct positive divisors: 1 and itself. They cannot be divided evenly by any other numbers. Ex: 2, 3, 5, 7, 11, and 13. The number 1 is not prime, and 2 is the only even prime number.
10
Q
Causation
A
Means that a change in the independent variable causes a change in the dependent variable
11
Q
Box plot
A
Uses a box and whiskers to display data
12
Q
Dot plot
A
Graph that uses dots to show the frequency counts of a group of data
13
Q
Line Graph
A
Use line segments to connect data points
14
Q
Double Bargraph
A
Displays 2 bars next to each other and is used to compare 2 groups of data within each category
15
Q
Bar graph
A
Use rectangular bars to show comparisons between categories of data
16
Q
Scientific Notation (come back)
A
expressed as the product of a base-10 # and 1 and 10
17
Q
Y-Intercept
A
Is the place where the graph crosses the y-axis. Parabolas will always have 1 y-intercept. This parabola’s y-intercept is at (0,-6). (y=0)
18
Q
Base 10 System
*On Test
Thousands| Hundreds|Tens|Ones| . | Tenths| Hundredths
When a digit is in a specific position, it’s value is equal to the product of that digit and the power of 10 that is assigned to its position.
A
Called the decimal system, is the number system that uses ten digits (0-9) to represent numbers. Each digit has a value determined by it’s place value: a digit in one place is worth 10 times the value of a digit in the place to it’s right. Numbers are organized in powers of 10, such as ones, tens, hundreds, and thousands.
-Each place location for a # has a value that is a power of 10.
19
Q
Place value
A
To show the value of each digit in the number based on its location, or place, we can deconstruct, larger # to see the value of each digit
20
Q
Expanded Form
A
Uses place value to show the value of each digit, rather than writing the number as a whole. (Find ex)
21
Q
Expanded Notation
A
Break apart each digit in the number and show the digits true value. Ex: (8,436) -> 8,000 + 400 + 30 + 6
22
Q
Irrational numbers
A
Real numbers that cannot be represented exactly
23
Q
Magnitude
A
Size of a number. It is important to be able to determine how numbers are related to each other
24
Q
Absolute Value
A
Greater of negative number, the smaller it is. Ex: 123> 122 but -123< -122
25
Number Line
Straight line and each value whole number is equal distance from the next one.
26
Unit Fractions
Are fractions that have “1” in the numerator. Ex: (1/2), (1/7),(1/8) numerators: are the same, smaller the denominator, larger the fraction.
Denominator: are the same, larger the numerator, the larger the fraction
27
Benchmark Fraction
Estimate the value of an uncommon fraction using a familiar, easy to deal with fraction, such as 1/2, and compare accordingly. Ex: 2/3 or 3/7 or 1/10 or 1/4 or 1/2.
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Common Denominator
Between 2 fractions and then compare the numerators. The larger numerator will be the fraction.
29
Multiplicative Identity Property
A number that, when multiplied by (x), yields x. these are one or more forms of one such as x/x. Ex: 6 x 1=6
30
Texas Essential Knowledge and skills (TEKS)
Base curriculum for every subject in every grade level taught at a Texas Education Agency (TEA) approved school. TEKS determines the information each student should know and skills they should be able to do and provides an outline for curriculum design and learning goals that classrooms should accomplish for the year.
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Homogeneous Group
Composed of students on similar levels with similar academic needs. Used for targeting specific skills or learning styles
32
Heterogeneous Group
Composed of students working on various levels with varying academic needs
33
Flexible Group
A fluid grouping strategy based on students needs. Formed based on common goal
34
Culturally Responsive Teaching (CRT)
Approach that recognizes the importance of learning students cultures in all aspects of learning
35
Backward Design/Planning
Approach that lesson planning where a teacher starts with the goal and work backwards to identify all skills and activities needed to ensure student success.
Ex: 1. Goal/Objective|2. Assessment|3. Lessons|
36
Thematic Unit
Organization of a curriculum and a central theme lends itself to the integration of all subjects, etc.
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*Behaviorism
On Test*
Learning new behaviors based on the response they get to current behaviors.
38
*Cognitivism
On Test*
Learning new behaviors by adjusting our current view of the world
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*Constructivism
On Test*
Learning new behaviors by adjusting our current view of the world
40
Concrete Stage
Introduce and model a concept using physical manipulatives
## Footnote
CRA order
41
Representative Stage
Replace the physical manipulative with pictures and/or symbols. This is sometimes called the symbolic or pictorial stage
## Footnote
CRA order
42
Abstract Stage
Replace the symbols with proper numbers and mathematical notations
## Footnote
CRA order
43
Auditory
Learn by hearing
44
Tactile/Kinethetic
Learn by touch or movement
45
Visual
Learn by seeing
46
Inquiry-based teaching
Students arrive instruction by asking questions and creating projects to answer the questions
47
Circle
Is the set all points equidistant (same distance) from a given point (the center). A circle is not considered a polygon because it does not have straight sides or vertices. The line segment from the center of a circle to any on the circle is called a "radius".
48
Polygon
Is a multisided, closed figured made up of vertices (corners) and sides (segments connects consecutive corners). A polygon does not have curved sides.
49
Regular Polygon
All sides congruent to each other and all angle measures congruent to each other. Ex: Regular Pentagon
50
Irregular Polygon
Sides and angle measures that are not the same. Ex: Trapezoid
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Convex Polygon
All interior angles are less than 180* vertices seem to point outward. All diagonals will be contained within the polygon. Ex: (look up)
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Concave Polygon
At least one interior angles that is more than 180*. At least one vertex seems to point inward. Diagonals pass outside of the polygon. Ex: Concave Hexagon
53
Scalene Triangle
Triangle with polygon no sides or angles congruent to each other; all the three sides are of different lengths. “Mnemonic”- an S has zero horizontal lines.
54
***Area of Irregular Shape
To find the area break the shape into smaller common squares
55
*Pyramid and Prism
Named for their bases. Pyramid have one base and one apex. prisms are 2 bases
56
Isosceles Triangle
Triangle with (at least) two sides congruent to each other which also produces two congruent two congruent angles. A serif I has 2 horizontal lines
57
Acute Triangle
Triangle with each angle being an angle; each angle measuring less than 90*. A-cute little angle is here
58
Equilateral/Equiangular Triangle
Triangle with all sides congruent to each other and all angles congruent to each other E an e has horizontal lines
59
Obtuse Triangle
Triangle with one obtuse angle; one angle measuring more than 90*. Obtuse angles are obese
60
Symmetric
You can draw a line to create a mirror image. Otherwise, it is “asymmetric".
61
Perimeter
Is the distance of a figure around the outside of that figure.
62
Area
Is the amount of surface inside of a figure.
63
Radius (r)
Is the distance from the center of a circle to any point the circle.
64
Diameter (d)
Is the distance from one point on a circle through its circle, to another point on the other side of the circle.
-The diameter it’s always twice as long as long as the radius (d=2r)
65
Circumference of a circle
(Pi)
Is the distance around the circle. It can be found by the formula.
Formula: (c= 2 (Pi)r = (Pi)d)
66
Area of circle
Is the area within it. It can be found by the formula. Where r = radius.
Formula: A= (Pi)r^2
67
Common Three- dimensional shapes:
Name: Cube| Rect. Prism| Tri. Prism|Square Pyramid|
Vertices-8| 8|4 |5
Edges-12|12| 6|8
Faces-6|6|4| 5
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Rectangular Prism
69
Percentages
Are a special type of ratio used to represebt part to whole relationships, where the ratio is always "out of 100". In other words, "percent" means for every one hundred".
-If you had a bucket of 100 apples and 20% of them were green apples, you'd expect 20 out of the 100 to be green and 80 out of the 100 to be a different color. This percentage can be used to scale any total quantity. For example, if you have 200 apples you'd expect to be green.
-Percentages always need to be converted into a decimal before they are used in a month equation. This is done by dividing the percentage by 100. This moves the decimal place 2 places to the left. For example 20& =.20
-When this decimal is multiplied by a number, the result tells us how much of the "inhole" the percentage represents.
Ex: What is 25% of 54? (Convert 25% to .25) (Use multiplication symbol for "of") 0.25x 54|x= 13.5 so 13.5 is 25% of 54.
Ex: What is 20% of 82? Convert the percentage to a decimal- (20% x 100=0.20), set up the problem: x= 0.20 x 82, solve: x=16.4
Look at notes for rest of example.
70
Proportions
## Footnote
On test*
Is a pair of equal fractions. It is a statement that two ratio's are equvalient. Two numbers are proportional to another pair of numbers if their ratios are the same. In other words, if you multiply or divide both number in a ratio by the same value, the resulting ratio is equivilent and the numbers as proportional. 1/2-> 1/2-> x 3/3= 3/6 x 2/2 = 6/12
1/2= 3/6=6/12
These fractions are proportional because they all reduce to 1/2.
-Note that creating proportional ratios only work when multiplying dividing. It is a common misconception to try and create proportional ratios with additional subtraction. If a number to be added or subtracted from both the numerator and denominator, the result would not be a proportional relation.
Ex: Jasmine brought 32 flowers for $16. Julianne would like to know how many flowers she can buy if she only has $4. Create a proportion to solve this problem. Both the numerator and denominator must be divided by the same amount 32/16 divided by ?/?= ?/14. Since $16 /4 = $4, both numbers in the original ratio must be divided by 4 to find an equavelent ratio, the other half of the proportion.
71
Sphere
Set of points in 3-dimensional space that are all the same distance from a given point( the center). It has no faces, edges, or verticals. Ex: Sphere
72
Prisms
Is a shape in three dimensions that has two of the same polygons for the base; prisms are named by the shape of their polygonal bases.
73
Pyramid
Is a shape in three dimensions that has one polygon for a base and triangular faces that meet at a point (the apex); pyramids are named by the shape of their polygonal base.
Pyramid- |Tri Pyramid |Quadrilateral Pyramid|Square Pyramid|Pentagonal Pyramid| Hexagonal Pyramid|
Vertices-|4| 5|5 |6|7|
Edges-6|8|8|10|12|
Faces-|4|5|5|6|7|
74
Symbolic/ Representational Stage
Drawing pictures or symbols to represent number in a equation
75
Faces, Edges, Verticles
F: are the sides the shape
E: where faces meet
V: corners of the shapes
76
Slant Height (s) and Height (h)
-Distance from the apex(top vertex) to an edge of the base.
- The height, h, is the distance from the apex (top vertex) to the base of the pyramid.
-The slant height, (s), is the distance from the apex to the middle of an edge of the base
77
Surface Area
Is the area on the outside of a 3 dimensional object
78
Total surface area
Of a solid figure is the sum of all the areas or all faces.
79
Lateral surface Area
Of a solid figure is the sum of the areas of all faces excluding the base(s).
Ex: The lateral surface area of a soup can is the curved part (what is typically covered by a label). The total surface area is the lateral surface area plus the top (lid) and bottom. This is the entire metal surface of the can.
80
Nets
Can also be useful for computing the surface area of a 3 dimensional figure. This is particularly helpful for pyramids & prisms.
Figures that use net: Triangular Prism, Rectangular Prism (box), Rectangular Pyramid, Triangular Pyramid
81
Volume
Of 3 dimensional figures is the measure of the total 3 dimensional space contained in an object. These objects include spheres, rectangle prism, triangular prism, rectangular pyramid, triangular pyramid, cylinder, and cone.
-In general, volume can be found by V=Bh, where B is the area of the base.
-There are more specific formulas for each shape.
82
Volumes of Common Shapes
Shapes | Volume
Sphere V= (4/3)(pi)r^3
Cone V=(1/3)(pi)r^2h
Cylinder V= Bh=(pi)r^2h
Rectangular Prism (box) V= lwh=Bh
Triangular Prism V=(1/2)lwh=Bh
Rectangular Prism V= 1/3Bh
Triangular Pyramid V=1/3Bh
83
Transformation
Is a change to a geometric objects take in an input (x) and create an output (y), geometric transformation s, use rules to take pre-images(the original object) and create images (the resulting object)
84
Rigid Motions
Which maintain congruence (equal measures for all angles and lengths) of the object with the image. Translations, reflections, and rotations.
85
Rigid Transformations
Always produces a congruent image with a new orientation
86
Translation
On test*
Is sometimes known as a “slide”. It is a movement to the right or left, up, or down, or a combination of movements that are both vertical and horizontal
87
Reflection
On test *
Produces a mirror image of the original so it can (flip)
88
Rotation
On test*
Is sometimes known as a “turn”. Occurs around a point, known as the center of rotation. Origin (0,0)
89
Non-Rigid Transformations
Produces the same shape, with congruent angles but a different size
90
Dilation
A type of transformation that either enlarges or reduces the size of an object, given a scale factor
91
Tessellation
A pattern of shapes that fit perfectly together
92
Regular Tessellation
Made up of only the same regular polygons. They can only be made using a regular triangle, square, or hexagon.
93
Semi regular Tessellation
Are made of different regular polygons arranged in a pattern
94
Spatial Reasoning
Helpful in solving problems. Ability to think about how things appear in real life. Ex: Drawing pictures or diagrams
95
Slope-Intercept Form
Y= mx + b
96
Parallel Lines
Lines that never intersect because they are changing at the same rate. Therefore, lines that are parallel have the same slope.
97
Perpendicular Lines
Lines that intersect at a right 90* angle
98
Axiom
A truth that is accepted as being self evident. In math, an axiom is a beginning point from which all other statements are derived
99
Theorems
Must be proven before they can be accepted or used
100
Coordinate Plane
Lines can be graphed; x- and y- axis
101
Origin
Intersection of x and y axis
102
Quadrant
Each of the 4 areas
103
Ordered Pairs
Always in the (x,y) form. Ex: (0,0)
104
Point
Is a location in space without any dimension
105
Line
Is a straight path of infinite length but no thickness
106
Line segment
A straight path with two endpoints
107
Ray
Straight path that has one defined endpoint that has one defined endpoint and extends infinitely in the other direction
108
Collinear Points
Any two or more points on the same line.
109
Coplanar Points
Any points found within the same plane. Any 3 points will determine a unique plane
110
Complementary Angle
Two angles that have a sum of 90*degress
111
Supplementary Angle
Two angles that have a sum of 180* degrees
112
Commutative Property **
Order doesn’t matter. Ex: a+b+c= a+c+b
113
Associative Property **
Grouping symbols don’t matter. Ex: (a+b) + c= a+(b+c)
114
Distributive Property***
Multiplying a factor by the terms inside a quantity. Ex: a(b+c)= ab+ac
115
How many different outcomes are possible when a pair of six-sided dice are rolled?
There are 36 possible outcomes.
116
Addition and Multiplication are both commutative and associative.
Subtraction and division are neither.
117
X-intercept
Are the coordinates where the group crosses the x-axis. There can be 2,1,0. Roots, zeros, and solutions are other words used to describe the x-intercepts of the parabola. Use the acronym ROXS (Rocks) to remember the roots, O's, x-intercepts and solutions all refer to the same characteristics of parabolas.
118
Vertex
Lowest point of a parabola, which occurs if the parabola opens upward, or the highest point, which occurs if the parabola opens downward is called... The y coordinate of the vertex is the minimum or maximum value of the function.
119
Quadratic Equation
Is an equation where the highest exponent of the variable, usually (y), is 2. This means that there is an x^2 term in the equation.
-A quadratic equation is typically written in "standard form", shown below, where a,b,c are known values. y=ax^2+bx+c.
-When graphed, all quadratic equations make a U-shaped form, called a "parabola". It can open up or down. The graph of the equation y=-2x^2+8x-6 is shown below, and some key characteristics of the parabola are noted.
120
Verbal to symbolic linear equations
1. Identify unknowns and assign variable's
2. Identify important values, such as rates and constants
3. Determine the independent and the dependent variable's.
4. Identify words that relate to the operations, equality symbols, and groupings.
5. Write the equation.
121
Slope
The rate at which the x and y values change is and typically represented as fraction, with the change in y values in the numerator and change in y values in the denominator. Rise over run.
122
Axis of Symmetry
Parabolas are symmetrical. If you were to draw a vertical line through the parabola, starting at the vertex, the graph would be the same on either side. This vertical line is known as the axis of sym, and it always corresponds with x-value of the vertex.
123
Linear Function
Is a function with a constant slope, often represented vy a linear equation, and written in function notation. Functions use the notation f(x) , pronounced "f of x", to represent the function output. The following defines function f, a function of x: f(x)= mx+b.
124
Vertical Line Test
To examine the graph of relation to determine if the relation is a function.
125
Mapping Diagram
Shows a relations inputs and their corresponding outputs using arrows. The same relations shown as ordered pairs above are represented in the mapping diagrams below.
-A quick way to check for a function is to look fir any repeated values in the x column,
-Remember the graph of a function must pass the "vertical line test"
126
Function
Is a special type of relation where each input has only one output. One way to understand the concept of a function versus a relation is to consider real word examples.
127
Improper Fraction
Step 1: Divide the numerator by the denominator 14/ 3= 4.666
Step 2: Multiply the whole number part of the result from step 1 by the denominator 4 14-12/3= 4 2/3
Step 3: Subtract the result from step 2 from the orginal numerator.
128
Relation
Is a relationship between set of values. In math, the relation is often between x values (inputs) and y values (outputs).
129
Dependent Varible
Is the output of a function and is the result after solving the function using the independent variable. It is commonly represented by the variable y.
(Extra Info) "Five less than x" y-5
130
Independent Variable
In the input into a function and represents the variable that is known. Normally, it is represented by the variable x.
(Extra Info) "x less than eight" 8-x
131
System
Is a set of 2 or more equations or inequalities with the same set of variables, or unknowns.
-A solution to a system is where the 2 equations intersect or the two inequalities overlap.
132
Coefficient
Is a number that muliples a varible. There are 3 visible coefficients in the expression (2,4,9). Although, the varibles 9 has no visible coefficient, any varible written without a coefficient etc.
133
Constant
Is a number without a variable it is called a constant because its value does not change (it stays constant)
134
Variable
Is a letter or non-numeric symbol that represent an unknown value. This expression has 4 different variables (x,y,z,q)
135
Term
Is each part of an expression that is seperated by a (+) or (-) sign. This expression has five terms (2x,4y,-9z,-10,q)
136
Algebra
Is the branch of mathematics in which letters and symbols are used to represent unknown values. Here are some forms of the equations you will see in algebra.
137
Symbolic to Verbal
Addition- add(ed), all together, both, in all combined, plus, sum, total, more, more than, increased by, perimeter.
Subtraction- subtract, minus, how many more, take away, left, remaining, decreased by, minus, difference, deduct, less, fewer than, less than.
Multiplication- area, times, multiplied by, triple, of, twice, per, rate, product of, each.
Division- ratio split, divided, quarter, out of, half, shared, percent, quotient of, how many of each.
*(<) is less than, is fewer than| (=) is equal to is the same as yields, equals is|(>) is greater than, is more than|(≤) is less than or equal to, is no more than 0 doesn't exceed is at most| ( ≠) is not equal to is not the same as| (≥) is greater than or equal to is at least, is not less than|
138
Inequality
Is a statement that two expressions are not equal.
139
Equation
Is a statement that two expressions are equal to each other.
140
Figures formulas area and perimeter
*On Test
w= Width
h= Height
l= Length
b= Base
Figure Perimeter Area
Rectangle | P=2(W+1) | A= l(x)w |
Square | P=4s | A= s^2
Triangle|P= Sum of all 3 sides| A= 1/2bh
Parallelogram|P=2(a+b) | A= bh
Trapezoid|P= Sum of all sides|A= 1/2(B1+B2)h
141
Polygon figure shapes based on (sides, vertices, shape) *
*Note that a shape with all sides having equal length is described as regular.
Name |Triangle| Quadrilateral| Pentagon|Hexagon|Octagon
Vertices|3|4|5|6|8|
Sides|3|4|5|6|8|
All squares are rectangle's, but not all rectangles are squares.
All rectangles are parallelograms, but all parallelograms are rectangles.
142
Quadrilateral
Is any polygon woth four vertices and four sides. Types of quadrilaterals differ based on their side lengths and angles.
-Same polygons, like rectangles, are represented by a square in shape digrams.
143
Surface Area of Common Shapes *
Shapes | Total Surface are
Sphere | SA= 4(pi)r^2 | r=radius h= height
Cone | SA= (pi)r+ (√ h^2+r^2) | r= radius h=height
Cylinder| SA= 2B+ 2(pi)rh B=Area of Base r=radius h=height |SA= 2(pi)rh+2(pi)r^2|
Rectangular Prism (box)|SA= 2(wh+lw+lh) w=weight l=length h=height
144
Mixed Number
Is the combination of a whole number and a fraction (e.g. 3 (1/2). To perform operations with mixed numbers, first convert the mixed number into an improper fraction, a fraction in which the numerator is larger than the denominator. (e.g. (7/2)
- To convert a mixed number, such as 4(2/3), to an improper fraction.
- Step 1: Multiply the whole number by the denonminator.[ 4 (2/3) 4 x 3=12
- Step 2: Add the product from step 1 to the numerator (12+2=14)
- Step 3: Write the sum from step 2 over the original denominator (14/3)
EC-6 Core Info
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