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Ec-6 > Mathematics > Flashcards

Mathematics Flashcards

1
Q

Inductive teaching

Deduction approach

A
  • learning through example

- learning step by step

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2
Q

Jean Piaget development stages

A

Sensorimotor stage: birth - 2 years
Preoperational stage: years 2-7
-symbolic functioning, centration, intuitive thought, and inability to conserve
Concrete Operational: years 7-11
-decentering, reversibility, conservation, classification
Formal Operational stage: years 11- adult
-the ability to use symbols and think abstractly

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3
Q

Issues with preoperational stage

A

years 2- 7

Centration: focusing on only one aspect of a situation or problem
Conservation: understanding that quantity, length. or number of items is unrelated to the arrangement or appearance of the object of items

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4
Q

Concrete operational stage

A

2-7 years

Decentering: child can take into account multiple aspects of a problem to solve it
Reversibility: child understands that the objects can be changed and the3n returned to the original state
Conservation: child understands that quantity, length, or number of items is unrelated to the arrangement or appearance of the object
Serialization: child able to arrange objects in an order according to size, etc.
Classification: child can name and identify sets of objects according to appearance
Elimination of Egocentrism: child is able to view things from another’s perspective

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5
Q

The Professional Standards for Teaching Math (NCTM) presents standards for teaching math

A

Task: projects, questions, problems, construction, application

Environment: the setting for learning

Analysis: the systematic reflection in which teachers engage

Discourse: the manner of representing, thinking, talking, agreeing, and disagreeing

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6
Q

Pre-K

A

explores concrete models and materials
counts to 10 or higher by ones
begins to describe the concept of zero
identifying first and last in a series

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7
Q

6th grade

A

Compares and orders non-negative rational numbers, generates equivalent forms of rational numbers

Able to write prime factorizations using exponents, identifies factors of a positive integer, common factors, and greatest common factors

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8
Q

Integer

A

a whole number includes all positive and negative numbers, including zero
-6, - 5, -4-3, -2, -1, 0, 1, 2, 3, 4, 5, 6,…

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9
Q

Natural Numbers

A

a positive integer (not zero) or a nonnegative integer (whole numbers includes “0”)
0, 1, 2, 3, 4, 5, 6…

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10
Q

Rational Numbers

A

a number that can be expressed as a ratio of quotient of two nonzero integers- Fractions and Decimals

Finite decimals, repeating decimals, mixed numbers, whole numbers

Nonrepeating decimals cannot be expressed in this way- said to be irrational

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11
Q

Irrational Numbers

A

is a number that cannot be represented as an exact ratio of two integers

The decimal form of the number never terminates and never repeats

Ex: pi

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12
Q

Real Numbers

A

describes any number that is positive, negative, or zero and can be used to measure continuous quantities

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13
Q

Adding and Subtracting Homogenous Fractions

A

same denominator- add or subtract the numerator and keep the denominator the same

2/5+ 1/5= 3/5

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14
Q

Change improper fraction to Mixed Numbers

A

divide the numerator by the denominator and represent the remainder as a fraction

5/2= 2 1/2

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15
Q

Adding and Subtracting Mixed Numbers

A

denominators must be the same- add/ subtract the whole numbers and then add/subtract the numerator and keep the denominators the same

2 5/10 + 1 4/10= 3 9/10
7 9/12 - 5 4/12= 2 5/12

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16
Q

Changing Mixed Numbers to Improper Fractions

A

numerator greater then the denominator- multiply the denominator by the whole number, then add the resulting numerators

2 3/4= (2x4=3)/ 4= (8+3)/ 4= 11/4

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17
Q

multiplying fractions

A

multiply horizontally- multiple the numerators together and the denominators together

2/3 x 3/4= (2x3)/ (3x4)= 6/12= 1/2

If the numbers being multiplied are mixed fractions, first rewrite them as improper fractions

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18
Q

Dividing Fractions

A

take the reciprocal of the second fraction ( the one doing the dividing) and multiply the fractions

reciprocal: a fraction with the numerator and denominator switched

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19
Q

Multiplying Decimals

A

count the total numbers behind the decimal point in both numbers– this will be the number behind the decimal in the answer

2.3 x 4.56= 3 numbers behind the decimal point

Numbers do not have to be aligned

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20
Q

Dividing Fractions

A

Number doing the dividing needs to be a whole number so you must move the decimal– the number of places who move the decimal you do the same to the number being divided

1.44/ 0.3 ——– 14.4/ 3.0

decimal carries up to the answer from the number being divided

14.4/ 3.0= 4.8 ( 3 goes into 14 4 times)

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21
Q

Exponential notation

A

a symbolic way of showing how many times a number or variable is used as a factor
5^3 shows five is use three times (5 x 5 x 5)

Negative exponent indicates a reciprocal, therefore 5^-3 = 1/(5^3)= 1/ (5 x5 x5)= 1/125

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22
Q

Absolute Value

A

is the distance of a number from zero on the number line
ignores the + and - signs of a number

I-5I = 5 I5I= 5

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23
Q

Expanded Form

A

shows the place value of each digit

263= 200 + 60 + 3 which equals 2 hundreds 6 tens an d3 ones

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24
Q

Expanded notation

A

shows place value by multiplying each digit in a number by the appropriate power of ten

523= (5 x 10^2) +(2 x 10)+( 3 x 1) or (5 x 10^2) = (2x10^1) +(3x 10^0)

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25
Q

Scientific Notation

A

form of writing a number as the product of a power of 10 and a decimal number greater than or equal to 1 and less than 10

2,400,000= 2.4x10^6, 240.2= 2,402x 10^2, 0.0024=2.4x 10^-3

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26
Q

Estimation

A

is used to make an approximation that is still close enough to be useful

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27
Q

Prime Numbers

A

natural numbers greater than 1 that are divisible ony by themselves and 1
The first eight prime numbers are : 2 ,3, 5, 7, 11, 13, 17, 19

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28
Q

Composite Numbers

A

are natural numbers greater than zero that are divisible by at least one other number besides 1 and themselves

have at least three factors

9 is a composite number bc it has three factors: 1, 3, 9

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29
Q

Commutative Property

A

the order of the addends ( terms being added) or factors (in multiplication) do not change the result

a + b= b + a and a x b= b x a

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30
Q

Associative Property of Multiplication and Addition

A

the order of addends or factors will not change the sum or product

( a+ b) + c = a + (b + c) and (a x b) x c= a x (b x c)

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31
Q

Property of Zero

A

The sum of a number and zero is the number itself and the product of a number and zero is zero
8 + 0= 8
8 x 0= 0

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32
Q

Distributive Property

A

everything within the parentheses needs to be multiplied by the number outside

a (b + c) = ax (b +c) or
a (b + c) = (a x b) + (a x c)

8 (5+ 2) = 8x7= 56 or 8( 5 + 2)= (8 x5)+(8 x 2) = 56

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33
Q

Linear and Nonlinear Functional Relationships

A

Called the domain of F, a single real number designated as f (x). Variable X is called the independent variable. If y = f(x), we call y the dependent variable. Then, F(0) is the value of the funtion when x= 0.
Linear function is a straight line, nonlinear function does not satisfy the constraints of a linear function.

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34
Q

Function

A

Functions can be used to understand how one quality varies in relation to (or is a function of) changes in the second quantity.

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35
Q

Algebraic pattern

A

An algebraic pattern is a set of numbers and/or variables in a specific order.

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36
Q

Algebraic Expression

A

A mathematical phrase that is written by using one or more variables and constants, but does not contain a relation symbol (e.g., 5y + 8)

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37
Q

Variable

A

a letter that stands for a number in an algebraic expression.

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38
Q

Coefficient

A

a number that precedes the variable to give the quantity of the variable in the expression.

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39
Q

Addition and subtraction

A

like algebraic terms (same variable bases with the same exponents) can be added or subtracted to produce simpler expressions. example 2x³ and 3x³ can be added together to get 5x³.

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40
Q

Multiplying exponential terms

A

The constant terms are multiplied, but the exponents of the terms with the same variable bases are added together.

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41
Q

Multiplication of Binomials

A

FOIL stands for “first,outer,inner,last” or First,outside,inside,last. to multiple (x +3) and (2x-5) multiply x by 2x (the first terms), x by -5 (outer terms), 3 by 2x (inner terms), and 3 by -5(last terms).

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42
Q

Factoring

A

opposite of polynomial, a polynomial means rewriteing it as the product of factors (often two binomials). The trinomial x2 (small 2) - 11x + 28, for instance, can be factored into (x-4)(x-7)

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43
Q

Algebraic Solution

A

A process of solving a mathematical problem by using the principles of algebra.

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44
Q

Graphs and Symbolic representations

A

Four kinds of graphs are generally used in grades pre-K to grade 6- pictorial,bar,line,and pie. Pictorial graphs are the most concrete representations of information. They represent a transition from the real object graphs to symbolic graphs.

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45
Q

Bar graphs

A

Used to represent two elements of a single subject.

46
Q

Line graphs

A

Presents information in a fashion similar to bar graphs, but they use points and lines. A line graph tracks one or more subjects.

47
Q

Pie charts

A

Used to help visualize relationships based on percentrages of a possible 100%.

48
Q

Linear and nonlinear functions

A

A linear function is one whose graph is a straight line. A nonlinear function, is not linear. example quadratic x2 + x-1=0.

49
Q

Proportional Reasoning

A

Often they involve two unlike values that are related in a certain way.

50
Q

Variables,equations,and inequalities

A

Variables are classified as either independent(free) or dependent (bound). An expression represents a function whose inputs are the values assigned to the independent variables and whose output is the resulting value of the expression. Evaluation of an expression is dependent on the definition of the mathematical operators and on the system of values applied in the context of the expression.

51
Q

Algebraic Inequality

A

An algebraic statement about the relative size of one or more variables and/or constants. Inequalities are used to determine the relationship between these values. example- taking x as a variable and saying, “x is less than 5,” may be written as x <5

52
Q

Multiplying or dividing

A

Same negative number on both sides and changing the orientation of the inequality sign. The inequality 2x > 6 has the same solution as the inequality x > -2 (dividing by (-2) on both sides and switching “>” to “

53
Q

Van Hieles levels of Geometric thinking

A

0-Visualization, develop a mental picture of each shape
1- Analysis, begin to talk and notice the properties of the shapes.
2-informal deduction, stop relying on visualization, and now use relationships to make a conclusion.
3-Formal deduction, Focus is on higher levels of geometry, using various theorems to teach how two traingles are congruent
4-Rigor, Rigor is associated with college level geometry.

54
Q

Straight line

A

straight line, lines are one-dimensional. meaning they have infinite length and width but no depth

55
Q

line segment

A

any portion of a line between two points on that line. definite start and definite end called the endpoints, from point A to point B is AB.

56
Q

A Ray

A

Like a line segment, except it extends forever in one direction.

57
Q

Angle

A

Formed when two rays or lines share an endpoint. If two angles have the same size (regardless of how long their rays might be drawn), they are congruent.

58
Q

Supplementary angles

A

Two angles that add up to 180°

59
Q

Complementary angles

A

Two angles that add up to 90°

60
Q

Vertical angles

A

If two lines intersect, they form two pairs of equal angles.

61
Q

Polygons

A 
Is a many-sided plane (two dimensional) figure bounded by a finite number of straight lines. Described based on the number of sides, which are equal to the number of vertices.
Triangles= three sided polygons
Quadrilaterals= Four sided
Pentagons= Five sided
Hexagons= Six sided
Octagons=Eight-sided
62
Q

Properties of Triangles

A

Three sided polygons

63
Q

Isosceles traingle

A

Has two Equal sides and two equal angles

64
Q

Equilateral triangle

A

If the measures of all sides of the triangle are equal

65
Q

Scalene triangle

A

Triangle has three unequal sides

66
Q

Acute triangle

A

All three angles are acute

67
Q

Right triangle

A

One of the angles is a right angle

68
Q

Obtuse traingle

A

One of the angles is obtuse

69
Q

Pythagorean theorem

A

Any right triangle with legs (shorter sides) a and b, and hypotenuse (the longest side) c, the sum of the squares of the legs will be equal to the square of the hypotenuse.

70
Q

SAS

A

SAS(side angle side) two pairs of sides of two triangles are equal in length

71
Q

SSS

A

SSS ( side-side-side) three pairs of sides of two triangles are equal in length.

72
Q

ASA

A

ASA (angle-side-angle) Two pairs of angles of two triangles are equal in measurement, and the included sides are equal in length, then the triangles are congruent.

73
Q

AAS

A

Angle-Angle-Side, two pairs of angles of two traingles are equal in measurement and a pair of corresponding sides is of equal length, then the trangles are congruent.

74
Q

Parallelograms

A

Four sided polygon with two pairs of equal and parallel sides. the height of a parallelogram is not necessarily the same as the length of the other side.

75
Q

Rhombus

A

Special type of parallelogram in which all the sides are the same length

76
Q

Rectangles

A

A type of parallelogram with four right angles

77
Q

Squares

A

A type of parallelogram with four right angles and four equal sides

78
Q

Circles

A

unique shapes in geometry because they have no angles.

79
Q

Diameter

A

Straight line of a circle that segments that goes from one edge of a circle to the other side.

80
Q

Perimeter

A

Found by adding the measures of the three sides of the triangle.

81
Q

Circumference

A

Can be thought of as the perimeter of the circle, the distance around the circle.

82
Q

Area of the Parallelogram

A

Found by multiplying the measure of the base by the measure of the height, or a=bh

83
Q

Area of a rectangle

A

Similarly found by multiplying the measure of the length or base of the rectangle by the measure of the width of the rectangle.

84
Q

Area of a square

A

Found by squaring the measure of the side of the square.

85
Q

Area of a circle

A

Found by squaring the length of its radius, then multiplying that product by pi

86
Q

Congruent

A

Having the same shape and size

87
Q

Volume of a cylinder

A

Pi r squared x height

Area of base x height

88
Q

Symmetry

A

Correspondence in size,form, and arrangement of parts on opposite sides of a plane, line, or point.

89
Q

Tessellations

A

The arrangement of polygons that forms a grid, a pattern formed by the repetition of a single unit or shape that, when repeated, fills the plane with no gaps and no overlaps.

90
Q

Coordinate plane

A

A grid made of two main perpendicular lines, the x-axis and the y-axis.

91
Q

Origin

A

Defined by the ordered pair, sets of ordered pairs may be plotted on a coordinate plane to create different lines,rays,shapes,and so on.

92
Q

Temperature

A

Water boils at 212F or 100C, and freezes at 32F or 0C

93
Q

Translation

A

Also called a slide, simply means moving. Every translation has a direction and distance. Known as a transformation that moves a geometric figure by sliding.

94
Q

Linear measurement

A

Customary units of length include inches,feet,yards,and miles

95
Q

Measurement of mass

A

Customary units of weight include ounces,pounds and tons

96
Q

Volume

A

Customary units of capacity unclude teaspoons, tablespoons,cups, pints,quats, and gallons

97
Q

Metric units

A

Units of length include millimeters, centimeters, meters, and kilometers

98
Q

Measurement of mass

A

Metric units of weight include grams and kilograms

99
Q

Volume measurement

A

Metric units of capacity include milliliters and liters

100
Q

Deductive reasoning

A

Requires moving from an assumption to a conclusion.

example: “It is raining so i need to take my umbrella to school”

101
Q

Inductive reasoning

A

Involves examining particular instances to come to some general assumptions. This type of reasoning is informal and intuitive.
example: If I do my homework all this week, I think my mother will take me to the concert on Saturday”

102
Q

Axiomatic Structure

A

A mathematical rule, This basic assumption about a system allows theorems to be developed
example: The system could be the points and lines in the plane, then an axiom would be that given any two distinct points in the plane, there is a unique straight line through them.

103
Q

Range of a set data

A

The difference between the greatest and the least numbers in the data set. subtract these numbers to find the difference, which is the range.

104
Q

The mean of data

A

The average of the data values. To find the mean, add all the data values and then divide this sum by the number of values in the set.

105
Q

The median of data

A

The middle value of all the numbers, to find the middle value, list the numbers in order from the least to greatest or from greatest to least. Cross out one value on each end of the list until you reach the middle.

106
Q

The mode of data

A

The value or values that appear in a set of data more frequently

107
Q

Probability

A

A way of describing the likelihood of a particular outcome.

108
Q

Basics to probability and statistics

A

Data collection, sampling, organizing and representing data, interpreting data, assigning probabilities, making inferences

109
Q

Sample space

A

Is the set of all possible outcomes of an experiment.

110
Q

Line plot

A

represents a set of data by showing how often a piece of data appears in that set

Ec-6 (3 decks)

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