Final Exam Flashcards
1
Q
_______ + _______ = ________
A
Addend + Addend = Sum
2
Q
_______ - _______ = ________
A
minuend - subtrahend = difference
3
Q
_______ x _______ = ________
A
factor x factor = product
4
Q
_______ / _______ = ________
A
dividend / divisor = quotient
5
Q
Zero can be a ____
A
Dividend
6
Q
Zero CANNOT be a ___
A
Divisor
7
Q
Define a Fact Family
A
A collection (+,-,x,/) of related number sentences that all use the same numbers.
8
Q
Define a scenario
A
A setting or context that helps children decide whether they should +,-,x, or /.
9
Q
Counting Numbers
A
1, 2, 3, 4, 5… (Pre-K)
10
Q
Whole Numbers
A
0, 1, 2, 3, 4, 5… (K-4th)
11
Q
Integers (Signed #s)
A
The whole numbers together with their opposites (neg).
…, -3, -2, -1, 0, 1, 2, 3…
12
Q
Is zero even or odd?
A
Even
13
Q
Is zero positive or negative?
A
Neither!
14
Q
Pos x pos =
neg x neg =
neg x pos =
pos x neg=
A
pos
pos
neg
neg
15
Q
neg / neg =
pos / neg =
neg/ pos =
pos/ pos =
A
pos
neg
neg
pos
16
Q
pos + neg =
neg + pos =
neg + neg =
pos + pos =
A
either
either
neg
pos
17
Q
pos - pos =
neg - neg =
neg- pos =
pos - neg =
A
either
either
neg
pos
18
Q
Number Sentence Pattern
A
List of changing number sentences that use familiar knowledge to get unfamiliar integer answers. Starts with 3 familiar number sentences.
3 - 3 = 0
3- 2 = 1
3 - 1 = 0
3 - 0 = 3
3 - (-1) = 4
etc.
19
Q
What is the purpose of decimal numbers?
A
To extend the idea of place value to allow fractional values.
20
Q
Define place value
A
concept; the value of a digit (0-9) is partly determined by where that digit is placed.
21
Q
Word Forms: Hundreds, tens, ones, ., tenths, hundredths, thousandths, ten thousandths
A
Exponents: 10^2, 1^1, 10^0, 10^-1, 10^-2, 10^-3, 10^-4
22
Q
Standard Form Example
A
300.017
23
Q
Word Form Example
A
Three hundred and seventeen thousandths
24
Q
Expanded Form Example
A
3 x 100 + 1 x 1/100 + 7 x 1/1,000
25
Expanded Form With Exponents Example
3 x 10^2 + 1 x 10^-2 + 7 x 10^-3
26
Define Algorithms
A step-by-step process for doing something
27
5 Rules of Division
1- The dividends point moves the same number of positions as the divisor point.
2-Why? It is a shortcut for fraction work
3- the quotient's decimal point moves straight up from the dividend's new point
4- Why? we choose to use partitioning division and the DIVIDEND AND QUOTIENT are the SAME KINDS OF THINGS in partitioning.
5- The divisor's point moves to create a whole number. Why? In partitioning the divisor tells how many groups to make.
28
What are the Addition Scenario(s) - Whole #
1- Combine Scenario
29
What are the Subtraction Scenario(s) - Whole #
1- Take-Away
2- Missing Addend
3- Comparison
30
What are the Multiplication Scenario(s) - Whole #
1- Repeated Addition
2- Array/Area
3- Cartesian Product
31
What are the Division Scenario(s) - Whole #
1- Repeated Subtraction
2- Partitioning
32
What are the Addition Scenario(s) - Fractions
1- Combine
33
What are the Subtraction Scenario(s) - Fractions
1- Take Away
2- Missing Addend
3- Comparison
34
What are the Multiplication Scenario(s) - Fractions
1- Repeated Sets/ Repeated Addition
2- Array/Area
3- Part of a Part
4- Ratio
35
What are the Division Scenario(s) - Fractions
1- Repeated Subtraction
2- Partitioning
36
Changing the order of the addends does not change the sum
Commutative Property of Addition
37
Changing the order of the factors does not change the product
Commutative Property of Multiplication
38
Changing the grouping of the addends does not change the sum
Associative Property of Addition
39
Changing the grouping of the factors does not change the product
Associative Property of Multiplication
40
Adding zero to any number leaves that number unchanged
Identity Property of Additions
41
Multiplying any number 1 leaves that number unchanged
Identity Property of Multiplication
42
Multiplying any number by 0 gives 0
Zero Property of Multiplication
43
Every property is an ______
Equality
44
Three Decimal Appearances
1. Terminating
2. Repeating
3. Non-Terminating and Non-Repeating
45
Terminating Decimal
decimal stops after a finite number of decimal positions
ex. 0.5
Rational Number
46
Define a Rational Number
a number that can be written as a fraction of integers
47
Define an Irrational Number
A number that CANNOT be written as such a fraction.
48
Define a Real Number
Any number that that can be written using decimal notations
49
Repeating Decimal
Repeating the same exact block of numbers forever, to the right
Rational Number
50
Non-Terminating and Non-Repeating
Number does not stop and does not repeat
Irrational Number "Growing Pattern"
51
What is the concept of Denseness
The idea that between any two unequal decimal numbers there is always another.
52
"per cent"
out of 100
53
Three kinds of notation to convert
1. percent sign %
2. fractions
3. decimals
54
fraction to decimal
divide numerator / denominator
55
decimal to fraction
sometimes not possible
56
decimal to percent
multiply by 100 and attach the % sign
57
percent to decimal
divide by 100 and remove % sign
58
fraction to percent
divide to create decimal and then multiply by 100 and add the % sign
59
percent to fraction
put percent over 100
60
Non-contextual word problems (visual technique)
is over of = % over 100
61
Non-contextual word problems
1. what number is 68.4% of 23.9?
2. What % of 132 is 158?
3. 19.7 is 36.2% of what number?
62
Big Rule of %
Always take % of older number in context
63
Percent Applications
1. Percent increase/decrease
2. discount and mark up
64
Define Statistics
A field of math that involves gathering information (data), summarizing it, and deciding what it means.
65
Three types of statistics
1. Experimental statistics
2. Descriptive statistics
3. Inferential statistics
66
Define Experimental Statistics
gathering or collecting data
67
Define Descriptive Statistics
summarizing or communicate data/share with others
68
Define Inferential Statistics
make meaning or drawing conclusions from data
69
Two types of data
1. Numerical
2. Categorical
70
Central Tendency
A single number that represents the "center" of a set of data
71
Measures of spread
range, standard deviation,
72
Mode
gives the most frequent score
73
Median
the middle score, after all of the scores are put in order
74
Mean
add all of the values and divide by how many values
75
Range
biggest value - smallest value
76
Standard Deviation
the smaller it is, the closer all of the scores cluster
77
Order of Operations
PEMDAS
78
Define Exponents
When A is a real number, and n is a counting number.
79
A^m x A^n
A^m+n
80
(A^m)n
A^mxn
81
A^m / A^n
A^ m-n
82
Define Probability
A field of mathematics that studies chance or likelihood
83
4 kinds of probability
1. Intuitive probability
2. Geometric probability
3. Experimental probability
4. Theoretical probability
84
Ways to express probability
words
percent
decimal
fraction
ratio
85
Define experiment
an activity whose results can be observed and recorded.
ex. toss coin, weather
86
Define outcome
a single result that can happen in an experiment
ex. heads, snow
87
Define sample space
a set or collection of all possible outcomes for an experiment
using set notation { }
ex. {heads, tails}
88
Define event
a collection or set of (usually) related outcomes.
ex. {snow, sleet, hail}
89
How many outcomes need to be in an outcome to say that an event DID happen
One
90
Define Intuitive Probability
Uses words to describe chance
ex. certain, impossible, even chance, likely, and unlikely
91
Define Geometric Probability
The probability of events is based on their area in some shape
P(E)= area devoted to E / total area of SS
92
Define trial
performing or simulating the experiment ONE time.
93
Define Experimental Probability
finds probabilities by actually performing/simulating the experiment, and P(E) = # of times E occurred / total # of trials
94
Define Uniform Sample Space
The outcomes are equally likely
95
Define Theoretical Probability
It's based on thinking about ideal situations
P(E) = # of favorable outcomes / total # of outcomes in uniform ss
96
Define the Fundamental Counting Principle
Describes how we can count the number of ways to complete a step-by-step task
97
4 steps in the process of measurement
1. choose (be given) an attribute to measure
2. Choose (be given) appropriate units to measure the attribute
3. Line up/cover/fill the attribute with units
4. Count how many units you used and Report the answer
98
Define Personal Reference
a mental image/idea of how big a particular unit is
99
2 main systems of measurement
1. Metric system
2. English/customary system
100
What is 12 inches in feet
1 foot
101
What is 3 feet in yards
1 yard
102
What is 5,280 feet in miles
1 mile
103
What is 16 oz in lbs
1 pound
104
What is 2,000 lbs in tons
1 ton
105
What is 4 quarts in gallons
1 gallon
106
BIG IDEA for common sense/number sense
Big # of small units = small # of big units
107
Order of prefixes
kilo
hecto
deka
base
deci
centi
milli
