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Praxis 5003 KJ > Numbers And Operations > Flashcards

Numbers And Operations Flashcards

1
Q

What is an addend?

A

A number that is added to another number

Addends are the numbers in an addition problem.

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2
Q

What is the result of an addition operation called?

A

Sum

The sum is the total obtained after adding the addends.

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3
Q

What is the term for the result of a subtraction operation?

A

Difference

The difference is what you get when you subtract one number from another.

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4
Q

What do you call the result of a multiplication operation?

A

Product

The product is the result obtained by multiplying two or more numbers.

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5
Q

What is the term for the result of a division operation?

A

Quotient

The quotient is the result of dividing one number by another.

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6
Q

What are manipulatives used for in education?

A

To represent counting, patterns, operations, geometric figures, and formulas.

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7
Q

What are attribute blocks?

A

Blocks that come in five different geometric shapes and colors, used for sorting, patterns, and teaching attributes of geometric figures.

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8
Q

What do base 10 blocks represent?

A

Visual models in powers of 10 representing ones, tens, hundreds, and thousands.

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9
Q

How can base 10 blocks be used in teaching?

A

To teach place value, regrouping with addition or subtraction, fractions, decimals, percents, and area and volume.

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10
Q

What are tangrams used for?

A

To represent parts and wholes and often used for finding a missing value in a number sentence.

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11
Q

What are counters used for?

A

Used for sorting and counting, available in different shapes and colors.

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12
Q

What is a geoboard?

A

A pegboard grid on which students stretch rubber bands to make geometric shapes.

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13
Q

What concepts can be taught using a geoboard?

A

Basic shapes, symmetry, congruency, perimeter, and area.

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14
Q

What do fraction strips demonstrate?

A

The relationship between the numerator and denominator of a fraction and how parts relate to a whole.

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15
Q

What are snap cubes?

A

Cubes in various colors that can be snapped together from any face.

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16
Q

How can snap cubes be used in teaching?

A

To teach number sense, basic operations, counting, patterns, and place value.

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17
Q

What are tiles in education?

A

1-inch squares that come in different colors.

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18
Q

What topics can tiles be used to teach?

A

Counting, estimating, place value, multiplication, fractions, and probability.

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19
Q

What is the Commutative Property of Addition?

A

a + b = b + a

This property states that changing the order of two numbers being added does not change their sum.

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20
Q

What is the Commutative Property of Multiplication?

A

ab = ba

This property states that changing the order of two numbers being multiplied does not change their product.

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21
Q

What does the Associative Property of Addition state?

A

(a + b) + c = a + (b + c)

This property indicates that changing the grouping of the addends does not change their sum.

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22
Q

What does the Associative Property of Multiplication state?

A

(ab)c = a(bc)

This property indicates that changing the grouping of the factors does not change their product.

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23
Q

What is the Additive Identity Property?

A

a + 0 = a

This property states that adding 0 to a number does not change the value of that number.

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24
Q

What is the Multiplicative Identity Property?

A

a * 1 = a

This property states that multiplying a number by 1 does not change the value of that number.

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25
What is the Inverse Property of Addition?
For every a, there exists a number -a such that a + (-a) = 0 ## Footnote This property states that adding a number and its opposite results in a sum equal to 0.
26
What is the Inverse Property of Multiplication?
For every a (a ≠ 0), there exists a number 1/a such that a * (1/a) = 1 ## Footnote This property states that multiplying a number and its multiplicative inverse results in a product equal to 1.
27
What does the Distributive Property of Multiplication over Addition state?
a(b + c) = ab + ac ## Footnote This property states that multiplying a sum is the same as multiplying each addend by that number, then adding their products.
28
What does the Distributive Property of Multiplication over Subtraction state?
a(b - c) = ab - ac ## Footnote This property states that multiplying a difference is the same as multiplying the minuend and subtrahend by that number, then subtracting their products.
29
30
What was Michael's average mileage last month?
5 miles per day
31
What was Michael's average mileage this month?
6 miles per day
32
How do you find the percent of change?
Percent of change = (new number - original number) / original number
33
What does a positive percent indicate?
An increase
34
What does a negative percent indicate?
A decrease
35
What is the formula to convert a fraction to a decimal?
Divide the numerator by the denominator
36
What is the next step after converting a fraction to a decimal?
Convert the decimal to a percent
37
What is the percent of increase for Michael's mileage?
20%
38
Fill in the blank: The percent of change was an _______ if the percent is positive.
increase
39
Fill in the blank: The percent of change was a _______ if the percent is negative.
decrease
40
41
What is the result of dividing a number by zero?
Undefined ## Footnote A denominator of zero makes no sense in mathematics.
42
What is the sum of two odd numbers?
Always even.
43
What is the sum of two even numbers?
Always even.
44
What type of number is 1 categorized as?
Neither prime nor composite.
45
What is unique about the number 2 in terms of prime numbers?
It is the only even prime number.
46
Is 0 an even number?
Yes.
47
Define an odd number.
A number that is not divisible by 2.
48
Define an even number.
A number that is divisible by 2.
49
Define a prime number.
A positive integer that only has 1 and itself as factors.
50
Provide examples of prime numbers.
* 2 * 3 * 13 * 29
51
Define a composite number.
A positive integer that has factors other than 1 and itself.
52
Provide examples of composite numbers.
* 4 * 12 * 27 * 44
53
What is a rational number?
Any number that can be written as a fraction a/b, where a and b are integers.
54
What are integers?
* -5 * -4 * -3 * -2 * -1 * 0 * 1 * 2 * 3 * 4 * 5
55
What are whole numbers?
* 0 * 1 * 2 * 3 * 4 * 5 * 6
56
What are counting numbers?
* 1 * 2 * 3 * 4 * 5 * 6
57
What is the greatest common factor (GCF)?
The largest factor that two or more numbers have in common.
58
What is prime factorization?
Expressing a number as the product of its prime factors.
59
What is the real number system?
A classification of all numbers including rational and irrational numbers.
60
What is a terminating decimal?
A decimal that has a finite number of digits.
61
What is a repeating decimal?
A decimal that has a digit or group of digits that repeats indefinitely.
62
63
What is prime factorization?
Finding all the prime numbers that multiply together to result in a composite number ## Footnote For example, the prime factorization of 24 is 2²·3 or 2³·3.
64
How can prime factorization be found?
Using factor trees ## Footnote A factor tree breaks down a number into its prime factors.
65
What is the greatest common factor (GCF)?
The largest number that divides into all numbers in a given set ## Footnote The GCF can only be as large as the smallest number in the set.
66
What is the least common multiple (LCM)?
The smallest multiple that all the numbers in a set have in common ## Footnote For elementary students, multiples can be found by skip counting.
67
What is one method for finding the GCF or LCM?
Using a list ## Footnote The method of using a list becomes less practical with larger numbers.
68
What is the GCF of 8 and 12?
The pair of 2s they have in common ## Footnote Multiplying the common factors gives the GCF. If no common factors exist, the GCF is 1.
69
What are the prime factors of 8?
2 and 2 ## Footnote 8 can be expressed as (2)(2)(2).
70
What are the prime factors of 12?
2 and 3 ## Footnote 12 can be expressed as (2)(2)(3).
71
How do you find the LCM of 8 and 12?
Multiply each factor the greatest number of times it occurs between the numbers ## Footnote The 2 occurs three times in 8 and the 3 occurs only once in 12.
72
Fill in the blank: The GCF of 8 and 12 is ______.
4
73
Fill in the blank: The LCM of 8 and 12 is ______.
24
74
True or False: The method of using a list to find GCF or LCM is practical for large numbers.
False
75
What happens if no common factors exist when finding the GCF?
The GCF is 1 ## Footnote This indicates that the numbers are coprime.
76
What is the role of prime factorization in determining GCF and LCM?
It is a method for finding both ## Footnote Prime factorization simplifies the process of identifying common factors and multiples.
77
78
What is the estimated value of 412 + 58 + 1,780 when rounded to the greatest place value?
2,460 ## Footnote This estimation is achieved by rounding each number to the nearest hundred.
79
How would you estimate the sum of 412 + 58 + 1,780 using rounding?
400 + 60 + 2,000 = 2,460 ## Footnote Rounding each number to the nearest hundred simplifies the calculation.
80
What is the estimated value of 42 + 38 + 41 using clustering?
40 + 40 + 40 + 40 = 160 ## Footnote Clustering involves estimating sums when numbers are close to a single value.
81
How do you estimate 31.8 + 5.2?
30 + 5 = 35 ## Footnote This estimation involves rounding both numbers to compatible pairs for easier addition.
82
What are the three types of estimation strategies?
* Rounding * Clustering * Compatible numbers ## Footnote Each strategy is helpful in different situations for finding rough calculations.
83
Define estimation in the context of mathematics.
Finding a rough calculation or approximation. ## Footnote Estimation helps assess the reasonableness of a solution.
84
True or False: Estimation is a strategy used to arrive at an exact answer.
False ## Footnote Estimation is intended for approximations rather than exact calculations.
85
Fill in the blank: Estimation can help assess the _______ of a solution.
reasonableness ## Footnote This aspect of estimation is crucial in problem-solving.

Praxis 5003 KJ (3 decks)

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