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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
Q

What is the Inverse Property of Addition?

A

For every a, there exists a number -a such that a + (-a) = 0

This property states that adding a number and its opposite results in a sum equal to 0.

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26
Q

What is the Inverse Property of Multiplication?

A

For every a (a ≠ 0), there exists a number 1/a such that a * (1/a) = 1

This property states that multiplying a number and its multiplicative inverse results in a product equal to 1.

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27
Q

What does the Distributive Property of Multiplication over Addition state?

A

a(b + c) = ab + ac

This property states that multiplying a sum is the same as multiplying each addend by that number, then adding their products.

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28
Q

What does the Distributive Property of Multiplication over Subtraction state?

A

a(b - c) = ab - ac

This property states that multiplying a difference is the same as multiplying the minuend and subtrahend by that number, then subtracting their products.

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29
Q
A
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30
Q

What was Michael’s average mileage last month?

A

5 miles per day

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31
Q

What was Michael’s average mileage this month?

A

6 miles per day

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32
Q

How do you find the percent of change?

A

Percent of change = (new number - original number) / original number

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33
Q

What does a positive percent indicate?

A

An increase

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34
Q

What does a negative percent indicate?

A

A decrease

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35
Q

What is the formula to convert a fraction to a decimal?

A

Divide the numerator by the denominator

36
Q

What is the next step after converting a fraction to a decimal?

A

Convert the decimal to a percent

37
Q

What is the percent of increase for Michael’s mileage?

38
Q

Fill in the blank: The percent of change was an _______ if the percent is positive.

39
Q

Fill in the blank: The percent of change was a _______ if the percent is negative.

41
Q

What is the result of dividing a number by zero?

A

Undefined

A denominator of zero makes no sense in mathematics.

42
Q

What is the sum of two odd numbers?

A

Always even.

43
Q

What is the sum of two even numbers?

A

Always even.

44
Q

What type of number is 1 categorized as?

A

Neither prime nor composite.

45
Q

What is unique about the number 2 in terms of prime numbers?

A

It is the only even prime number.

46
Q

Is 0 an even number?

47
Q

Define an odd number.

A

A number that is not divisible by 2.

48
Q

Define an even number.

A

A number that is divisible by 2.

49
Q

Define a prime number.

A

A positive integer that only has 1 and itself as factors.

50
Q

Provide examples of prime numbers.

51
Q

Define a composite number.

A

A positive integer that has factors other than 1 and itself.

52
Q

Provide examples of composite numbers.

A
  • 4
  • 12
  • 27
  • 44
53
Q

What is a rational number?

A

Any number that can be written as a fraction a/b, where a and b are integers.

54
Q

What are integers?

A
  • -5
  • -4
  • -3
  • -2
  • -1
  • 0
  • 1
  • 2
  • 3
  • 4
  • 5
55
Q

What are whole numbers?

A
  • 0
  • 1
  • 2
  • 3
  • 4
  • 5
  • 6
56
Q

What are counting numbers?

A
  • 1
  • 2
  • 3
  • 4
  • 5
  • 6
57
Q

What is the greatest common factor (GCF)?

A

The largest factor that two or more numbers have in common.

58
Q

What is prime factorization?

A

Expressing a number as the product of its prime factors.

59
Q

What is the real number system?

A

A classification of all numbers including rational and irrational numbers.

60
Q

What is a terminating decimal?

A

A decimal that has a finite number of digits.

61
Q

What is a repeating decimal?

A

A decimal that has a digit or group of digits that repeats indefinitely.

63
Q

What is prime factorization?

A

Finding all the prime numbers that multiply together to result in a composite number

For example, the prime factorization of 24 is 2²·3 or 2³·3.

64
Q

How can prime factorization be found?

A

Using factor trees

A factor tree breaks down a number into its prime factors.

65
Q

What is the greatest common factor (GCF)?

A

The largest number that divides into all numbers in a given set

The GCF can only be as large as the smallest number in the set.

66
Q

What is the least common multiple (LCM)?

A

The smallest multiple that all the numbers in a set have in common

For elementary students, multiples can be found by skip counting.

67
Q

What is one method for finding the GCF or LCM?

A

Using a list

The method of using a list becomes less practical with larger numbers.

68
Q

What is the GCF of 8 and 12?

A

The pair of 2s they have in common

Multiplying the common factors gives the GCF. If no common factors exist, the GCF is 1.

69
Q

What are the prime factors of 8?

A

2 and 2

8 can be expressed as (2)(2)(2).

70
Q

What are the prime factors of 12?

A

2 and 3

12 can be expressed as (2)(2)(3).

71
Q

How do you find the LCM of 8 and 12?

A

Multiply each factor the greatest number of times it occurs between the numbers

The 2 occurs three times in 8 and the 3 occurs only once in 12.

72
Q

Fill in the blank: The GCF of 8 and 12 is ______.

73
Q

Fill in the blank: The LCM of 8 and 12 is ______.

74
Q

True or False: The method of using a list to find GCF or LCM is practical for large numbers.

75
Q

What happens if no common factors exist when finding the GCF?

A

The GCF is 1

This indicates that the numbers are coprime.

76
Q

What is the role of prime factorization in determining GCF and LCM?

A

It is a method for finding both

Prime factorization simplifies the process of identifying common factors and multiples.

78
Q

What is the estimated value of 412 + 58 + 1,780 when rounded to the greatest place value?

A

2,460

This estimation is achieved by rounding each number to the nearest hundred.

79
Q

How would you estimate the sum of 412 + 58 + 1,780 using rounding?

A

400 + 60 + 2,000 = 2,460

Rounding each number to the nearest hundred simplifies the calculation.

80
Q

What is the estimated value of 42 + 38 + 41 using clustering?

A

40 + 40 + 40 + 40 = 160

Clustering involves estimating sums when numbers are close to a single value.

81
Q

How do you estimate 31.8 + 5.2?

A

30 + 5 = 35

This estimation involves rounding both numbers to compatible pairs for easier addition.

82
Q

What are the three types of estimation strategies?

A
  • Rounding
  • Clustering
  • Compatible numbers

Each strategy is helpful in different situations for finding rough calculations.

83
Q

Define estimation in the context of mathematics.

A

Finding a rough calculation or approximation.

Estimation helps assess the reasonableness of a solution.

84
Q

True or False: Estimation is a strategy used to arrive at an exact answer.

A

False

Estimation is intended for approximations rather than exact calculations.

85
Q

Fill in the blank: Estimation can help assess the _______ of a solution.

A

reasonableness

This aspect of estimation is crucial in problem-solving.

Praxis 5003 KJ (3 decks)

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