Math
In a bag there are 12 green marbles, 11 red marbles, and 7 blue marbles. What is
the probability of drawing a blue marble?
A. 7.4
B. 7/30
C. 11/30
D. 12/30 - correct answer-B.
(B) Since there are 7 blue marbles and a total of 30 marbles in the bag, the odds of
drawing a blue marble are 7/30. (802-005 Probability and Statistics)
As a formative assessment, Mr. Williams asked his students to create and draw a
map of the town. Johana and Giovani drew complementary angles for their roads.
Which of the following statements should the students include in their angle
explanations?
A. Complementary angles are each 90°.
B. Complementary angles are made of two angles whose sum is 90°.
C. Complementary angles are made of two angles whose sum is 180°.
D. None of the above. - correct answer-B.
(B) The sum of complementary angles must equal 90°. (802-004 Geometry and
Measurement)
In the Texas curriculum, the teaching of place value is required in which of the
following?
A. First grade
B. Third grade
C. Kindergarten
D. Fourth grade - correct answer-A.
A) One of the primary focal areas in grade 1 is the teaching of place value as a way
to teach problems involving addition and subtraction. Teaching place values
represent a concrete way to teach basic arithmetic in a tangible fashion. In second
,grade this continues being a focal point to aid in building a foundation to teach
multiplication. In grade 6, place values continue being used to teach number and
operation, parts-to-whole relationships and equivalence. Based on this explanation,
the rest of the options are ruled out. (802-001 Mathematics Instruction)
What is the probability of rolling a 7 with a pair of dice?
A. 1/6
B. 1/36
C. 1/12
D. 5/36 - correct answer-A.
(A) With a pair of dice there are 36 different combinations of outcomes. Of the 36
outcomes there are 6 different ways to roll a 7: 1 + 6, 2 + 5, 3 + 4, 4 + 3, 5 + 2, 6 + 1.
Note that 1 + 6 is not the same as 6 + 1. If one die is green and the other red, 1 red,
6 green is not the same as 6 red, 1 green. Therefore there is a 6/36 chance of rolling
a 7. This may be simplified to 1/6. (802-005 Probability and Statistics)
What is 7.5−4 1/4 represented as a decimal?
A. 1.75
B. 2.25
C. 3.35
D. 3.25 - correct answer-D.
(D) There are numerous methods that can be used to solve this problem. Since the
problem asks for the answer as a decimal, we will convert all numbers into decimal
form before carrying out any other operation. The fraction represented as a decimal
is 4.25. Subtracting this from 7.5 yields a difference of 3.25. (802-002 Number
Concepts and Operations)
What is 5 less than three times a number represented as?
A. (5−x)3
B. (x−5)3
C. (x−5)/3
D. 3x−5 - correct answer-D.
(D) To find the proper representation of the question it is easiest to work backwards.
5 less than three times a number means that we are subtracting 5 from a number
multiplied by 3. Therefore, we multiply a number x by 3 and then subtract 5.
(802-002 Number Concepts and Operations)
What is the result when 7x^5 and 5x^4 are multiplied together?
,A. 12x^9
B. 35x^9
C. 35x^20
D. 12x^20 - correct answer-B.
(B) When multiplying exponential numbers, we multiply the constant terms and then
add the exponents of the terms with the same base. So, we multiply the constants 7
and 5 to obtain 35 and then add the 5 and 4 exponents associated with the x base.
(802-003 Patterns and Algebra)
What is one of the greatest accomplishments achieved by the Babylonians?
A. Concept of 0
B. Rational numbers cannot accurately express all mathematical values
C. Base-60 number system
D. Angles at the base of an isosceles triangle are equal - correct answer-C.
(C) Typically the Arabs are given credit for incorporating the concept of 0 in our
current number system. The Greeks are given credit for the equal angles at the base
of an isosceles triangle and for discovering that rational numbers cannot accurately
express all mathematical values. The Babylonians implemented a base-60 number
system. (802-006 Mathematical Processes)
The use of digital cameras, balanced metric weight sets, and virtual manipulatives
available on the Internet is most appropriate for children in which of the following
grade levels?
A. Grades 1 to 6
B. Upper elementary
C. Kindergarten to grade 2
D. Grade 6 - correct answer-B.
(B) The use of electronic equipment, virtual manipulatives, and devices to measure
using the metric system are generally used in upper elementary. Teaching the metric
system begins in third or fourth grade. Allowing young learners (K-2) the use of
digital cameras can be risky. Students in early childhood enjoy working with objects
that they can touch and manage. The use of virtual manipulatives is less concrete
, than physical ones, and for that reason they are more effective with children in upper
elementary. (802-001 Mathematics Instruction)
What is an example of a rational number? - correct answer-15/4
When represented in decimal format is 3.75. Recalling that an irrational number is
one which cannot be represented by a fraction and whose decimal form never
repeats or ends (it cannot be represented by a ratio of integers.
Solve the following equation for x
44−7x=3x+5+7x−4x
A. 39
B. 93
C. 3
D. 9 - correct answer-(C) In this problem we are asked to find the value of x. In order
to aid in solving this problem we want to group like terms and simplify. Therefore, the
first step is to group all of the terms associated with x on one side of the equals sign
and all of the constant whole numbers on the other. Once this is done we are left
with 13x=39. To solve for x we divide both the left and right hand sides of the
equation by 13 to isolate the variable. When this is done we are left with x=3.
(802-003 Patterns and Algebra)
Dana uses 2 gallons of milk in 3 weeks. How many gallons of milk would she use in
9 weeks?
A. 5
B. 6
C. 13.5
D. 7 - correct answer-B.
(B) This problem can be solved multiple ways. One method is to set up a
proportional problem. This can be done by placing the number of gallons she uses
over the time period in which they are used. (2 gallons)/(3 weeks)= (x gallons)/(9
weeks). Multiplying both sides of the equation by 9 weeks to find out how many will
be used in this amount of time we obtain gallons = (9 weeks x 2 gallons)/(3
weeks)=6 gallons. (802-003 Patterns and Algebra)
In a bag there are 12 green marbles, 11 red marbles, and 7 blue marbles. What is
the probability of drawing a blue marble?
A. 7.4
B. 7/30
C. 11/30
D. 12/30 - correct answer-B.
(B) Since there are 7 blue marbles and a total of 30 marbles in the bag, the odds of
drawing a blue marble are 7/30. (802-005 Probability and Statistics)
As a formative assessment, Mr. Williams asked his students to create and draw a
map of the town. Johana and Giovani drew complementary angles for their roads.
Which of the following statements should the students include in their angle
explanations?
A. Complementary angles are each 90°.
B. Complementary angles are made of two angles whose sum is 90°.
C. Complementary angles are made of two angles whose sum is 180°.
D. None of the above. - correct answer-B.
(B) The sum of complementary angles must equal 90°. (802-004 Geometry and
Measurement)
In the Texas curriculum, the teaching of place value is required in which of the
following?
A. First grade
B. Third grade
C. Kindergarten
D. Fourth grade - correct answer-A.
A) One of the primary focal areas in grade 1 is the teaching of place value as a way
to teach problems involving addition and subtraction. Teaching place values
represent a concrete way to teach basic arithmetic in a tangible fashion. In second
,grade this continues being a focal point to aid in building a foundation to teach
multiplication. In grade 6, place values continue being used to teach number and
operation, parts-to-whole relationships and equivalence. Based on this explanation,
the rest of the options are ruled out. (802-001 Mathematics Instruction)
What is the probability of rolling a 7 with a pair of dice?
A. 1/6
B. 1/36
C. 1/12
D. 5/36 - correct answer-A.
(A) With a pair of dice there are 36 different combinations of outcomes. Of the 36
outcomes there are 6 different ways to roll a 7: 1 + 6, 2 + 5, 3 + 4, 4 + 3, 5 + 2, 6 + 1.
Note that 1 + 6 is not the same as 6 + 1. If one die is green and the other red, 1 red,
6 green is not the same as 6 red, 1 green. Therefore there is a 6/36 chance of rolling
a 7. This may be simplified to 1/6. (802-005 Probability and Statistics)
What is 7.5−4 1/4 represented as a decimal?
A. 1.75
B. 2.25
C. 3.35
D. 3.25 - correct answer-D.
(D) There are numerous methods that can be used to solve this problem. Since the
problem asks for the answer as a decimal, we will convert all numbers into decimal
form before carrying out any other operation. The fraction represented as a decimal
is 4.25. Subtracting this from 7.5 yields a difference of 3.25. (802-002 Number
Concepts and Operations)
What is 5 less than three times a number represented as?
A. (5−x)3
B. (x−5)3
C. (x−5)/3
D. 3x−5 - correct answer-D.
(D) To find the proper representation of the question it is easiest to work backwards.
5 less than three times a number means that we are subtracting 5 from a number
multiplied by 3. Therefore, we multiply a number x by 3 and then subtract 5.
(802-002 Number Concepts and Operations)
What is the result when 7x^5 and 5x^4 are multiplied together?
,A. 12x^9
B. 35x^9
C. 35x^20
D. 12x^20 - correct answer-B.
(B) When multiplying exponential numbers, we multiply the constant terms and then
add the exponents of the terms with the same base. So, we multiply the constants 7
and 5 to obtain 35 and then add the 5 and 4 exponents associated with the x base.
(802-003 Patterns and Algebra)
What is one of the greatest accomplishments achieved by the Babylonians?
A. Concept of 0
B. Rational numbers cannot accurately express all mathematical values
C. Base-60 number system
D. Angles at the base of an isosceles triangle are equal - correct answer-C.
(C) Typically the Arabs are given credit for incorporating the concept of 0 in our
current number system. The Greeks are given credit for the equal angles at the base
of an isosceles triangle and for discovering that rational numbers cannot accurately
express all mathematical values. The Babylonians implemented a base-60 number
system. (802-006 Mathematical Processes)
The use of digital cameras, balanced metric weight sets, and virtual manipulatives
available on the Internet is most appropriate for children in which of the following
grade levels?
A. Grades 1 to 6
B. Upper elementary
C. Kindergarten to grade 2
D. Grade 6 - correct answer-B.
(B) The use of electronic equipment, virtual manipulatives, and devices to measure
using the metric system are generally used in upper elementary. Teaching the metric
system begins in third or fourth grade. Allowing young learners (K-2) the use of
digital cameras can be risky. Students in early childhood enjoy working with objects
that they can touch and manage. The use of virtual manipulatives is less concrete
, than physical ones, and for that reason they are more effective with children in upper
elementary. (802-001 Mathematics Instruction)
What is an example of a rational number? - correct answer-15/4
When represented in decimal format is 3.75. Recalling that an irrational number is
one which cannot be represented by a fraction and whose decimal form never
repeats or ends (it cannot be represented by a ratio of integers.
Solve the following equation for x
44−7x=3x+5+7x−4x
A. 39
B. 93
C. 3
D. 9 - correct answer-(C) In this problem we are asked to find the value of x. In order
to aid in solving this problem we want to group like terms and simplify. Therefore, the
first step is to group all of the terms associated with x on one side of the equals sign
and all of the constant whole numbers on the other. Once this is done we are left
with 13x=39. To solve for x we divide both the left and right hand sides of the
equation by 13 to isolate the variable. When this is done we are left with x=3.
(802-003 Patterns and Algebra)
Dana uses 2 gallons of milk in 3 weeks. How many gallons of milk would she use in
9 weeks?
A. 5
B. 6
C. 13.5
D. 7 - correct answer-B.
(B) This problem can be solved multiple ways. One method is to set up a
proportional problem. This can be done by placing the number of gallons she uses
over the time period in which they are used. (2 gallons)/(3 weeks)= (x gallons)/(9
weeks). Multiplying both sides of the equation by 9 weeks to find out how many will
be used in this amount of time we obtain gallons = (9 weeks x 2 gallons)/(3
weeks)=6 gallons. (802-003 Patterns and Algebra)
