TExES Core Subjects EC-6 (291)
Mathematics Diagnostic Test
A newscaster commenting on President Obama's interest in opening American markets to
more Asian trade indicated that at the beginning of his presidency, Obama had opposed this
idea, but now he was promoting it. To conceptualize this change of heart, he suggested that
President Obama had undergone a 360-degree change in his stance. From a mathematical
point of view, what is the problem with this characterization of the Obama policy?
A. The president's policy is being presented by the newscaster in a subjective manner. B.
Having a 360-degree change is an exaggeration.
C. The use of the 360-degree allusion implies that the president has not changed his policy
at all.
D. He misled the audience because most Americans are not familiar with how the
mathematical concept of degree can be used in politics. - ANS-(C) Mathematically, if you
make a 360-degree change, you end up in the position that you started from. The
newscaster should have stated that the president had made a 180-degree shift if he wanted
to imply that he had changed his position. Based on this explanation, the rest of the options
are ruled out. (802-001 Instruction in Mathematics) Anu has a pocket full of change. She
has a total of 3 quarters, 7 dimes, and 10 nickels. She goes to the vending machine to
purchase a soda. What is the probability that Anu will pull out 60 cents if she reaches into
her pocket twice, removes a single coin on each draw, and does not place the coin back in
her pocket before drawing the second coin?
A. 0.16%
B. 43%
C. 0%
D. 6% - ANS-(C) The correct answer is (C). The problem asks you to analyze the
probability of Anu removing $0.60 from her pocket while only removing a single coin from her
pocket on 2 consecutive opportunities. Knowing that with the specific coins in Anu's pockets
(3 quarters, 7 dimes, and 10 nickels) there is no way for any 2 coins to sum to $0.60 reveals
a probability of 0 that this can happen. (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. The students
should include which of the following statements 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. - ANS-(B) The sum of complementary angles must equal 90°.
(802-004 Geometry and Measurement)
Carlos wanted to bring cookies for the entire school. He is going to bring in 400 cookies in
bags. If each bag can hold 38 cookies, how many bags will he need?
A. 10.52
B. 10
C. 12
, D. 11 - ANS-(D) Divide the number of cookies by the number of cookies that can fit in a
single bag to determine how many bags Carlos will need to package the cookies for his
classmates. Using a technique called dimensional analysis, we can see that the answer will
then have the units of bag (or bags). # cookies divided by # cookies/bag, and using our
properties of division with fractions we can change this to be # cookies x # bag/cookies .
Since cookies are both in the numerator and the denominator, these cancel and our answer
when using the actual numbers will be shown in units of bags. This produces 10.52 bags.
We round up to 11 because we were counting the bags because Carlos cannot have even a
fraction of a bag. (802-006 Mathematical Processes)
Within three weeks, Dana consumes 2 gallons of milk. How many gallons of milk would she
use in 9 weeks?
A. 5
B. 6
C. 13.5
D. 7 - ANS-(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)
How many unique factors are there for the number 9?
A. 3
B. 4
C. 2
D. None of the above. - ANS-(A) In order to make 9 using multiplication, one can multiply 1
and 9 or one can multiply 3 and 3. The problem asks for the unique factors are 1, 3, and 9.
(802-002 Concepts and Operations of Numbers) 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. 730
C. 1130
D. 1230 - ANS-(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 Statistics and Probability) 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 - ANS-(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. The remaining options are ruled out based on this
explanation. (802-001 Mathematics Instruction)
Jennifer Gray, a third grade teacher, took her class grocery shopping at the local
supermarket. She organized the class in groups of five and guided them to study and
purchase products based on best value and caloric content of the products. The goal is to
Mathematics Diagnostic Test
A newscaster commenting on President Obama's interest in opening American markets to
more Asian trade indicated that at the beginning of his presidency, Obama had opposed this
idea, but now he was promoting it. To conceptualize this change of heart, he suggested that
President Obama had undergone a 360-degree change in his stance. From a mathematical
point of view, what is the problem with this characterization of the Obama policy?
A. The president's policy is being presented by the newscaster in a subjective manner. B.
Having a 360-degree change is an exaggeration.
C. The use of the 360-degree allusion implies that the president has not changed his policy
at all.
D. He misled the audience because most Americans are not familiar with how the
mathematical concept of degree can be used in politics. - ANS-(C) Mathematically, if you
make a 360-degree change, you end up in the position that you started from. The
newscaster should have stated that the president had made a 180-degree shift if he wanted
to imply that he had changed his position. Based on this explanation, the rest of the options
are ruled out. (802-001 Instruction in Mathematics) Anu has a pocket full of change. She
has a total of 3 quarters, 7 dimes, and 10 nickels. She goes to the vending machine to
purchase a soda. What is the probability that Anu will pull out 60 cents if she reaches into
her pocket twice, removes a single coin on each draw, and does not place the coin back in
her pocket before drawing the second coin?
A. 0.16%
B. 43%
C. 0%
D. 6% - ANS-(C) The correct answer is (C). The problem asks you to analyze the
probability of Anu removing $0.60 from her pocket while only removing a single coin from her
pocket on 2 consecutive opportunities. Knowing that with the specific coins in Anu's pockets
(3 quarters, 7 dimes, and 10 nickels) there is no way for any 2 coins to sum to $0.60 reveals
a probability of 0 that this can happen. (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. The students
should include which of the following statements 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. - ANS-(B) The sum of complementary angles must equal 90°.
(802-004 Geometry and Measurement)
Carlos wanted to bring cookies for the entire school. He is going to bring in 400 cookies in
bags. If each bag can hold 38 cookies, how many bags will he need?
A. 10.52
B. 10
C. 12
, D. 11 - ANS-(D) Divide the number of cookies by the number of cookies that can fit in a
single bag to determine how many bags Carlos will need to package the cookies for his
classmates. Using a technique called dimensional analysis, we can see that the answer will
then have the units of bag (or bags). # cookies divided by # cookies/bag, and using our
properties of division with fractions we can change this to be # cookies x # bag/cookies .
Since cookies are both in the numerator and the denominator, these cancel and our answer
when using the actual numbers will be shown in units of bags. This produces 10.52 bags.
We round up to 11 because we were counting the bags because Carlos cannot have even a
fraction of a bag. (802-006 Mathematical Processes)
Within three weeks, Dana consumes 2 gallons of milk. How many gallons of milk would she
use in 9 weeks?
A. 5
B. 6
C. 13.5
D. 7 - ANS-(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)
How many unique factors are there for the number 9?
A. 3
B. 4
C. 2
D. None of the above. - ANS-(A) In order to make 9 using multiplication, one can multiply 1
and 9 or one can multiply 3 and 3. The problem asks for the unique factors are 1, 3, and 9.
(802-002 Concepts and Operations of Numbers) 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. 730
C. 1130
D. 1230 - ANS-(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 Statistics and Probability) 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 - ANS-(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. The remaining options are ruled out based on this
explanation. (802-001 Mathematics Instruction)
Jennifer Gray, a third grade teacher, took her class grocery shopping at the local
supermarket. She organized the class in groups of five and guided them to study and
purchase products based on best value and caloric content of the products. The goal is to
