MTTC TEST EXAM PRACTICE QUESTIONS
WITH VERIFIED ANSWERS
1. A kindergarten teacher observes as a small group of students practice comparing
numbers and quantities using manipulatives. Each student has four counters. One
student's counters are spaced farther apart than the other students' counters, and several
members of the group claim that student has more counters than everyone else. The
teacher can build on the students' understanding of counting and cardinality by:
A. encouraging the one student to count their counters for the group.
B. identifying the error and moving the one student's counters closer together.
C. asking probing questions about the total number of counters each student has.
D. prompting the group to combine their counters and count how many they have in all.
A. Having one student count their own set of counters aloud does not address the misconception
that the number of counters in a set depends on how they are arranged.
B. This manner of addressing the misconception does not necessarily build upon the students'
understanding because the teacher did not check whether they grasped the explanation or provide
them with opportunities to explain in their own words why the total number of objects in each
group is the same.
C. CORRECT. By asking probing questions about the total number of counters each student has,
the teacher can help students move beyond a naïve conception that bigger equals more and
deepen their conceptual understanding of counting and cardinality.
D. The affordances created by combining the counters into a large group do not offer these
students more substantive insights into understanding counting and cardinality concepts than the
affordances created by using smaller groups of counters.
2. A first-grade teacher plans initial lessons on comparing number values. Which of the
following activities would be developmentally appropriate and engaging when introducing
this concept?
A. Students form multiple-digit numbers using index cards labeled with the digits 1, 2, 3,
and 4.
B. Students measure the lengths of classmates' shoes and then sort the shoes from smallest
to largest.
,C. Students discuss the values of different piles of coins, such as a pile of 5 quarters and a
pile of 5 pennies.
D. Students stand between two different quantities and arrange their arms into a greater-
than or less-than symbol.
A. This activity does not require students to compare numbers.
B. The skills required to measure and sort rational numbers—the numbers that would be used to
describe shoe lengths—are too advanced to be included in a first-grade lesson activity about
comparing number values.
C. This activity is not developmentally appropriate because the concepts of number comparison
should be introduced to students without requiring them to also apply additional mathematical
knowledge that does not directly support their understanding of these concepts.
D. CORRECT. The alignment and rigor of the activity is developmentally appropriate for
introducing first-grade students to the concept of comparing number values and the kinesthetic
activity promotes their engagement.
3. First-grade students consider the following equations.
7 = 10 − 37 = 5 + 210 − 3 = 5 + 2
Most students state that the last equation is incorrect. In order to address the students'
misconception, the teacher should plan a review of which of the following concepts?
A. meaning and function of the equal sign
B. how addition and subtraction are related
C. the use of benchmark equations to find the answer
D. the concepts of "greater than," "less than," and "equal to"
A. CORRECT. The teacher should review the meaning and function of the equal sign because
students who agree that only the first two equations are correct may be interpreting the equal sign
to be a symbol that indicates the result of the last operation (i.e., they would likely believe that
the third equation should be written as 10 − 3 = 7 + 2 or 10 − 7 = 5 + 2).
B. None of the equations shown makes use of addition and subtraction as inverse operations.
C. A review of benchmark equations (e.g., sums and differences involving 5 and 10) is not
necessary because students have previously agreed that 7 = 10 − 3 and 7 = 5 + 2.
,D. There is evidence that the students are interpreting "=" to mean "the result of the last
operation," and reviewing the concepts of "greater than" and "less than" would not address this
misconception directly or efficiently.
4. A first-grade teacher uses an activity involving dice to help students make the jump from
counting to addition. Students roll two dice, then determine the sum of the dots that are
face up. On a piece of paper, students draw their dice as an addition problem and write the
problem using numbers. One student's work is shown.
Two dice are shown above an equation. The left die shows 3 pips, the right die shows 4 pips,
and the equation reads 3 plus 4 equals 7.
The teacher can increase students' success by taking which of the following actions before
explaining the activity?
A. teaching students how to add without using a counting strategy
B. providing context by describing games in which dice may be used
C. giving students the opportunity to become familiar with dice and their dots
D. posting addition tables at the front of the room and on each student's desk
A. Students should explore the relationship between counting and addition before they learn to
add without a counting strategy.
B. Describing games in which dice may be used does not direct students' attention to attributes of
dice that makes them useful manipulatives for learning addition: the neat arrangement of dots on
the faces, the unique numbers of dots on each side, and the many different outcomes that can be
formed by rolling two dice.
C. CORRECT. Providing students with opportunities to explore manipulatives on their own
stimulates their curiosity, interest, and comfort with them and prepares students to explore how
they may be used as mathematical tools.
D. Posting addition tables does not support students' ability to understand how the mathematical
concepts used to count a single collection of objects can be extended to count two combined
collections of objects through addition.
5. The dramatic play area of a prekindergarten classroom is set up a like a kitchen, with
three-dimensional blocks standing in for plates and cups. While children work in stations
pretending to make and serve food to each other, the teacher can help the children extend
their understanding of three-dimensional attributes by asking them:
, A. to find the yellow cup.
B. which plate is their favorite.
C. to bring a certain object to the table.
D. how the plate and the cup are the same and different.
A. The color yellow and the object name "cup" are not used to describe attributes of three-
dimensional shapes.
B. This question does not direct students to focus on the three-dimensional attributes of different
plates.
C. The name of an object is not a three-dimensional attribute.
D. CORRECT. Students answer this question by describing the similarities and differences of the
three-dimensional attributes of the plate and the cup (e.g., "The plate is short and flat, and the
cup is tall", "The plate and the cup both have round edges").
6. A teacher shares this geometric pattern with the class.
A pattern formed from geometric shapes arranged in a row is shown. The shapes, from left
to right, are a triangle, a square, a pentagon, a hexagon, a triangle, and a square.
The teacher asks students to explain the order of the shapes in the pattern. As students
share their explanations, the teacher writes these student explanations on the board.
"The shapes go from smallest to biggest. Then they start over."
"They are in order by the number of corners."
"The pattern is the least number of sides to the greatest number of sides, then it starts
again."
By writing these explanations on the board, the teacher:
A. highlights the most efficient ways to explain the geometric pattern.
B. encourages students to revise their explanations if they misinterpreted the pattern.
C. offers students an entry point for collaboratively refining explanations of the geometric
pattern.
WITH VERIFIED ANSWERS
1. A kindergarten teacher observes as a small group of students practice comparing
numbers and quantities using manipulatives. Each student has four counters. One
student's counters are spaced farther apart than the other students' counters, and several
members of the group claim that student has more counters than everyone else. The
teacher can build on the students' understanding of counting and cardinality by:
A. encouraging the one student to count their counters for the group.
B. identifying the error and moving the one student's counters closer together.
C. asking probing questions about the total number of counters each student has.
D. prompting the group to combine their counters and count how many they have in all.
A. Having one student count their own set of counters aloud does not address the misconception
that the number of counters in a set depends on how they are arranged.
B. This manner of addressing the misconception does not necessarily build upon the students'
understanding because the teacher did not check whether they grasped the explanation or provide
them with opportunities to explain in their own words why the total number of objects in each
group is the same.
C. CORRECT. By asking probing questions about the total number of counters each student has,
the teacher can help students move beyond a naïve conception that bigger equals more and
deepen their conceptual understanding of counting and cardinality.
D. The affordances created by combining the counters into a large group do not offer these
students more substantive insights into understanding counting and cardinality concepts than the
affordances created by using smaller groups of counters.
2. A first-grade teacher plans initial lessons on comparing number values. Which of the
following activities would be developmentally appropriate and engaging when introducing
this concept?
A. Students form multiple-digit numbers using index cards labeled with the digits 1, 2, 3,
and 4.
B. Students measure the lengths of classmates' shoes and then sort the shoes from smallest
to largest.
,C. Students discuss the values of different piles of coins, such as a pile of 5 quarters and a
pile of 5 pennies.
D. Students stand between two different quantities and arrange their arms into a greater-
than or less-than symbol.
A. This activity does not require students to compare numbers.
B. The skills required to measure and sort rational numbers—the numbers that would be used to
describe shoe lengths—are too advanced to be included in a first-grade lesson activity about
comparing number values.
C. This activity is not developmentally appropriate because the concepts of number comparison
should be introduced to students without requiring them to also apply additional mathematical
knowledge that does not directly support their understanding of these concepts.
D. CORRECT. The alignment and rigor of the activity is developmentally appropriate for
introducing first-grade students to the concept of comparing number values and the kinesthetic
activity promotes their engagement.
3. First-grade students consider the following equations.
7 = 10 − 37 = 5 + 210 − 3 = 5 + 2
Most students state that the last equation is incorrect. In order to address the students'
misconception, the teacher should plan a review of which of the following concepts?
A. meaning and function of the equal sign
B. how addition and subtraction are related
C. the use of benchmark equations to find the answer
D. the concepts of "greater than," "less than," and "equal to"
A. CORRECT. The teacher should review the meaning and function of the equal sign because
students who agree that only the first two equations are correct may be interpreting the equal sign
to be a symbol that indicates the result of the last operation (i.e., they would likely believe that
the third equation should be written as 10 − 3 = 7 + 2 or 10 − 7 = 5 + 2).
B. None of the equations shown makes use of addition and subtraction as inverse operations.
C. A review of benchmark equations (e.g., sums and differences involving 5 and 10) is not
necessary because students have previously agreed that 7 = 10 − 3 and 7 = 5 + 2.
,D. There is evidence that the students are interpreting "=" to mean "the result of the last
operation," and reviewing the concepts of "greater than" and "less than" would not address this
misconception directly or efficiently.
4. A first-grade teacher uses an activity involving dice to help students make the jump from
counting to addition. Students roll two dice, then determine the sum of the dots that are
face up. On a piece of paper, students draw their dice as an addition problem and write the
problem using numbers. One student's work is shown.
Two dice are shown above an equation. The left die shows 3 pips, the right die shows 4 pips,
and the equation reads 3 plus 4 equals 7.
The teacher can increase students' success by taking which of the following actions before
explaining the activity?
A. teaching students how to add without using a counting strategy
B. providing context by describing games in which dice may be used
C. giving students the opportunity to become familiar with dice and their dots
D. posting addition tables at the front of the room and on each student's desk
A. Students should explore the relationship between counting and addition before they learn to
add without a counting strategy.
B. Describing games in which dice may be used does not direct students' attention to attributes of
dice that makes them useful manipulatives for learning addition: the neat arrangement of dots on
the faces, the unique numbers of dots on each side, and the many different outcomes that can be
formed by rolling two dice.
C. CORRECT. Providing students with opportunities to explore manipulatives on their own
stimulates their curiosity, interest, and comfort with them and prepares students to explore how
they may be used as mathematical tools.
D. Posting addition tables does not support students' ability to understand how the mathematical
concepts used to count a single collection of objects can be extended to count two combined
collections of objects through addition.
5. The dramatic play area of a prekindergarten classroom is set up a like a kitchen, with
three-dimensional blocks standing in for plates and cups. While children work in stations
pretending to make and serve food to each other, the teacher can help the children extend
their understanding of three-dimensional attributes by asking them:
, A. to find the yellow cup.
B. which plate is their favorite.
C. to bring a certain object to the table.
D. how the plate and the cup are the same and different.
A. The color yellow and the object name "cup" are not used to describe attributes of three-
dimensional shapes.
B. This question does not direct students to focus on the three-dimensional attributes of different
plates.
C. The name of an object is not a three-dimensional attribute.
D. CORRECT. Students answer this question by describing the similarities and differences of the
three-dimensional attributes of the plate and the cup (e.g., "The plate is short and flat, and the
cup is tall", "The plate and the cup both have round edges").
6. A teacher shares this geometric pattern with the class.
A pattern formed from geometric shapes arranged in a row is shown. The shapes, from left
to right, are a triangle, a square, a pentagon, a hexagon, a triangle, and a square.
The teacher asks students to explain the order of the shapes in the pattern. As students
share their explanations, the teacher writes these student explanations on the board.
"The shapes go from smallest to biggest. Then they start over."
"They are in order by the number of corners."
"The pattern is the least number of sides to the greatest number of sides, then it starts
again."
By writing these explanations on the board, the teacher:
A. highlights the most efficient ways to explain the geometric pattern.
B. encourages students to revise their explanations if they misinterpreted the pattern.
C. offers students an entry point for collaboratively refining explanations of the geometric
pattern.
