MTTC Test (Lower Elementary Test
#119) Questions Answered Correctly
(Qs) 2026 update
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. - CORRECT
ANSWERS 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. - CORRECT ANSWERS 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" - CORRECT ANSWERS 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 - CORRECT ANSWERS
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.
#119) Questions Answered Correctly
(Qs) 2026 update
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. - CORRECT
ANSWERS 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. - CORRECT ANSWERS 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" - CORRECT ANSWERS 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 - CORRECT ANSWERS
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.
