MTTC Lower Elementary Test 119
Questions Complete With Verified
Answers
\Q\.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.
\Q\.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.
\Q\.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.
\Q\.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
Questions Complete With Verified
Answers
\Q\.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.
\Q\.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.
\Q\.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.
\Q\.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
