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
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.
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
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.
