MTTC Test (Lower Elementary Test #119)
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.
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.
