MTTC #123 (3-6 Math) Exam with
Complete Solutions
A. Correct. These resources empower parents/guardians to understand the relevant
mathematics and provide their children with effective learning support.
B. This summary focuses on students' performance, which provides very limited
information for parents/guardians to use to support their child.
C. This information may prove useful in specific instances, but it does not encourage
parents/guardians to connect with the relevant mathematical concepts that their child is
learning.
D. This information does not provide parents/guardians with strategies that they can use
to support their child's mathematical learning. - ANS-1. A sixth-grade teacher prepares
for parent-teacher conferences. Based on data from a recent survey, the teacher is
aware that many parents/guardians have questions about supporting their children's
mathematical understanding outside of school. Which of the following resources is most
effective for promoting parents'/guardians' ability to support their child?
A. workshop demonstrations and tutorial videos that explain relevant mathematics
concepts and models
B. a summary of assessment data illustrating students' progress in mathematics
C. a list of online resources for mathematics definitions and articles
D. printed copies of student learning standards for mathematics
A. Correct. Different configurations of the tiles result in shapes that must always have
the same area but can have different perimeters.
B. The square tiles limit the scope of the activity to rectilinear area, so it would be
difficult to model and solve problems involving various polygons such as triangles,
pentagons, etc.
C. The activity focuses on how perimeter can vary in shapes with the same area, which
is not well-aligned to an investigation of unit fractions as described in this response.
D. Representations with the distributive property would require the squares to be
arranged into arrays, but the activity encourages students to create compositions that
may differ from this configuration. - ANS-2. A third-grade teacher finds this activity about
area and perimeter online:
1) Give each student twelve 1-inch squares.
2) Tell the students to arrange the squares so that they make a shape with no gaps or
overlaps.
3) Ask the students to count the tiling to determine the area and count the side lengths
to determine the perimeter.
4) Have students compare their observations about the shapes and measurements with
a classmate.
Which of the following learning goals aligns to this activity?
, A. Determine that two shapes can have the same area but different perimeters.
B. Solve real-world problems involving the area and perimeter of several polygons.
C. Divide shapes into equal areas and express each part as a unit fraction of the whole.
D. Represent the distributive property using area models with whole-number side
lengths.
A. This task allows students to use symbols and justify their decision, but it does not
provide students with the information necessary to support their correct use of the
symbols.
B. The primary goal of any assessment should not be to collect artifacts for reflection.
C. The primary goal of this type of pre-assessment is to help the teacher establish
students' baseline levels of understanding before they receive instruction, not to identify
specific skills that require additional testing.
D. Correct. The pre-assessment allows the teacher to establish students' baseline levels
of understanding about the inequality symbols and the concept of fraction comparison
before they receive instruction. - ANS-3. A teacher has students complete this task
before instruction on comparing fractions with unlike denominators.
Compare 1/5 and 1/10, explain
Compare 1/3 and 2/6, explain
Compare 3/8 and 4/7, explain
This type of pre-assessment supports instruction primarily by allowing the teacher to:
A. support students' ability to express mathematical understanding using symbols and
representations.
B. support reflective practice by collecting classroom artifacts to discuss with other
teachers.
C. determine which mathematics concepts require additional assessment.
D. determine students' level of understanding of a mathematics concept.
A. Tasks that focus on reasoning (e.g., deduction, inference, sense-making) do not
necessarily foster habits associated with productive struggle (e.g., perseverance,
flexible thinking, curiosity).
B. Encouraging students to spend significant time on a task does not necessarily
encourage them to learn strategies to engage in productive struggle.
C. Providing extra time does not inherently support students' engagement with
productive struggle.
D. Correct. Non-routine problems with student-centered solutions support productive
struggle by promoting creative risk-taking, flexible thinking, and perseverance. - ANS-4.
Which of the following teacher practices best facilitates students' productive struggle
during complex mathematical tasks?
A. planning tasks that support a foundation for reasoning
B. praising students for the amount of time they spend on task
C. allowing students extra time to process mathematics questions
D. providing nonroutine problems that support student-centered solutions
Complete Solutions
A. Correct. These resources empower parents/guardians to understand the relevant
mathematics and provide their children with effective learning support.
B. This summary focuses on students' performance, which provides very limited
information for parents/guardians to use to support their child.
C. This information may prove useful in specific instances, but it does not encourage
parents/guardians to connect with the relevant mathematical concepts that their child is
learning.
D. This information does not provide parents/guardians with strategies that they can use
to support their child's mathematical learning. - ANS-1. A sixth-grade teacher prepares
for parent-teacher conferences. Based on data from a recent survey, the teacher is
aware that many parents/guardians have questions about supporting their children's
mathematical understanding outside of school. Which of the following resources is most
effective for promoting parents'/guardians' ability to support their child?
A. workshop demonstrations and tutorial videos that explain relevant mathematics
concepts and models
B. a summary of assessment data illustrating students' progress in mathematics
C. a list of online resources for mathematics definitions and articles
D. printed copies of student learning standards for mathematics
A. Correct. Different configurations of the tiles result in shapes that must always have
the same area but can have different perimeters.
B. The square tiles limit the scope of the activity to rectilinear area, so it would be
difficult to model and solve problems involving various polygons such as triangles,
pentagons, etc.
C. The activity focuses on how perimeter can vary in shapes with the same area, which
is not well-aligned to an investigation of unit fractions as described in this response.
D. Representations with the distributive property would require the squares to be
arranged into arrays, but the activity encourages students to create compositions that
may differ from this configuration. - ANS-2. A third-grade teacher finds this activity about
area and perimeter online:
1) Give each student twelve 1-inch squares.
2) Tell the students to arrange the squares so that they make a shape with no gaps or
overlaps.
3) Ask the students to count the tiling to determine the area and count the side lengths
to determine the perimeter.
4) Have students compare their observations about the shapes and measurements with
a classmate.
Which of the following learning goals aligns to this activity?
, A. Determine that two shapes can have the same area but different perimeters.
B. Solve real-world problems involving the area and perimeter of several polygons.
C. Divide shapes into equal areas and express each part as a unit fraction of the whole.
D. Represent the distributive property using area models with whole-number side
lengths.
A. This task allows students to use symbols and justify their decision, but it does not
provide students with the information necessary to support their correct use of the
symbols.
B. The primary goal of any assessment should not be to collect artifacts for reflection.
C. The primary goal of this type of pre-assessment is to help the teacher establish
students' baseline levels of understanding before they receive instruction, not to identify
specific skills that require additional testing.
D. Correct. The pre-assessment allows the teacher to establish students' baseline levels
of understanding about the inequality symbols and the concept of fraction comparison
before they receive instruction. - ANS-3. A teacher has students complete this task
before instruction on comparing fractions with unlike denominators.
Compare 1/5 and 1/10, explain
Compare 1/3 and 2/6, explain
Compare 3/8 and 4/7, explain
This type of pre-assessment supports instruction primarily by allowing the teacher to:
A. support students' ability to express mathematical understanding using symbols and
representations.
B. support reflective practice by collecting classroom artifacts to discuss with other
teachers.
C. determine which mathematics concepts require additional assessment.
D. determine students' level of understanding of a mathematics concept.
A. Tasks that focus on reasoning (e.g., deduction, inference, sense-making) do not
necessarily foster habits associated with productive struggle (e.g., perseverance,
flexible thinking, curiosity).
B. Encouraging students to spend significant time on a task does not necessarily
encourage them to learn strategies to engage in productive struggle.
C. Providing extra time does not inherently support students' engagement with
productive struggle.
D. Correct. Non-routine problems with student-centered solutions support productive
struggle by promoting creative risk-taking, flexible thinking, and perseverance. - ANS-4.
Which of the following teacher practices best facilitates students' productive struggle
during complex mathematical tasks?
A. planning tasks that support a foundation for reasoning
B. praising students for the amount of time they spend on task
C. allowing students extra time to process mathematics questions
D. providing nonroutine problems that support student-centered solutions
