Mathematics Methods UPDATED ACTUAL
QUESTIONS AND CORRECT ANSWERS
A teacher writes a fifth-grade lesson plan in which students will use a pan balance to demonstrate
equalities in equations. The students will use counters and the pan balance to make the equations
balance for ten open-sentence equations (15 + 34 = n + 21).
The following standard was included within the plan:
NCTM (National Council of Teachers of Mathematics): Principles & Standards for School
Mathematics:
Analyze characteristics and properties of two- and three-dimensional geometric shapes and
develop mathematical arguments about geometric relationships.
How would an administrator rate the learning activity for its overall quality and alignment with
the standard?
A. The activity was ineffective in demonstrating the concept, but the standard aligned with the
lesson.
B. The activity was effective in demonstrating the concept of equality in equations, and the
standard aligned with the lesson.
C. The activity - Correct answers✔✔D. The activity was effective in demonstrating the concept
of equality in equations, but the standard did not align with the lesson.
A lesson is being designed to address the Communication standard from Principles and
Standards for School Mathematics (PSSM). The lesson requires that students write out directions
for using fraction bars to model several addition problems.
,How does this lesson meet the Communication standard?
A. Students recognize and use connections among mathematical ideas.
B. Students use the language of mathematics to express ideas precisely.
C. Students create and use their own measurement units to measure an object.
D. Students model physical phenomenon with algebraic equations and appropriate technology. -
Correct answers✔✔B. Students use the language of mathematics to express ideas precisely.
Students are learning about the concept of the perimeter of a rectangle.
Which tool would help to effectively teach this concept?
A. Geometry software to construct at least five rectangles
B. A ruler to measure side lengths of at least five rectangles
C. A spreadsheet to enter side lengths of at least five rectangles and a formula to compute the
perimeter of each
D. A calculator to compute the perimeter of at least five rectangles with the side length
measurement provided - Correct answers✔✔B. A ruler to measure side lengths of at least five
rectangles
,Which two tools can help a student visualize similar triangles?
Choose 2 answers
A. Grid paper
B. Concept map
C. Online discussion
D. Dynamic geometry software - Correct answers✔✔A. Grid paper and D. Dynamic geometry
software
A teacher has designed a statistics lesson that requires students to visually present their analysis
of the data.
How can students use technology or concrete tools to enhance their presentations?
A. Use a spinner to model the data
B. Use an online forum to discuss the data
C. Use a spreadsheet to create a graph of the data
D. Use a software application to develop a concept map of the data - Correct answers✔✔C. Use
a spreadsheet to create a graph of the data
, What is an appropriate use of manipulatives from web-based technology in mathematical
instruction?
A. A teacher shows a website and instructs the students to follow along and model.
B. A teacher shows a website and asks students to talk with each other to see how each thinks.
C. A teacher shows a website and makes it accessible for school or home use for further
exploration.
D. A teacher shows a website and demonstrates how to effectively interact with virtual
manipulatives. - Correct answers✔✔D. A teacher shows a website and demonstrates how to
effectively interact with virtual manipulatives.
Which two tools can be used to teach a lesson on fractions?
Choose 2 answers
A. Tangram
B. Compass
C. Cuisenaire rods
D. Isometric drawing tool - Correct answers✔✔A. Tangram and C. Cuisenaire rods
A teacher asks her students to solve this problem:
QUESTIONS AND CORRECT ANSWERS
A teacher writes a fifth-grade lesson plan in which students will use a pan balance to demonstrate
equalities in equations. The students will use counters and the pan balance to make the equations
balance for ten open-sentence equations (15 + 34 = n + 21).
The following standard was included within the plan:
NCTM (National Council of Teachers of Mathematics): Principles & Standards for School
Mathematics:
Analyze characteristics and properties of two- and three-dimensional geometric shapes and
develop mathematical arguments about geometric relationships.
How would an administrator rate the learning activity for its overall quality and alignment with
the standard?
A. The activity was ineffective in demonstrating the concept, but the standard aligned with the
lesson.
B. The activity was effective in demonstrating the concept of equality in equations, and the
standard aligned with the lesson.
C. The activity - Correct answers✔✔D. The activity was effective in demonstrating the concept
of equality in equations, but the standard did not align with the lesson.
A lesson is being designed to address the Communication standard from Principles and
Standards for School Mathematics (PSSM). The lesson requires that students write out directions
for using fraction bars to model several addition problems.
,How does this lesson meet the Communication standard?
A. Students recognize and use connections among mathematical ideas.
B. Students use the language of mathematics to express ideas precisely.
C. Students create and use their own measurement units to measure an object.
D. Students model physical phenomenon with algebraic equations and appropriate technology. -
Correct answers✔✔B. Students use the language of mathematics to express ideas precisely.
Students are learning about the concept of the perimeter of a rectangle.
Which tool would help to effectively teach this concept?
A. Geometry software to construct at least five rectangles
B. A ruler to measure side lengths of at least five rectangles
C. A spreadsheet to enter side lengths of at least five rectangles and a formula to compute the
perimeter of each
D. A calculator to compute the perimeter of at least five rectangles with the side length
measurement provided - Correct answers✔✔B. A ruler to measure side lengths of at least five
rectangles
,Which two tools can help a student visualize similar triangles?
Choose 2 answers
A. Grid paper
B. Concept map
C. Online discussion
D. Dynamic geometry software - Correct answers✔✔A. Grid paper and D. Dynamic geometry
software
A teacher has designed a statistics lesson that requires students to visually present their analysis
of the data.
How can students use technology or concrete tools to enhance their presentations?
A. Use a spinner to model the data
B. Use an online forum to discuss the data
C. Use a spreadsheet to create a graph of the data
D. Use a software application to develop a concept map of the data - Correct answers✔✔C. Use
a spreadsheet to create a graph of the data
, What is an appropriate use of manipulatives from web-based technology in mathematical
instruction?
A. A teacher shows a website and instructs the students to follow along and model.
B. A teacher shows a website and asks students to talk with each other to see how each thinks.
C. A teacher shows a website and makes it accessible for school or home use for further
exploration.
D. A teacher shows a website and demonstrates how to effectively interact with virtual
manipulatives. - Correct answers✔✔D. A teacher shows a website and demonstrates how to
effectively interact with virtual manipulatives.
Which two tools can be used to teach a lesson on fractions?
Choose 2 answers
A. Tangram
B. Compass
C. Cuisenaire rods
D. Isometric drawing tool - Correct answers✔✔A. Tangram and C. Cuisenaire rods
A teacher asks her students to solve this problem:
