EC-6 Practice Content Exam Math Test
Questions With 100% Correct
Answers(2025) Updated.
Students in Ms. Cook's fourth-grade class are learning about different types of angle. Students
are given a worksheet with several different angles and asked to identify each angle as acute,
obtuse, or right. Ms. Cook notices that one student, Amari, is correctly labeling all right angles,
but is labeling all acute angles as obtuse and vice versa. Based on this observation, Ms. Cook
can best help Amari by: - Answer Reviewing the definitions of acute and obtuse angles and
providing a mnemonic device to remember each definition.
Below is the outline of a mathematics activity a third-grade teacher recently completed with her
students.
Learning Goal:
The learner will be able to identify and create models of the following fraction: 1/3, 1/4, 1/2
Lesson Plan:
*Ask the students if they have ever eaten a pizza and show them a fake pizza in slices in a pizza
box. Have students discuss the different ways a pizza could be divided.
*Students sit with a partner and complete a worksheet titles, "Equal Parts or Unequal Parts?"
*Using manipulatives, the teacher uses the document camera to show students how to take a
whole pie and turn it into the following fractions: 1/3, 1/4, 1/2.
*Students sit with a partner and complete a worksheet titles, "Draw the Pizza Pie."
*Have each group come up to the board one at a time and draw one of the fraction pies with a
dry erase marker.
Teacher Notes:
Around half of the group draws the correct fraction on the board. Th - Answer Engaging
students in the lesson's content
A second-grade teacher is planning a group activity in which students will sort 3D shape models
based on their defining attributes. How should the teacher plan on grouping students for this
activity, and why? - Answer Heterogeneously, so that struggling students can learn from their
peers and other students can benefit from explaining their reasoning
Mr. Meadows is a third-grade teacher in a low performing school. There is a high rate of
absenteeism and low rate of students doing homework. He makes a public star chart where
students get a sticker for each assignment they complete. Which of the following learning
,struggling with the concept of factoring. Which of the following strategies would be best for Ms.
Wilson to use in her next lesson on factoring to help the students solidify their conceptual
understand of factoring? - Answer Using manipulatives to show factoring as the reverse, or un-
doing, of distribution
Joshua is learning about volumes of three-dimensional figures. First, his teacher explains what
volume is. Then, she writes the formula for area of a cube on the board v = s3. Next, she has the
students recite "the volume of a cube is the side lengthen cubed." Finally, she has students take
six-sided dice of various sizes and measure them to determine their volume. Which best
describes the teaching method is the teacher attempting to use? - Answer Task variety
A third-grade teacher is introducing the concept of multiplication using manipulatives, pictures,
and arrays. Last year several parents asked why their child wasn't learning to multiply the same
way that they did. What should the teacher do in order to address potential questions this year?
- Answer Send an email to parents that explains how multiplication will be introduced and
include tips for practicing these skills with their child.
Ms. Nakaroti wants to teach her students about properties of points, lines, planes, and angles.
Which of the following should she include in her planning for the unit? - Answer Analyze the
standards to determine learning objectives before she starts writing lesson plans.
A sixth-grade teacher is beginning a unit on probability. She utilizes the following steps in
planning her unit:
1. Determine the necessary prerequisite skills.
2. Begin planning probability activities that involve the collection of data.
3. Determine what the students already know by using a KWL chart.
4. Plan the final assessment for the unit.
What is the best order for the teacher to organize these steps? - Answer IV, I, III, II
Which of the following corresponds to the progression of stages of learning about a new
mathematical concept from most basic to most advanced? - Answer Concrete,
representational, abstract
A third-grade teacher is introducing the idea of adding areas of smaller rectangles to make one
larger rectangle. Which would be the most effective beginning activity? - Answer Having the
students explore rectangles that all have the same width
, Ms. Miller is a student teacher in a fourth-grade classroom. She has heard that group work is
important so she wants to plan for group activities. On her first day student teaching, she briefly
says "today we'll be doing group work about fractions" before she sends the students to
stations. How could she best improve her teaching? - Answer Give a whole group lesson on
fractions before breaking into groups
Mrs. Herschend decided not to give a test about ratios and instead had her students do a
project to display their knowledge. She has decided that she will do this for every unit going
forward. What is the main disadvantage to this approach? - Answer Students need to practice
test taking skills periodically
Mrs. Hoyt is excited to be teaching fifth-grade math this year. She would like to encourage her
students' independent skills. How can she facilitate this in her classroom? - Answer Allow for a
variety of choices when it comes to assignments
A third-grade teacher is teaching a whole group lesson on counting money. After the lesson is
complete, she asks students to form groups of four and find the total of different sets of bills
and coins that she will display on the board. During the group activity, there is a lot of
commotion and off-task behavior, and several students begin working independently instead of
with their group. What could the teacher have done differently to improve the group activity? -
Answer Assigned groups ahead of time and established clearer expectation for group
members
A second-grade teacher is finishing up a lesson on using graphs to analyze data and make
predictions. She wants to make sure that students continue to use this knowledge instead of
learning it as an isolated skill. Which of the following would be the best way for the teacher to
achieve this? - Answer Plan a science lesson in the upcoming weeks in which students graph
the daily temperature using bar graphs
A math teacher plans her instructional delivery method on resolving the difficulty students have
distinguishing between mode and median. She plans to have students first work alone
calculating the mode and median of sets of performance results from the school track team.
Next, her students will work in group of 2 or 3 to discuss and interpret their results, and record
a summary of the significance of the results on whiteboards. Finally, the groups will present
their summaries to the class, along with a teacher-led discussion of the findings.
By planning such an activity, the teacher demonstrates that she understand: - Answer How to
apply a variety of instructional delivery methods that can help students develop their
mathematical thinking
Questions With 100% Correct
Answers(2025) Updated.
Students in Ms. Cook's fourth-grade class are learning about different types of angle. Students
are given a worksheet with several different angles and asked to identify each angle as acute,
obtuse, or right. Ms. Cook notices that one student, Amari, is correctly labeling all right angles,
but is labeling all acute angles as obtuse and vice versa. Based on this observation, Ms. Cook
can best help Amari by: - Answer Reviewing the definitions of acute and obtuse angles and
providing a mnemonic device to remember each definition.
Below is the outline of a mathematics activity a third-grade teacher recently completed with her
students.
Learning Goal:
The learner will be able to identify and create models of the following fraction: 1/3, 1/4, 1/2
Lesson Plan:
*Ask the students if they have ever eaten a pizza and show them a fake pizza in slices in a pizza
box. Have students discuss the different ways a pizza could be divided.
*Students sit with a partner and complete a worksheet titles, "Equal Parts or Unequal Parts?"
*Using manipulatives, the teacher uses the document camera to show students how to take a
whole pie and turn it into the following fractions: 1/3, 1/4, 1/2.
*Students sit with a partner and complete a worksheet titles, "Draw the Pizza Pie."
*Have each group come up to the board one at a time and draw one of the fraction pies with a
dry erase marker.
Teacher Notes:
Around half of the group draws the correct fraction on the board. Th - Answer Engaging
students in the lesson's content
A second-grade teacher is planning a group activity in which students will sort 3D shape models
based on their defining attributes. How should the teacher plan on grouping students for this
activity, and why? - Answer Heterogeneously, so that struggling students can learn from their
peers and other students can benefit from explaining their reasoning
Mr. Meadows is a third-grade teacher in a low performing school. There is a high rate of
absenteeism and low rate of students doing homework. He makes a public star chart where
students get a sticker for each assignment they complete. Which of the following learning
,struggling with the concept of factoring. Which of the following strategies would be best for Ms.
Wilson to use in her next lesson on factoring to help the students solidify their conceptual
understand of factoring? - Answer Using manipulatives to show factoring as the reverse, or un-
doing, of distribution
Joshua is learning about volumes of three-dimensional figures. First, his teacher explains what
volume is. Then, she writes the formula for area of a cube on the board v = s3. Next, she has the
students recite "the volume of a cube is the side lengthen cubed." Finally, she has students take
six-sided dice of various sizes and measure them to determine their volume. Which best
describes the teaching method is the teacher attempting to use? - Answer Task variety
A third-grade teacher is introducing the concept of multiplication using manipulatives, pictures,
and arrays. Last year several parents asked why their child wasn't learning to multiply the same
way that they did. What should the teacher do in order to address potential questions this year?
- Answer Send an email to parents that explains how multiplication will be introduced and
include tips for practicing these skills with their child.
Ms. Nakaroti wants to teach her students about properties of points, lines, planes, and angles.
Which of the following should she include in her planning for the unit? - Answer Analyze the
standards to determine learning objectives before she starts writing lesson plans.
A sixth-grade teacher is beginning a unit on probability. She utilizes the following steps in
planning her unit:
1. Determine the necessary prerequisite skills.
2. Begin planning probability activities that involve the collection of data.
3. Determine what the students already know by using a KWL chart.
4. Plan the final assessment for the unit.
What is the best order for the teacher to organize these steps? - Answer IV, I, III, II
Which of the following corresponds to the progression of stages of learning about a new
mathematical concept from most basic to most advanced? - Answer Concrete,
representational, abstract
A third-grade teacher is introducing the idea of adding areas of smaller rectangles to make one
larger rectangle. Which would be the most effective beginning activity? - Answer Having the
students explore rectangles that all have the same width
, Ms. Miller is a student teacher in a fourth-grade classroom. She has heard that group work is
important so she wants to plan for group activities. On her first day student teaching, she briefly
says "today we'll be doing group work about fractions" before she sends the students to
stations. How could she best improve her teaching? - Answer Give a whole group lesson on
fractions before breaking into groups
Mrs. Herschend decided not to give a test about ratios and instead had her students do a
project to display their knowledge. She has decided that she will do this for every unit going
forward. What is the main disadvantage to this approach? - Answer Students need to practice
test taking skills periodically
Mrs. Hoyt is excited to be teaching fifth-grade math this year. She would like to encourage her
students' independent skills. How can she facilitate this in her classroom? - Answer Allow for a
variety of choices when it comes to assignments
A third-grade teacher is teaching a whole group lesson on counting money. After the lesson is
complete, she asks students to form groups of four and find the total of different sets of bills
and coins that she will display on the board. During the group activity, there is a lot of
commotion and off-task behavior, and several students begin working independently instead of
with their group. What could the teacher have done differently to improve the group activity? -
Answer Assigned groups ahead of time and established clearer expectation for group
members
A second-grade teacher is finishing up a lesson on using graphs to analyze data and make
predictions. She wants to make sure that students continue to use this knowledge instead of
learning it as an isolated skill. Which of the following would be the best way for the teacher to
achieve this? - Answer Plan a science lesson in the upcoming weeks in which students graph
the daily temperature using bar graphs
A math teacher plans her instructional delivery method on resolving the difficulty students have
distinguishing between mode and median. She plans to have students first work alone
calculating the mode and median of sets of performance results from the school track team.
Next, her students will work in group of 2 or 3 to discuss and interpret their results, and record
a summary of the significance of the results on whiteboards. Finally, the groups will present
their summaries to the class, along with a teacher-led discussion of the findings.
By planning such an activity, the teacher demonstrates that she understand: - Answer How to
apply a variety of instructional delivery methods that can help students develop their
mathematical thinking
