Module 3

Question 1

An understanding of which of the following mathematical concepts is most helpful when working with probabilities?
A. place value
B. divisibility rules
C. factors and multiples
D. ratios and proportions

Answer 1

D. ratios and proportions

Question 2

A Venn diagram would be most appropriate for visually representing which of the following problems?
A. What are the common multiples of 2, 3, and 5 that are less than 40?
B. If 15 students in a class ride the bus to school and 10 do not, how many students are in the class?
C. What is the probability that out of 3 flips of a coin, the coin will come up heads every time?
D. If 4 students are wearing green shirts and 7 students are wearing blue shirts, how many students are wearing either a green or a blue shirt?

Answer 2

A. What are the common multiples of 2, 3, and 5 that are less than 40?

Question 3

A teacher wants to help students develop their understanding of the relative magnitude of numbers. Which of the following types of mathematics learning materials would be most effective for the teacher to use for this purpose?

A. number lines
B. plastic coins
C.pattern blocks
D. number cubes

Answer 3

A. number lines

Question 4

Which of the following strategies is most appropriate for solving the problem below?

One week Liam baked some cookies and gave half of them away. The next week Liam baked twice as many cookies as the week before and gave half of them away. The third week Liam again baked twice as many cookies as the week before and gave half of them away. If Liam gave away 24 cookies the third week, how many cookies did he give away altogether?

A. looking for a pattern
B. guessing and checking
C. working backward
D. solving a simpler problem

Answer 4

C. working backward

Question 5

To correctly use the ordinal numbers first through fifth with a group of five objects placed in a row, a young child must first be able to:
A. recognize and write the numerals one through five.
B. understand that the order of the objects in the group does not affect the total number.
C. recognize that the last number counted is the number of objects in the group.
D. understand that the number five is made up of smaller numbers.

Answer 5

C. recognize that the last number counted is the number of objects in the group.

Question 6

A preschool child measures the length of a long rectangular block by lining up several smaller blocks along the length of the longer block. This demonstrates that the child has an understanding of which of the following measurement concepts?
A. conservation
B. unit iteration
C. partitioning
D. transitivity

Answer 6

B. unit iteration

Question 7

With respect to mathematics instruction, a standardized developmental screening test would be most appropriate for helping a second-grade teacher:
A. determine students’ background knowledge of mathematics before beginning an instructional unit.
B. modify the curriculum based on students’ mathematical abilities in second grade.
C. identify whether any student is at risk of a possible learning problem in mathematics.
D. assess the progress students have made in their mathematical thinking throughout the school year.

Answer 7

C. identify whether any student is at risk of a possible learning problem in mathematics.

Question 8

A kindergarten teacher wants to promote students’ ability to interpret data. The teacher provides stickers of various colors and asks students to select the sticker that best matches the color of the shirts they are wearing. The students then place the stickers in columns based on color on a large sheet of paper. To meet the objective of the lesson, the most appropriate step for the teacher to take next would be to:

A. show the students how the same data can be displayed using different types of graphs.
B.ask students to identify which columns have more stickers and which have fewer.
C.help students predict how many students will be wearing each color shirt the next day and how to confirm the results.
D. guide students in repeating the activity using stickers that best match the color of the pants or skirts they are wearing.

Answer 8

B.ask students to identify which columns have more stickers and which have fewer.

Question 9

A second-grade teacher is having students work on adding double-digit numbers. The teacher writes a problem on the board, asks students to estimate the answer, and then asks them to explain how they arrived at their answers. As students listen to their peers’ explanations, some students are able to revise their answers correctly while others are not. Which of the following follow-up activities would be most appropriate?
A. working with students in small groups to help students at different ability levels construct their understanding of the concept of addition
B. providing more challenging problems such as triple-digit numbers addition for students to practice their estimation and reasoning skills
C. drawing on students’ understanding of double-digit numbers addition to introduce other arithmetic concepts involving double-digit numbers
D. having students take a short test to find out who has grasped the concept and who may need more individual focused instruction

Answer 9

A. working with students in small groups to help students at different ability levels construct their understanding of the concept of addition

Question 10

Which of the following mathematics activities would be most appropriate for promoting preschool students’ skills in measurement?
A. telling time to the nearest half hour on an analog or digital clock
B. sequencing three different events that occur in the daily classroom routine
C. combining play coins in different ways to equal one dollar
D. using a ruler to measure the length of an object to the nearest quarter inch

Answer 10

B. sequencing three different events that occur in the daily classroom routine

Question 11

A third-grade teacher is developing a criterion-referenced test for a mathematics unit on multiplication. During the unit, students use arrays to solve multiplication problems involving one- and two-digit numbers. To produce a valid criterion- referenced test for this unit, the teacher must:
A. align the test questions with the national mathematics standards for multiplication at the third-grade level.
B. establish a cut-score that will show which students need remedial work with multiplication tables.
C. include test questions that allow students to solve multiplication problems using arrays as they did during the unit.
D. provide standardized questions based on the state curriculum so that students’ scores can be compared across districts.

Answer 11

C. include test questions that allow students to solve multiplication problems using arrays as they did during the unit.

Question 12

A preschool teacher wants to promote children's skills related to counting and comparing numbers. Which of the following activities is most appropriate to use for this purpose?
A. asking the children to look around the classroom for the largest numeral they can find
B. letting the class vote on which book the teacher should read next and then asking the class which book won based on the votes
C. having the class count the number of times a flipped coin comes up heads and predicting whether or not heads will come up on the next flip
D. selecting one child each day to count the number of children in the class and set the appropriate number of cups out for juice at snack time

Answer 12

B. letting the class vote on which book the teacher should read next and then asking the class which book won based on the votes

Question 13

A third-grade student is having difficulty solving word problems in mathematics. Which of the following strategies would be most helpful for the teacher to suggest the student use first?
A. restating the problem in his or her own words
B. determining whether there is extraneous information in the problem
C. estimating what might be a reasonable answer to the problem
D. identifying two different strategies that might be helpful in solving the problem

Answer 13

A. restating the problem in his or her own words

Question 14

A teacher provides mathematics instruction using manipulatives, worksheets, games, and class discussion. The primary benefit of providing instruction in multiple formats is that it:

A. helps students engage their prior knowledge.
B. encourages the development of social skills through group participation.
C. addresses a variety of learning styles.
D. allows students to see different ways to solve the same problem.

Answer 14

C. addresses a variety of learning styles.

Question 15

A teacher gives groups of students a number of triangles, squares, and semicircles and asks the students to combine these shapes to make as many different figures as they can. This activity will help build a foundation for students’ future development of which of the following skills?
A. generating rules for patterns made of shapes
B. representing shapes on a coordinate grid
C. identifying three-dimensional geometric shapes
D. determining the area of irregular shapes

Answer 15

D. determining the area of irregular shapes

Question 16

During group time, a preschool teacher uses shapes made out of felt to create a circle-circle-square, circle-circle-square pattern. The teacher asks children which shape should come next to continue the pattern. Some of the children say a circle and some say a square. Which of the following teacher strategies will best help the children construct their own understanding of the concept?
A. asking the children to identify the differences between the two shapes
B. having the children say the pattern out loud as a group and again asking which shape should come next
C. asking the children to vote on whether a circle or a square should come next
D. continuing the pattern first with a square and then with a circle and asking which shape seems best

Answer 16

B. having the children say the pattern out loud as a group and again asking which shape should come next

Question 17

A third-grade teacher asks teams of students to develop a scientific way for determining what types of materials can become charged with static electricity when rubbed against another material. To produce scientifically valid results from their investigations, it is most important that the student teams:
A. develop a system for recording how strong a static charge develops on each material.
B. keep other variables constant as they test the different materials.
C. explain in scientific language why some materials are more easily charged than others.
D. describe why they chose the materials that they did for testing.

Answer 17

B. keep other variables constant as they test the different materials.

Question 18

A second-grade class is beginning a unit on weather. Which of the following activities associated with this unit would be most effective for helping the students develop an understanding of the foundations of scientific inquiry?
A. The students watch a regular weather report and discuss how meteorologists make predictions.
B. The teacher demonstrates how water vapor condenses on the outside of a glass of ice water when it is humid.
C. Student teams research historic weather events and make class presentations of their findings.
D. The teacher sets up a simple weather station and has the class keep regular rainfall and temperature records.

Answer 18

D. The teacher sets up a simple weather station and has the class keep regular rainfall and temperature records.

Question 19

Which of the following provides the best inquiry-based learning activity for a third- grade class studying rocks and minerals?

A. constructing a poster of the rock cycle and providing written explanations of each stage
B. watching a video on how rocks and minerals form and then answering related questions
C. performing simple tests on a set of minerals and then using a key to identify them
D. summarizing an article about a rock or mineral resource for a class presentation

Answer 19

C. performing simple tests on a set of minerals and then using a key to identify them

Question 20

To present the concept of the conservation of mass to children in a prekindergarten class, it would be most appropriate for the teacher to ask the children to:
A. create stories about where water goes when it evaporates from a puddle on a hot day.
B. roll out balls of clay into flat pancake shapes and then discuss the concepts of shape and weight.
C. compare the cumulative weight of the food they eat every day with their body weight.
D. observe the expansion of water that has turned from liquid to ice and then give possible explanations.

Answer 20

B. roll out balls of clay into flat pancake shapes and then discuss the concepts of shape and weight.

Question 21

A teacher is planning an activity to introduce the concept of density to first graders. The teacher would like to get students interested in the topic by using a discrepant event that surprises them with a result they do not expect. Which of the following activities would be most effective for stimulating students’ interest in this topic?
A. After filling one glass with a saturated salt solution and one glass with tap water, the teacher asks students to predict what will happen when an egg is placed in each of the two glasses.
B. The teacher shows students that sound travels differently through the air and through a solid by having them place their ears against the surface of their desks while gently tapping the desk.
C. After placing an ice cube in a glass of water, the teacher asks students to explain why the ice cube floats.
D. The teacher mixes 50 mL of rubbing alcohol with 50 mL of water and asks students to explain why the combined volume of the two substances is less than 100 mL.

Answer 21

A. After filling one glass with a saturated salt solution and one glass with tap water, the teacher asks students to predict what will happen when an egg is placed in each of the two glasses.

Question 22

A first-grade teacher is planning a unit on insects with the goal of motivating students to be good scientific observers of the natural world. The most effective way to achieve this goal would be to have the students:
A. watch a video about ants and then answer questions about ant behavior depicted in the video.
B. separate pictures of a variety of ant species by appearance and then come up with ideas to explain why they are different.
C. memorize the names of the body parts of ants and then identify those parts in various pictures of different ant species.
D. make drawings of ants from memory to share with the class and then observe real ants and draw them again.

Answer 22

D. make drawings of ants from memory to share with the class and then observe real ants and draw them again.

Question 23

A third-grade teacher is planning a science unit on human body systems, a topic that has quite a bit of specialized scientific terminology associated with it. In presenting information during the unit, it is most advisable for the teacher to:
A. avoid scientific terminology whenever possible.
B. include only those terms that are already familiar to the students.
C. explain the Latin or Greek roots of the terms as they are used.
D. use the appropriate scientific terminology.

Answer 23

D. use the appropriate scientific terminology.

Question 24

A fourth-grade teacher wants to integrate the arts into the science curriculum. Which of the following student activities would be most appropriate for this age group?

A. visiting an art museum to observe how animals are depicted in paintings
B. collecting different types of leaves for pressing
C. researching an animal’s habitat and creating a diorama
D. writing a short story or poem about a favorite pet

Answer 24

C. researching an animal’s habitat and creating a diorama

Question 25

A teacher wants to introduce a kindergarten class to the concept of structure and function in living systems. Which of the following activities would provide the most appropriate introduction to the biological concept of structure and function for this age group?
A. comparing what different insects look like with how they move
B. measuring pulse rates before and after physical activity
C. identifying where different animals live and what they eat
D. contrasting flowers from different types of plants

Answer 25

A. comparing what different insects look like with how they move

Question 26

As a third grader works on a diagram of the water cycle, the classroom teacher gives her specific feedback on the task while also asking the student to evaluate her own work. The teacher hopes the interaction will help him adapt his teaching approach to the student's learning style and encourage the student to become more involved in her own progress. Which of the following describes this type of interactive assessment?
A. summative assessment
B. performance assessment
C. formative assessment
D. criterion-referenced assessment

Answer 26

C. formative assessment

Question 27

A second-grade teacher wants to develop an assessment that evaluates student achievement in science over time and involves students in their own evaluations. The teacher could most effectively achieve this by using which of the following assessment strategies?
A. giving regular content quizzes that students correct
B. having each student maintain a portfolio containing a variety of work samples
C. observing students as they carry out experiments
D. meeting with students weekly during the year to discuss recent work

Answer 27

B. having each student maintain a portfolio containing a variety of work samples

Question 28

At the start of a fourth-grade unit on the physical environment, which of the following questions should a teacher ask to promote the idea that the rock cycle and water cycle interact as part of a larger earth system?
A. How do rivers change the surface of the land?
B. What causes the water level of rivers to change?
C. How do people use rivers to produce energy?
D. What is the relationship between rivers and oceans?

Answer 28

A. How do rivers change the surface of the land?

Question 29

One of the strongest arguments in favor of using an inquiry approach to teach elementary science is that with the inquiry approach elementary students can:
A. learn science content through a nonquantitative approach that is less intimidating.
B. participate in activities without having to learn challenging scientific concepts.
C. expand their innate curiosity about a topic into a more structured science investigation.
D. explore their own interests in a flexible setting without fear of failure.

Answer 29

C. expand their innate curiosity about a topic into a more structured science investigation.

Question 30

A first-grade teacher is modifying a weather activity to incorporate a mathematics component. The original activity involves reading to the class a children’s story about a large storm and then asking the class questions about how weather has affected their lives. Which of the following student-centered mathematics activities would provide the most age-appropriate link to the first-grade mathematics curriculum?

A. developing a chart of the average annual rainfall in different parts of the United States
B. estimating what fraction of the local area’s annual precipitation falls as snow during the winter
C. calculating the amount of rain that would fall if it rained for a whole day at a given rate
D. developing a histogram showing rainfall for a month based on data collected using a rain gauge

Answer 30

D. developing a histogram showing rainfall for a month based on data collected using a rain gauge

Question 31

A second-grade teacher introduces students to the concept of renewable and nonrenewable resources in a discussion about the environment. A student asks the teacher why water is considered a renewable resource when it disappears after it rains or goes down the drain after a bath. Which of the following facts about water should the teacher cover in order to answer the student’s question?
A. the role of evaporation, condensation, and stream flow in cycling water between the oceans, atmosphere, and land
B. the properties of aquifers that allow water that falls as precipitation to be stored underground
C. the importance of sewage treatment plants in turning waste water into clean water that can be returned to streams or used by people
D. the loss of some water resources for the foreseeable future due to contamination with pollutants

Answer 31

A. the role of evaporation, condensation, and stream flow in cycling water between the oceans, atmosphere, and land

Question 32

As part of a school program encouraging recycling, a second-grade teacher and her class decide to examine how their lunch and snack choices affect the trash the class generates. The students begin by setting aside all the plastic packaging materials from their lunches. For this grade level, which of the following activities would best help the students recognize the impact of their lunch choices on the plastic waste the class generates?
A. putting all plastic packaging materials in a recycling bin to see how long it takes to fill
B. researching the different types of plastic that can be recycled into new products
C. having students weigh the plastic packaging from their lunches daily for a month
D. making a poster showing the processes involved in turning recycled plastic into new products

Answer 32

A. putting all plastic packaging materials in a recycling bin to see how long it takes to fill

Question 33

Students in a second-grade class observe birds at a feeder hanging from a tree outside the classroom. The students observe that the birds have beaks of different shapes. Some birds are able to crack the seeds easily, while other birds pound at the seeds to open them. The students also notice that some of the birds can cling to the side of the tree, and others only perch on branches. Using the students' observations would be an appropriate way to introduce which of the following life science concepts?
A. inheritance
B. life cycles
C. adaptation
D. habitat

Answer 33

C. adaptation

Question 34

Which of the following assessment instruments would be most appropriate to use
to evaluate the gross-motor development of a five-year-old student?
A. self-evaluation
B. observational checklist
C. fitness test
D. summative exam

Answer 34

B. observational checklist

Question 35

A first-grade teacher has assessed students’ abilities in various gross-motor movements such as skipping, galloping, and sliding. Some of the students can do some of the movements but not all three. Based on these assessment results, the teacher could best promote the gross-motor development of all students in the class by:

A. playing a simple game in which students skip, gallop, or slide.
B. asking students to model skipping, galloping, and sliding movements for those who have trouble.
C. having students practice skipping skills daily until all students are able to skip.
D. referring those students who lag behind in skipping skills for further evaluation by a physical therapist.

Answer 35

A. playing a simple game in which students skip, gallop, or slide.

Question 36

Which of the following activities is more developmentally appropriate for fourth- grade students than for first-grade students?
A. playing team sports that require strategy
B. engaging in creative movement that focuses on imagery and make-believe
C. moving rhythmically to music
D. participating in activities with one or two rules that are reinforced

Answer 36

A. playing team sports that require strategy

Question 37

Formative assessments in motor development would best be used for which of the following purposes?
A. documenting achievement of motor development goals
B. evaluating overall performance to assign a grade related to motor skills
C. screening for possible delays in motor development
D. identifying strengths and weaknesses in performance of motor skills

Answer 37

D. identifying strengths and weaknesses in performance of motor skills

Question 38

According to the USDA, which of the following is a component of a healthy diet?
A. consuming a variety of fruit juices as the primary source of fruit in the diet
B. replacing dairy products with soy-based and other nondairy substitutes
C. consuming less protein from animal sources and increasing consumption of beans and nuts
D. replacing the majority of red and yellow vegetables with root vegetables such as potatoes

Answer 38

C. consuming less protein from animal sources and increasing consumption of beans and nuts

Question 39

Which of the following actions is most effective for reducing the risk of respiratory problems in children due to poor indoor air quality?
A. replacing older carpets and fabric-covered cushions with newer ones as they become worn
B. eliminating dust by washing plastic toys with a mild soap solution once a week
C. using aerosol sprays rather than liquid cleaning products whenever possible
D. improving ventilation by opening windows and doors for a part of each day

Answer 39

D. improving ventilation by opening windows and doors for a part of each day

Question 40

A kindergarten teacher wants to promote the development of students’ manipulative skills. The most developmentally appropriate activity for this purpose would be for the teacher to have the students:
A. practice dribbling a soccer ball from one end of the room to the other.
B. strike a thrown ball with a bat.
C. use an underhand throw to toss beanbags to a partner from various distances.
D. move around the room at varying speeds without bumping into one another.

Answer 40

C. use an underhand throw to toss beanbags to a partner from various distances.

Question 41

A prekindergarten teacher would like to support students' safety knowledge and skills by promoting their ability to make 911 calls in an emergency. The teacher can best accomplish this goal by first:
A. reading aloud a story in which a child calls 911 and discussing the story with the class.
B. inviting emergency responders to speak to the class about when it is appropriate to make 911 calls.
C. using a toy phone to model dialing 911 and having students use it to practice making 911 calls.
D. presenting scenarios to the class and asking students whether they would call 911 in the situation described.

Answer 41

A. reading aloud a story in which a child calls 911 and discussing the story with the class.

Question 42

Which of the following questions is most important for a kindergarten teacher to consider first when planning instruction to develop students’ motor skills?

A. Should activities focus on one type of movement, such as locomotor or nonlocomotor movements?
B. What equipment is available or needs to be obtained for students to participate in physical activities?
C. What kinds of physical games and activities do students initiate on their own during free playtime?
D. What activities are appropriate for the physical and cognitive levels of the students?

Answer 42

D. What activities are appropriate for the physical and cognitive levels of the students?

Question 43

In a first-grade class, the teacher introduces students to the conflict-resolution strategy below.
1. Stop before you lose your temper.
2. Say what you think the conflict is about.
3. Listen to the other person’s feelings and ideas.
4. Think of solutions that will satisfy both of you.
The teacher asks students to describe some conflicts or disagreements they have had with another person at school. The teacher then guides pairs of students in role-plays to explore how the conflict-resolution steps could be applied in similar situations. Which of the following ideas is most important for the teacher to emphasize to students as they practice using step 2 of the conflict-resolution strategy?
A. expressing the emotions they are experiencing as calmly and clearly as possible to the other person
B. talking about the conflict as if it involves two other people rather than themselves
C. using a what or why message to explain what is bothering them, instead of a message that blames the other person
D. incorporating words such as fair and peaceful into their ideas about how the conflict or disagreement can be resolved

Answer 43

C. using a what or why message to explain what is bothering them, instead of a message that blames the other person

Question 44

Which of the following is a developmentally appropriate physical activity goal for kindergarten students?
A. learning how to skip and gallop with ease
B. gaining experience in working with a partner
C. practicing striking a moving object with a racket
D. understanding and participating in competitive games

Answer 44

A. learning how to skip and gallop with ease

Question 45

A preschool program has just received four new tricycles. On the day that the tricycles arrive, the children are excited and anxious to get outside to play with them. Prior to having students ride the tricycles, it is most important that the teacher:
A. explain to the children the types of movements used while riding a tricycle.
B. reinforce to the children the importance of sharing the tricycles.
C. encourage the children to ride a tricycle in order to get exercise.
D. provide the children with helmets and instruction on how to safely ride the tricycles.

Answer 45

D. provide the children with helmets and instruction on how to safely ride the tricycles.

Question 46

A kindergarten teacher has several students who lack the fine-motor skills required for writing and forming letters. Which of the following instructional activities is likely to be most appropriate for these students?
A. providing increased time for worksheets that require tracing letters multiple times
B. engaging the students in building with small blocks and working with clay
C. teaching songs, rhymes, and chants that require coordination of hand movements to words
D. asking the students to create letters with their bodies before writing the letters with pencils or crayons

Answer 46

B. engaging the students in building with small blocks and working with clay

Question 47

A four-year-old child’s inability to perform which of the following tasks could indicate a need for further assessment of the child’s motor development?

A.hitting a ball with a bat
B. kicking a stationary ball
C. balancing on a balance beam
D. using an overhand throw

Answer 47

B. kicking a stationary ball

Question 48

Fourth graders are engaged in an online activity where they enter their age and keep a food and activity log for a week. The program gives them recommendations for healthy eating and activities. The primary benefit of this type of activity is that it:
A. provides students with a strategic plan for health and fitness.
B. fosters enjoyment in health and fitness activities.
C. promotes self-responsibility for personal health and fitness.
D. teaches students important vocabulary about health and fitness.

Answer 48

C. promotes self-responsibility for personal health and fitness.

Question 49

During an outdoor activity, a teacher throws a large ball to fourth-grade students. Instead of throwing the ball directly to the students, the teacher throws it so that the students need to move forward, backward, or laterally to catch the ball. This activity is likely to contribute most effectively to the students’ development of which of the following skills?
A. perceptual
B. fine-motor
C. manipulative D. nonlocomotor

Answer 49

A. perceptual