Prekindergarten/Primary PK–3

Mathematics Subtest

Test Format and Sample Questions

The Mathematics subtest contains approximately 40 multiple-choice questions. You will have 70 minutes to complete the subtest.

Each question will contain four response options, and you will indicate your answer by selecting A, B, C, or D. An on-screen reference sheet will be provided.

The table below presents types of questions on the exam and directs you to examples of these formats among the sample items that follow.

Table of Question Formats

Type of Question	Sample Question
Direct Question Choose the response option that best answers the question.	Question 1
Scenario Examine a situation, problem, or case study. Then answer a question, make a diagnosis, or recommend a course of action by selecting the best response option.	Question 2

Sample Questions

The following questions represent both the form and content of questions on the examination. These questions will acquaint you with the general format of the examination; however, these sample questions do not cover all of the competencies and skills that are tested and will only approximate the degree of examination difficulty.

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Mathematics Subtest

Competency 1—Knowledge of number concepts and operations in base-10

DIRECTIONS: Read the question and select the best response.

Which of the following expressions is equivalent to the number 255?

Choose an answer

1. 25 tens and 5
2. 3 hundreds minus 55
3. 200 + 5 + 5
4. 200 + 50 −minus 5

AnswerEnter to expand or collapse answer.Answer expanded

Correct Response: A.

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Mathematics Subtest

Competency 1—Knowledge of number concepts and operations in base-10

DIRECTIONS: Read the question and select the best response.

A 1^stfirst-grade child was asked to choose whether 81 or 19 is the greater of the two numbers. The child circled the number 19. When the child was asked why that number was chosen, the explanation was that 9 is greater than 8. This demonstrates a lack of understanding of

Choose an answer

1. estimation.
2. symmetry.
3. iterating.
4. place value.

Answer Enter to expand or collapse answer. Answer expanded

Correct Response: D.

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Mathematics Subtest

Competency 1—Knowledge of number concepts and operations in base-10

DIRECTIONS: Read the question and select the best response.

Which of the following is equivalent to 7,355?

Choose an answer

1. 7,000 + 300 + 55
2. 7,000 + 200 + 5
3. 7,000 + 300 + 5
4. 7,000 + 200 + 55

Answer Enter to expand or collapse answer. Answer expanded

Correct Response: A.

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Mathematics Subtest

Competency 1—Knowledge of number concepts and operations in base-10

DIRECTIONS: Read the question and select the best response.

Twelve pounds of peas are packed into freezer bags that each weigh ³/₄3 fourths pound. How many freezer bags are packed?

Choose an answer

1. 6
2. 9
3. 16
4. 18

AnswerEnter to expand or collapse answer.Answer expanded

Correct Response: C.

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Mathematics Subtest

Competency 1—Knowledge of number concepts and operations in base-10

DIRECTIONS: Read the question and select the best response.

A teacher is having 8 friends over for pizza. She bought 3 pizzas with 8 slices each. If the pizzas are shared equally, how much of a pizza will each person get?

Choose an answer

1. ²⁴/₃24 thirds
2. ²⁴/₉24 ninths
3. ³/₈3 eighths
4. ⁸/₉8 ninths

AnswerEnter to expand or collapse answer.Answer expanded

Correct Response: B.

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Mathematics Subtest

Competency 2—Knowledge of algebraic thinking

DIRECTIONS: Read the question and select the best response.

Which property was used to simplify the following expression?

2a + 4b + a = 2a + a + 4b

Choose an answer

1. commutative
2. identity
3. distributive
4. closure

Answer Enter to expand or collapse answer. Answer expanded

Correct Response: A.

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Mathematics Subtest

Competency 2—Knowledge of algebraic thinking

DIRECTIONS: Read the question and select the best response.

Which of the following algebraic equations shows the additive identity property?

Choose an answer

1. a + b = b + a
2. a + 0 = 0 + a = a
3. a(b + c) = ab + ac
4. (a + b) + c = a + (b + c)

AnswerEnter to expand or collapse answer.Answer expanded

Correct Response: B.

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Mathematics Subtest

Competency 2—Knowledge of algebraic thinking

DIRECTIONS: Read the question and select the best response.

Which of the following demonstrates the commutative property of multiplication?

Choose an answer

1. 4 ×times 12 = 12 ×times 4
2. 1,234 ×times 1 = 1,234
3. 3(4 + 5) 3 times, open parens, the quantity of 4 plus 5, close parens = 3 × times4 + 3 × times5
4. 3(2 ×times 5) 3 times, open parens, the product of 2 times 5, close parens = (3 ×times 2)5open parens, the product of 3 times 2, close parens, times 5

AnswerEnter to expand or collapse answer.Answer expanded

Correct Response: A.

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Mathematics Subtest

Competency 3—Knowledge of measurement, data collection, and analysis

DIRECTIONS: Read the question and select the best response.

A 1^stfirst-grade teacher has promised a small class reward for every ten compliments received for good conduct, and a larger reward when fifty compliments have been received. How would this data best be tracked and represented on the board?

Choose an answer

1. tally marks grouped by fives
2. a series of algebraic equations
3. concept maps involving numerals
4. number patterns showing trends

AnswerEnter to expand or collapse answer.Answer expanded

Correct Response: A.

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Mathematics Subtest

Competency 3—Knowledge of measurement, data collection, and analysis

DIRECTIONS: Read the question and select the best response.

According to the graph, how much warmer was it at 11:30 a.m. than at 8:30 a.m.?

The graph is a line graph with one data line. The title is Temperature change over four hours in Tampa, Florida, in Celsius. The vertical axis has values labeled from 18 to 35 in increments of one. The horizontal axis is labeled with time values from 7:30 to 11:30 in increments of half an hour. The data values are as follows.

1. 7:30, 25 degrees
2. 8:00, 25 degrees
3. 8:30, 25 degrees
4. 9:00, 26 degrees
5. 9:30, 28 degrees
6. 10:00, 29 degrees
7. 10:30, 30 degrees
8. 11:00, 30 degrees
9. 11:30, 31 degrees

Choose an answer

1. 5 degrees
2. 6 degrees
3. 25 degrees
4. 31 degrees

Answer Enter to expand or collapse answer. Answer expanded

Correct Response: B.

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Mathematics Subtest

Competency 4—Knowledge of geometry and spatial concepts

DIRECTIONS: Read the question and select the best response.

A group of 2^ndsecond-grade students were cutting out shapes. While cutting they noticed that when they opened the scissors to a certain position it looked like one of the corners on a square. They also noticed that as they closed the scissors the corner got smaller.

What geometric vocabulary term would be appropriate to introduce to these students?

Choose an answer

1. ray
2. angle
3. line segment
4. parallel lines

Answer Enter to expand or collapse answer. Answer expanded

Correct Response: B.

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Mathematics Subtest

Competency 4—Knowledge of geometry and spatial concepts

DIRECTIONS: Read the question and select the best response.

A child is using a rubber band and creates an 8-sided shape on a geoboard. This shape is called a(an)

Choose an answer

1. hexagon.
2. pentagon.
3. octagon.
4. nonagon.

AnswerEnter to expand or collapse answer.Answer expanded

Correct Response: C.

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Mathematics Subtest

Competency 4—Knowledge of geometry and spatial concepts

DIRECTIONS: Read the question and select the best response.

Which of the following pairs of shapes is congruent?

Choose an answer

1. 

   The figure shows two right triangles with the same proportions. The one on the left is larger.

2. 

   The figure shows two outlined arrows with the same dimensions, pointing toward each other.

3. 

   The figure shows two outlined arrows with right angle bends in the middle. The one on the left has an arrowhead at each end. The one on the right has an arrowhead at one end.

4. 

   The figure shows an ellipse and a circle. The horizontal axis of the ellipse is equal to the diameter of the circle. The vertical axis of the ellipse is shorter.

AnswerEnter to expand or collapse answer.Answer expanded

Correct Response: B.

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Mathematics Subtest

Competency 4—Knowledge of geometry and spatial concepts

DIRECTIONS: Read the question and select the best response.

A teacher was teaching her students about symmetry but decided to teach congruence at the same time. Which of the following statements illustrates the best reason these two concepts would be taught together?

Choose an answer

1. When a line of symmetry is drawn, both sides are congruent.
2. If a figure has line symmetry, then it is congruent.
3. Symmetry and congruent mean the same thing.
4. All congruent figures have a line of symmetry.

AnswerEnter to expand or collapse answer.Answer expanded

Correct Response: A.

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Mathematics Subtest

Competency 5—Knowledge of student reasoning and instructional practices

DIRECTIONS: Read the question and select the best response.

A kindergarten teacher is trying to assess her students’ abilities to identify and describe shapes. Which would be the best example of a formative assessment method designed to provide the most accurate reflection of student progress?

Choose an answer

1. Once a week, the teacher asks, “Who knows which shape is a triangle?” The teacher then records the names of students who raise their hands, selecting a different shape each week and monitoring responses.
2. At the end of the school year, the children take an online quiz with auditory directions such as, “Can you find the triangle? Click on the triangle now.” The teacher then reviews the resulting data.
3. On a daily basis, the teacher asks, “Can you draw a triangle and turn it into an animal?” The teacher then retains student drawings for a portfolio, offering different prompts for creativity each time such as fruits or toys.
4. Periodically, the teacher directs students to, “Draw a triangle on your paper.” The teacher then asks each child to explain what makes the shape a triangle, noting responses and alternating shapes.

AnswerEnter to expand or collapse answer.Answer expanded

Correct Response: D.

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Mathematics Subtest

Competency 5—Knowledge of student reasoning and instructional practices

DIRECTIONS: Read the question and select the best response.

Readiness for subtraction includes understanding of

Choose an answer

1. addends, missing addends, and sums.
2. counting, addition, and number families.
3. numberness, conservation of number, and regrouping.
4. associative property, identity element, and commutative property.

AnswerEnter to expand or collapse answer.Answer expanded

Correct Response: B.

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Mathematics Subtest

Competency 5—Knowledge of student reasoning and instructional practices

DIRECTIONS: Read the question and select the best response.

A teacher is planning strategies to help 2^ndsecond graders determine the appropriate operation for simple addition and subtraction word problems. Which would be the most effective beginning technique?

Choose an answer

1. teaching key phrases that indicate the correct action
2. providing practice with worksheets made up of mixed problems
3. having the students use manipulatives to represent the problems
4. demonstrating examples of each type of problem

AnswerEnter to expand or collapse answer.Answer expanded

Correct Response: C.

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Mathematics Subtest

Competency 5—Knowledge of student reasoning and instructional practices

DIRECTIONS: Read the question and select the best response.

A 2^ndsecond-grade teacher is teaching a unit on time. Which of the following skills is appropriate for 2^ndsecond-grade students?

Choose an answer

1. telling time to the nearest minute
2. identifying time to the nearest five minutes
3. calculating the number of minutes in a day
4. determining the time elapsed during an event

AnswerEnter to expand or collapse answer.Answer expanded

Correct Response: B.

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Mathematics Subtest

Competency 5—Knowledge of student reasoning and instructional practices

DIRECTIONS: Read the question and select the best response.

When teaching kindergarten children the meaning of the number 4, which of the following should the teacher introduce first?

Choose an answer

1. pictures showing four things
2. sets of four objects
3. four tally marks
4. the numeral 4

AnswerEnter to expand or collapse answer.Answer expanded

Correct Response: B.

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Mathematics Subtest

Competency 5—Knowledge of student reasoning and instructional practices

DIRECTIONS: Read the question and select the best response.

A kindergarten child should learn to

Choose an answer

1. draw a prism.
2. draw an octagon.
3. identify a pyramid.
4. identify a hexagon.

AnswerEnter to expand or collapse answer.Answer expanded

Correct Response: D.

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Mathematics Subtest

Competency 5—Knowledge of student reasoning and instructional practices

DIRECTIONS: Read the question and select the best response.

Which of the following would be an appropriate skill to teach 2^ndsecond-grade students?

Choose an answer

1. solving addition and subtraction word problems within 10
2. solving missing addend problems for sums of 10
3. fluently adding and subtracting within 40 using mental strategies
4. fluently adding and subtracting within 20 using mental strategies

AnswerEnter to expand or collapse answer.Answer expanded

Correct Response: D.

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Mathematics Subtest

Competency 5—Knowledge of student reasoning and instructional practices

DIRECTIONS: Read the question and select the best response.

At what grade level are students expected to draw shapes with a given number of faces or angles?

Choose an answer

1. preschool
2. kindergarten
3. 1^stfirst grade
4. 2^ndsecond grade

AnswerEnter to expand or collapse answer.Answer expanded

Correct Response: D.

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Mathematics Subtest

Competency 5—Knowledge of student reasoning and instructional practices

DIRECTIONS: Read the question and select the best response.

Which of the following options would be an appropriate mathematical concept to teach a class of 1^stfirst-grade students?

Choose an answer

1. telling time to the nearest minute
2. writing time to the nearest five minutes
3. comparing the lengths of two objects indirectly by using a third object
4. estimating the lengths of objects using inches, feet, centimeters, and meters

AnswerEnter to expand or collapse answer.Answer expanded

Correct Response: C.

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Mathematics Subtest

Competency 5—Knowledge of student reasoning and instructional practices

DIRECTIONS: Read the question and select the best response.

Which of the following is an appropriate manipulative for 1^stfirst-grade students to measure objects found in the classroom?

Choose an answer

1. ruler
2. string
3. yard stick
4. linking cubes

AnswerEnter to expand or collapse answer.Answer expanded

Correct Response: D.

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Mathematics Subtest

Competency 5—Knowledge of student reasoning and instructional practices

DIRECTIONS: Read the question and select the best response.

Which of the following are underlying concepts in patterning?

1. comparing,
2. estimating,
3. ordering,
4. scaffolding.

Choose an answer

1. 1 and 2
2. 1 and 3
3. 2 and 3
4. 2 and 4

AnswerEnter to expand or collapse answer.Answer expanded

Correct Response: B.

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Mathematics Subtest

Competency 5—Knowledge of student reasoning and instructional practices

DIRECTIONS: Read the question and select the best response.

Which of the following experiences would best introduce students to decomposing numbers less than or equal to 10 into pairs?

Choose an answer

1. providing students with a given number of cubes to sort into two groups
2. allowing students to write equations to show ways to compose a given number
3. counting sets of objects up to ten
4. giving missing addend word problems

Answer Enter to expand or collapse answer. Answer expanded

Correct Response: A.

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Mathematics Subtest

Competency 5—Knowledge of student reasoning and instructional practices

DIRECTIONS: Read the question and select the best response.

In the given situation, which of the following would provide the most appropriate structured experience?

A 1^stfirst-grade teacher observes the scores on a recent test and discovers the class has not mastered the concept of fractional parts.

Choose an answer

1. assigning fraction homework
2. making fractions with pizza
3. providing additional problems
4. varying the level of difficulty on the test

Answer Enter to expand or collapse answer. Answer expanded

Correct Response: B.

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Mathematics Subtest

Competency 5—Knowledge of student reasoning and instructional practices

DIRECTIONS: Read the question and select the best response.

A 1^stfirst-grade teacher observes that five of her students are not able to complete subtraction problems with numbers over ten. They count on their fingers to take five away from seven to see that two remain, but do not know what to do when presented with problems such as 15 −minus 9.

Which of the following approaches would best address this situation?

Choose an answer

1. pairing advanced students with the struggling students so the latter will see the procedure from a peer
2. circling incorrect responses on tests and quizzes for these students to redo until mastery is achieved
3. having them practice subtraction problems with numbers over ten using manipulatives and then identify the corresponding addition fact
4. ignoring errors given that this concept is difficult to master and comprehension will increase over time

AnswerEnter to expand or collapse answer.Answer expanded

Correct Response: C.

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Mathematics Subtest

Competency 5—Knowledge of student reasoning and instructional practices

DIRECTIONS: Read the question and select the best response.

Some of the children in a 2^ndsecond-grade class are having difficulty understanding customary units of linear measurement. They are able to correctly identify between inches, feet, and yards; but they are unable to determine which unit should be used for a specific purpose. Which of the following would be the most effective strategy to help those students develop a better comprehension of these concepts?

Choose an answer

1. assessing individual measurement abilities daily to hone in on strengths and weaknesses, communicating with parents to build partnerships to address deficiency and reward progress
2. placing them in small groups to measure specific large and small items in the classroom using rulers and yardsticks, recording their measurements and indicating which tool they used and why
3. teaching mnemonic devices to help them remember which unit to use to measure particular objects
4. assigning homework in which students measure household objects and report their results

AnswerEnter to expand or collapse answer.Answer expanded

Correct Response: B.

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Mathematics Subtest

Competency 5—Knowledge of student reasoning and instructional practices

DIRECTIONS: Read the question and select the best response.

Which of the following is the best example of a structured activity to introduce kindergarten students to properties of shapes?

Choose an answer

1. asking the children to draw or paint pictures of their favorite things with the teacher pointing out the shapes that are incorporated
2. showing pictures of shapes and have the children reach into bags filled with plastic shapes to remove the matching shape by touch
3. giving the children whole class time to build creative structures using wooden blocks that incorporate common geometric shapes
4. reading a story about different shapes and have the children practice their vocabulary development by writing the shape names

AnswerEnter to expand or collapse answer.Answer expanded

Correct Response: B.

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Mathematics Subtest

Competency 5—Knowledge of student reasoning and instructional practices

DIRECTIONS: Read the question and select the best response.

A 2^ndsecond-grade teacher wants to foster success in mathematical thinking. Which of the following situations would best foster student success?

Choose an answer

1. teaching skill isolation
2. teaching rote memorization
3. teaching conceptual understanding
4. teaching the fastest way to solve a problem

AnswerEnter to expand or collapse answer.Answer expanded

Correct Response: C.

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Mathematics Subtest

Competency 5—Knowledge of student reasoning and instructional practices

DIRECTIONS: Read the question and select the best response.

Which of the following patterns is an example of an “ABCC” pattern?

Choose an answer

1. The first image is a square. The second image is a circle. The third image is a triangle. The fourth image is a triangle.
2. The first image is a square. The second image is a circle. The third image is a triangle. The fourth image is a circle.
3. The first image is a circle. The second image is a circle. The third image is a triangle. The fourth image is a square.
4. The first image is a circle. The second image is a triangle. The third image is a triangle. The fourth image is a square.

Answer Enter to expand or collapse answer. Answer expanded

Correct Response: A.

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Mathematics Subtest

Competency 5—Knowledge of student reasoning and instructional practices

DIRECTIONS: Read the question and select the best response.

According to generally accepted principles of child growth and development, which of the following techniques should a teacher use to help 1^stfirst-grade students decide on the appropriate operation for simple one-step addition or subtraction word problems?

Choose an answer

1. teaching the key phrases that indicate the appropriate operation to use in solving problems
2. providing practice through worksheets made up of mixed problems
3. having the students draw pictorial representations of the problems to be solved
4. demonstrating how to solve one example of each type of problem on the overhead projector

AnswerEnter to expand or collapse answer.Answer expanded

Correct Response: C.

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Mathematics Subtest

Competency 5—Knowledge of student reasoning and instructional practices

DIRECTIONS: Read the question and select the best response.

Which of the selections below best represents seriation?

Choose an answer

1. A child knows where to stand in line based on number order.
2. A child stacks blocks of different sizes from largest to smallest.
3. A child recognizes that there are three cookies without counting them.
4. A child creates a pattern by alternating two different shapes of pasta.

AnswerEnter to expand or collapse answer.Answer expanded

Correct Response: B.

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Mathematics Subtest

Competency 5—Knowledge of student reasoning and instructional practices

DIRECTIONS: Read the question and select the best response.

A teacher can reduce the number of multiplication facts that must be memorized by teaching the

Choose an answer

1. commutative property.
2. associative property.
3. distributive property.
4. transitive property.

AnswerEnter to expand or collapse answer.Answer expanded

Correct Response: A.

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Mathematics Subtest

Competency 5—Knowledge of student reasoning and instructional practices

DIRECTIONS: Read the question and select the best response.

A 2^nd-grade student was having difficulty with the wording and problem structure for addition word problems. Which of the following would best facilitate his struggles with problem solving?

Choose an answer

1. teaching the student to look for key words
2. providing practice with basic addition facts
3. using counters to model or act out the problem
4. adjusting the numbers for more simple computation

Answer Enter to expand or collapse answer. Answer expanded

Correct Response: C.

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Mathematics Subtest

Competency 5—Knowledge of student reasoning and instructional practices

DIRECTIONS: Read the question and select the best response.

Which of the following activities would be most appropriate for a 1^stfirst-grade class?

Choose an answer

1. relating value of coins to a dollar
2. identifying the value of each coin
3. combining the values of groups of coins
4. skip counting by tens using dimes as models

AnswerEnter to expand or collapse answer.Answer expanded

Correct Response: B.

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Mathematics Subtest

Competency 5—Knowledge of student reasoning and instructional practices

DIRECTIONS: Read the question and select the best response.

A 1^st-grade child is working with a small pile of manipulative coins. The child is able to identify each coin, but cannot determine the sum of the coins. This is most likely due to the fact that

Choose an answer

1. the child has not reached the necessary developmental stage.
2. the child has had insufficient time to work with the manipulatives.
3. manipulatives are not accurate representations of real money.
4. manipulatives are not intended to assist in computational skills.

AnswerEnter to expand or collapse answer.Answer expanded

Correct Response: A.

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Mathematics Subtest

Competency 5—Knowledge of student reasoning and instructional practices

DIRECTIONS: Read the question and select the best response.

In 1^stfirst grade, students should be able to tell time to the nearest

Choose an answer

1. hour and half hour.
2. hour.
3. quarter hour and minute.
4. minute.

AnswerEnter to expand or collapse answer.Answer expanded

Correct Response: A.

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Mathematics Subtest

Competency 5—Knowledge of student reasoning and instructional practices

DIRECTIONS: Read the question and select the best response.

One of the centers in a teacher's class was one in which the students were to determine the sum of a quarter and 3 pennies. At what grade level are students first expected to know the value of the coins while also finding the sum of a group of coins?

Choose an answer

1. kindergarten
2. 1^st grade
3. 2^nd grade
4. 3^rd grade

Answer Enter to expand or collapse answer. Answer expanded

Correct Response: C.

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Mathematics Subtest

Competency 5—Knowledge of student reasoning and instructional practices

DIRECTIONS: Read the question and select the best response.

Which instructional aid would be least useful for teaching lines of symmetry?

Choose an answer

1. a mirror
2. folded paper
3. ink blots
4. tangrams

AnswerEnter to expand or collapse answer.Answer expanded

Correct Response: D.

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