Elementary Education K–6
For Testing until 12/31/2023
Subtest 4 – Mathematics
Test Format and Sample Questions
The Mathematics subtest contains approximately 35 multiple-choice items. You will have 70 minutes to complete the subtest.
Each of the questions will contain four response options. You will choose the best response out of the available options, and indicate A, B, C, or D. For the Mathematics Subtest, an on-screen mathematics reference sheet will be provided. Beginning October 1, 2023, an on-screen four-function calculator will be provided. Examinees may not bring their own calculator.
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 |
|
Graphics Choose the option that best answers a question involving a number line, a geometric figure, graphs of lines or curves, a table, or a chart. |
Question 9 |
|
Word Problem Apply mathematical principles to solve a real-world problem and choose the best response option. |
Question 17 |
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.
Question 1
Subtest 4 - Mathematics
Competency 1—Knowledge of student thinking and instructional practices
DIRECTIONS: Read the question and select the best response.
Which of the following sequences is the most appropriate learning progression through the levels of geometric thinking?
- Enter to expand or collapse answer.Answer expanded
- Correct Response: D.
Question 2
Subtest 4 - Mathematics
Competency 1—Knowledge of student thinking and instructional practices
DIRECTIONS: Read the question and select the best response.
A local school district requires all fifth graders to complete an untimed test containing 50 multiple choice mathematics problems. The tests are scored and the results are compared throughout the district. What component of mathematics fluency is most likely the goal of this type of assessment?
- Enter to expand or collapse answer.Answer expanded
- Correct Response: D.
Question 3
Subtest 4 - Mathematics
Competency 1—Knowledge of student thinking and instructional practices
DIRECTIONS: Read the question and select the best response.
Analyze the sample scenario to answer the following question.
A student is making belts for some shorts. The student bought 66 inches of fabric which will be cut into 22-inch pieces. How many belts can be made with the fabric purchased?
Which of the following describes the problem structure?
- Enter to expand or collapse answer.Answer expanded
- Correct Response: D.
Question 4
Subtest 4 - Mathematics
Competency 1—Knowledge of student thinking and instructional practices
DIRECTIONS: Read the question and select the best response.
A kindergarten class is learning about addition without regrouping. Which of the following strategies would be most appropriate to begin teaching students how to add two digits?
- Enter to expand or collapse answer.Answer expanded
- Correct Response: D.
Question 5
Subtest 4 - Mathematics
Competency 1—Knowledge of student thinking and instructional practices
DIRECTIONS: Read the question and select the best response.
A student is struggling to progress through the descriptive level of geometric thinking. Which of the following skills is considered the most basic in the levels of geometric thinking?
- Enter to expand or collapse answer.Answer expanded
- Correct Response: A.
Question 6
Subtest 4 - Mathematics
Competency 1—Knowledge of student thinking and instructional practices
DIRECTIONS: Read the question and select the best response.
Students in the third grade study multiplication in terms of equal groups, arrays, and area. What should students in the fourth grade be expected to do as the next step in this learning progression?
- Enter to expand or collapse answer.Answer expanded
- Correct Response: B.
Question 7
Subtest 4 - Mathematics
Competency 1—Knowledge of student thinking and instructional practices
DIRECTIONS: Read the question and select the best response.
Which of the following concepts is recommended to be taught first in the development of fractional understanding for students?
- Enter to expand or collapse answer.Answer expanded
- Correct Response: D.
Question 8
Subtest 4 - Mathematics
Competency 1—Knowledge of student thinking and instructional practices
DIRECTIONS: Read the question and select the best response.
In a fourth -grade mathematics meeting, two teachers are discussing ways to teach multiplication. Teacher A believes the class should be taught the standard algorithm as the best way to solve a multiplication problem. Teacher B believes the students should explore various multiplication strategies and decide which strategy is best for each problem.
What component of math fluency is Teacher B promoting?
- Enter to expand or collapse answer.Answer expanded
- Correct Response: B.
Question 9
Subtest 4 - Mathematics
Competency 2—Knowledge of operations, algebraic thinking, counting and number in base ten
DIRECTIONS: Read the question and select the best response.
A student was responsible for taking care of a plant over a 3 month period. The student measured and recorded the height of the plant at the end of each month as shown in the table.
Number of Months with the Plant Height of the Plant in Inches 0 7 1 9 2 11 3 13
Which of the following equations relates the height of the plant, h, and the number of months, m, that the student had taken care of the plant, assuming a constant rate of growth?
- Enter to expand or collapse answer. Answer expanded
- Correct Response: D.
Question 10
Subtest 4 - Mathematics
Competency 2—Knowledge of operations, algebraic thinking, counting and number in base ten
DIRECTIONS: Read the question and select the best response.
Simplify the expression.
90 minus 60 divided by 30 plus 10
- Enter to expand or collapse answer. Answer expanded
- Correct Response: D.
Question 11
Subtest 4 - Mathematics
Competency 2—Knowledge of operations, algebraic thinking, counting and number in base ten
DIRECTIONS: Read the question and select the best response.
Which step should be done first to simplify the expression?
8a minus 4a divided by 2a minus 16a times 8a + a
- Enter to expand or collapse answer.Answer expanded
- Correct Response: C.
Question 12
Subtest 4 - Mathematics
Competency 2—Knowledge of operations, algebraic thinking, counting and number in base ten
DIRECTIONS: Read the question and select the best response.
Which of the following is NOT equivalent to 22 over 7?
- Enter to expand or collapse answer.Answer expanded
- Correct Response: C.
Question 13
Subtest 4 - Mathematics
Competency 2—Knowledge of operations, algebraic thinking, counting and number in base ten
DIRECTIONS: Read the question and select the best response.
Simplify the following expression.
30 divided by open parens 7 minus 2 close parens times 2
- Enter to expand or collapse answer.Answer expanded
- Correct Response: C.
Question 14
Subtest 4 - Mathematics
Competency 2—Knowledge of operations, algebraic thinking, counting and number in base ten
DIRECTIONS: Read the question and select the best response.
Kruti just purchased 3 shirts, 1 skirt, and 2 pairs of shoes. She would like to compute the change she would receive from a $100 bill. Which operation should she use last?
- Enter to expand or collapse answer.Answer expanded
- Correct Response: D.
Question 15
Subtest 4 - Mathematics
Competency 2—Knowledge of operations, algebraic thinking, counting and number in base ten
DIRECTIONS: Read the question and select the best response.
Which equation illustrates the associative property of multiplication?
- Enter to expand or collapse answer.Answer expanded
- Correct Response: B.
Question 16
Subtest 4 - Mathematics
Competency 2—Knowledge of operations, algebraic thinking, counting and number in base ten
DIRECTIONS: Read the question and select the best response.
A teacher is explaining a mental mathematics strategy to the class and says:
Suppose we wanted to add 76 + 9. One way to do this addition problem is to think: 76 + 9 is the same as 76 plus 10 minus 1, because 10 minus 1 is 9. By adding 76 and 10, we get 86, then subtracting 1 gives the answer 85. This kind of thinking is also called "making 10."
What type of strategy is being taught?
- Enter to expand or collapse answer.Answer expanded
- Correct Response: A.
Question 17
Subtest 4 - Mathematics
Competency 3—Knowledge of fractions, ratios, and integers
DIRECTIONS: Read the question and select the best response.
A group of students are working on a project. They complete 30percent of the project in 12 hours. If they continue to work at the same speed, how many hours will it take the group to finish the project?
- Enter to expand or collapse answer. Answer expanded
- Correct Response: C.
Question 18
Subtest 4 - Mathematics
Competency 3—Knowledge of fractions, ratios, and integers
DIRECTIONS: Read the question and select the best response.
Which of the following numbers represents 75 thousandths?
- Enter to expand or collapse answer. Answer expanded
- Correct Response: B.
Question 19
Subtest 4 - Mathematics
Competency 3—Knowledge of fractions, ratios, and integers
DIRECTIONS: Read the question and select the best response.
A fourth -student is experiencing difficulty in understanding the concept of place value. Which of the following is the best strategy for reteaching the concept?
- Enter to expand or collapse answer. Answer expanded
- Correct Response: A.
Question 20
Subtest 4 - Mathematics
Competency 3—Knowledge of fractions, ratios, and integers
DIRECTIONS: Read the question and select the best response.
A teacher wants to build a scale model of the Earth and Pluto to compare their sizes. The Earth has a diameter of approximately 8000 miles and Pluto has a diameter of approximately 1500 miles. If the teacher builds a model of Earth with a diameter of 32 inches, what should be the diameter of her model of Pluto?
- Enter to expand or collapse answer.Answer expanded
- Correct Response: B.
Question 21
Subtest 4 - Mathematics
Competency 3—Knowledge of fractions, ratios, and integers
DIRECTIONS: Read the question and select the best response.
A teacher went to the store to buy treats for her classroom. At the store, she found the following deals. Which deal is the best buy?
- Enter to expand or collapse answer.Answer expanded
- Correct Response: A.
Question 22
Subtest 4 - Mathematics
Competency 4—Knowledge of measurement, data, and statistics
DIRECTIONS: Read the question and select the best response.
The following circle graph shows the results of a survey of 150 students. How many students chose baseball as their favorite sport?
Favorite Sport
A circle graph has four sections. Baseball is 20 percent of the chart. Football is 32 percent of the chart. Basketball is 8 percent of the chart and finally soccer is 40 percent of the chart.
- Enter to expand or collapse answer. Answer expanded
- Correct Response: C.
Question 23
Subtest 4 - Mathematics
Competency 4—Knowledge of measurement, data, and statistics
DIRECTIONS: Read the question and select the best response.
Which of the following shapes is on the missing side?
There are four objects, numbered 1 through 4. Each is a block with square ends and rectangular faces that share their short edge with the square end. Each block has a smiley face on the visible square end, and the top and right rectangular faces are visible. Block 1. The smiley face is upside down. The top face of the block has a black rectangle with its edges parallel to the long edges of the block face. The right face of the block has a shape composed of two four-sided shapes resembling skewed trapezoids, one black and one white, sharing their long side. The shape is angled so that the near end is closer to the top face of the block and the far end is closer to the bottom face of the block. Block 2. The smiley face has its top to the left. The top face of the block has a black right triangle with its long leg parallel to the long edge of the block face and its short leg close to the far edge of the block face. The right face of the block has a black parallelogram. The parallelogram is angled so that the near tip is closer to the top edge of the block face and the far tip is closer to the bottom edge of the block face. Block 3. The smiley face is top side up. The top face of the block has a rectangle divided in half along the short axis. The near half is white and the far half is black. The long sides of the rectangle are parallel to the long edge of the block face. The right face of the block has a black scalene triangle. The triangle is angled so that the near end is closer to the top edge of the block face and the far end is closer to the bottom edge of the block face. The longest side of the triangle is down, and the opposite angle points up. Block 4. The smiley face has its top to the right. The top face of the block has a shape composed of two trapezoids, one black and one white, sharing their long side. The long axis is parallel to the long edges of the block faces. The black portion is on the right. The right face of the block is blank with a question mark pointing to it.
- Enter to expand or collapse answer.Answer expanded
- Correct Response: A.
Question 24
Subtest 4 - Mathematics
Competency 4—Knowledge of measurement, data, and statistics
DIRECTIONS: Read the question and select the best response.
A student brought a small apple for lunch. Which measurement would best describe the mass of the small apple?
- Enter to expand or collapse answer.Answer expanded
- Correct Response: C.
Question 25
Subtest 4 - Mathematics
Competency 4—Knowledge of measurement, data, and statistics
DIRECTIONS: Read the question and select the best response.
Estimate the mass of a slice of bread.
- Enter to expand or collapse answer.Answer expanded
- Correct Response: A.
Question 26
Subtest 4 - Mathematics
Competency 4—Knowledge of measurement, data, and statistics
DIRECTIONS: Read the question and select the best response.
The math supervisor polled the teachers in the school district concerning which day of the week to hold a staff development workshop. The results showed that 20% of the teachers preferred Monday, 15% preferred Tuesday, 10% preferred Wednesday, 25% preferred Thursday, and 30% preferred Friday.
To decide which day to hold the workshop, which statistic should the supervisor use?
- Enter to expand or collapse answer.Answer expanded
- Correct Response: C.
Question 27
Subtest 4 - Mathematics
Competency 4—Knowledge of measurement, data, and statistics
DIRECTIONS: Read the question and select the best response.
Estimate the weight (mass) of an adult female.
- Enter to expand or collapse answer.Answer expanded
- Correct Response: C.
Question 28
Subtest 4 - Mathematics
Competency 4—Knowledge of measurement, data, and statistics
DIRECTIONS: Read the question and select the best response.
A bottle of children's cough syrup would most likely have a capacity of
- Enter to expand or collapse answer.Answer expanded
- Correct Response: D.
Question 29
Subtest 4 - Mathematics
Competency 4—Knowledge of measurement, data, and statistics
DIRECTIONS: Read the question and select the best response.
An 8 foot square floor is to be covered with square tiles measuring 8 inches on each side. If each tile costs 50 cents, how much will it cost to tile the floor?
- Enter to expand or collapse answer.Answer expanded
- Correct Response: C.
Question 30
Subtest 4 - Mathematics
Competency 5—Knowledge of geometric concepts
DIRECTIONS: Read the question and select the best response.
Which of the following polygons can be classified as regular?
- Enter to expand or collapse answer. Answer expanded
- Correct Response: B.
Question 31
Subtest 4 - Mathematics
Competency 5—Knowledge of geometric concepts
DIRECTIONS: Read the question and select the best response.
A right prism of height 15 cm has bases that are right triangles with legs 5 cm and 12 cm. Find the total surface area of the prism.
There is a diagram of the right prism. The top surface is a right triangle. The two sides of the right angle are dimensioned as 5 and 12. The remaining side of the triangular side is dimensioned as 13. The height of the prism is dimensioned as 15.
- Enter to expand or collapse answer.Answer expanded
- Correct Response: C.
Question 32
Subtest 4 - Mathematics
Competency 5—Knowledge of geometric concepts
DIRECTIONS: Read the question and select the best response.
A living room is two times as long and one and one-half times as wide as a bedroom. The amount of carpet needed for the living room is how many times greater than the amount of carpet needed for the bedroom?
- Enter to expand or collapse answer.Answer expanded
- Correct Response: C.
Question 33
Subtest 4 - Mathematics
Competency 5—Knowledge of geometric concepts
DIRECTIONS: Read the question and select the best response.
The center point of the circle is located at which point on the coordinate grid?
There is diagram of a circle plotted on a coordinate grid. The x axis has values marked from negative 10 to 1 in increments of 1. The y axis has values marked from negative 2 to 7 in increments of 1. The center point is labeled A, and there is a point on the circumference labeled B. The center point is located above the negative 6 on the y axis and to the left of the 4 on the y axis.
- Enter to expand or collapse answer.Answer expanded
- Correct Response: C.
Question 34
Subtest 4 - Mathematics
Competency 5—Knowledge of geometric concepts
DIRECTIONS: Read the question and select the best response.
A sixth-grade teacher is plotting the vertices of a rectangle on a coordinate grid. The first 3 points he plots are (3, 1), (negative 1, 1) and
(negative 1, negative 1). In what quadrant should the last vertex be plotted?
- Enter to expand or collapse answer.Answer expanded
- Correct Response: D.
Question 35
Subtest 4 - Mathematics
Competency 5—Knowledge of geometric concepts
DIRECTIONS: Read the question and select the best response.
On an old map, a student circled the Sun. In which quadrant is the Sun located?
The map is split on a 4 quadrant grid.
- Upper left quadrant: sun symbol with a circle around it
- Upper right quadrant: moon symbol
- Lower right quadrant: star symbol
- Lower left quadrant: lightning bolt symbol
- Enter to expand or collapse answer.Answer expanded
- Correct Response: B.
Question 36
Subtest 4 - Mathematics
Competency 5—Knowledge of geometric concepts
DIRECTIONS: Read the question and select the best response.
Two vertices of a triangle are plotted on the coordinate plane. Which of the following ordered pairs would result in the completed figure being a scalene triangle?
In the diagram of the coordinate plane, the x and y axis have tick marks from negative 10 to 10 in increments of 1, with labels at negative 5 and 5. There is a point at 4 on the x axis and one at the 4 on the y axis.
- Enter to expand or collapse answer.Answer expanded
- Correct Response: C.
Question 37
Subtest 4 - Mathematics
Competency 5—Knowledge of geometric concepts
DIRECTIONS: Read the question and select the best response.
Which statement is true about a triangular pyramid?
- Enter to expand or collapse answer.Answer expanded
- Correct Response: A.
Question 38
Subtest 4 - Mathematics
Competency 5—Knowledge of geometric concepts
DIRECTIONS: Read the question and select the best response.
A rectangular prism has a length of 3 units, width of 4 units, and a height of 5 units. What is the volume of this prism?
- Enter to expand or collapse answer.Answer expanded
- Correct Response: C.