Does ParaPathways provide a calculator?

Yes, an on-screen 4-function calculator is provided for the entire Mathematics subtest (ETS 5759). No personal calculators are permitted.

ETS 5759 Mathematics Subtest Practice, On-Screen Calculator Included, Free

ParaPathways Math Practice Test

36 fixed sample questions · single-select and numeric entry · ETS 5759 · free demo

36 Questions 60 min Calculator included Free · No account

Free ParaPathways Math Practice Test

Mathematics · ETS 5759 · 36 Questions

Question 1 of 36 0 correct

Question 1 Numeric entry numbers operations

What is the value of 2 × 5 + 3³?

Type your answer

Answer and explanation

Correct answer: 37

Follow order of operations (PEMDAS): First, calculate the exponent: 3³ = 27. Then multiply: 2 × 5 = 10. Then add: 10 + 27 = 37.

Question 2 Single-select numbers operations

Jamal has $25 to spend at a school store. He buys a notebook for $9 and a pen for $5. Which expression represents the amount of money Jamal has left?

A 25 + (9 + 5) B 25 − (9 + 5) C (25 − 9) + 5 D 25 × (9 − 5)

Answer and explanation

Correct answer: 25 − (9 + 5)

Jamal starts with $25 and spends $9 + $5 = $14. The amount left is $25 − ($9 + $5), which equals $25 − $14 = $11. Option B correctly represents subtracting the total spent from the starting amount. Option A adds instead of subtracts. Option C subtracts only the notebook then adds the pen back, giving a different result. Option D uses multiplication incorrectly.

Question 3 Single-select numbers operations

A recipe calls for 1½ cups of flour. A paraeducator wants to make only ½ of the recipe. How much flour is needed?

A ½ cup B 1 cup C ¾ cup D ¼ cup

Answer and explanation

Correct answer: ¾ cup

Half the recipe means multiplying 1½ by ½. Convert 1½ to an improper fraction: 3/2. Multiply: 3/2 × 1/2 = 3/4. So ¾ cup of flour is needed. You can verify: ¾ is half of 1½ because 1½ = 1.5 and 1.5 × 0.5 = 0.75 = ¾.

Question 4 Single-select numbers operations

To solve the equation 3x + 5 = 20, what should be the FIRST step?

A Multiply both sides by 3 B Divide both sides by 3 C Add 5 to both sides D Subtract 5 from both sides

Answer and explanation

Correct answer: Subtract 5 from both sides

To isolate the variable x, work in reverse order of operations. Since 5 is being added to 3x, subtract 5 from both sides first: 3x + 5 − 5 = 20 − 5, giving 3x = 15. Then divide by 3 to get x = 5. Multiplying (A) or dividing (B) first doesn't simplify the equation. Adding 5 (C) moves in the wrong direction.

Question 5 Single-select geometry data

A classroom has two square sections. One square has sides of 3 feet and the other has sides of 4 feet. What is the difference in area between the two squares?

A 1 square foot B 7 square feet C 12 square feet D 25 square feet

Answer and explanation

Correct answer: 7 square feet

Area of a square = side². Large square: 4² = 16 sq ft. Small square: 3² = 9 sq ft. Difference: 16 − 9 = 7 square feet. Option A (1) is just 4 − 3. Option C (12) is 3 × 4. Option D (25) is (3 + 4)²... actually (3+4)=7 and 7²=49, so D is not that. B is correct.

Question 6 Single-select geometry data

A teacher asks students to estimate the weight of a standard hardcover textbook. Which estimate is most reasonable?

A About 2 ounces B About 1 pound C About 5 pounds D About 10 pounds

Answer and explanation

Correct answer: About 5 pounds

A standard hardcover textbook (such as a science, math, or social studies text) typically weighs 3–5 pounds. C (about 5 pounds) is the most reasonable estimate. A (2 ounces) is far too light, that's less than a smartphone. B (1 pound) is too light for a hardcover text. D (10 pounds) would be a large reference atlas or encyclopaedia, not a typical classroom textbook.

Question 7 Numeric entry geometry data

A rectangular bulletin board is 8 feet long and 5 feet wide. What is the area of the bulletin board in square feet?

Type your answer

Answer and explanation

Correct answer: 40

Area of a rectangle = length × width = 8 × 5 = 40 square feet.

Question 8 Numeric entry geometry data

Find the median of this set of numbers: {5, 22, 17, 3, 8}

Type your answer

Answer and explanation

Correct answer: 8

To find the median, arrange in order: {3, 5, 8, 17, 22}. With 5 numbers, the median is the middle value (3rd value) = 8.

Question 9 Single-select geometry data

A bar graph shows how students voted for their favorite after-school activity. Sports: 14, Art: 8, Reading Club: 6, Music: 10. How many MORE students voted for Sports than for Art?

A 4 students B 5 students C 6 students D 8 students

Answer and explanation

Correct answer: 6 students

Sports received 14 votes. Art received 8 votes. Difference = 14 − 8 = 6 students. Option A (4) = 10 − 6 (Music vs Reading). Option B (5) is not a difference in the data. Option D (8) is the number who voted for Art, not the difference.

Question 10 Single-select numbers operations

A class of 25 students took a quiz. 60% of the students passed. How many students passed?

A 12 students B 15 students C 18 students D 20 students

Answer and explanation

Correct answer: 15 students

60% of 25 = 0.60 × 25 = 15 students. You can also calculate: 60/100 × 25 = 60 × 25 ÷ 100 = 1500 ÷ 100 = 15.

Question 11 Single-select numbers operations

A recipe uses 2 cups of sugar for every 3 cups of flour. If a baker uses 12 cups of flour, how many cups of sugar are needed?

A 6 cups B 7 cups C 8 cups D 9 cups

Answer and explanation

Correct answer: 8 cups

Set up the proportion: 2/3 = x/12. Cross-multiply: 3x = 24. Divide: x = 8. So 8 cups of sugar are needed. You can also think: 12 cups of flour is 4 times the original 3 cups, so multiply sugar by 4: 2 × 4 = 8.

Question 12 Numeric entry numbers operations

A school bus travels 15 miles to school and 15 miles back, 5 days a week. How many total miles does the bus travel in 4 weeks?

Type your answer

Answer and explanation

Correct answer: 600

Daily miles: 15 + 15 = 30 miles/day. Weekly miles: 30 × 5 = 150 miles/week. 4 weeks: 150 × 4 = 600 miles.

Question 13 Single-select geometry data

A classroom rug is shaped like a rectangle. It is 9 feet long and 6 feet wide. What is the perimeter of the rug?

A 15 feet B 30 feet C 54 feet D 27 feet

Answer and explanation

Correct answer: 30 feet

Perimeter of a rectangle = 2 × (length + width) = 2 × (9 + 6) = 2 × 15 = 30 feet. Option A (15) is just length + width without doubling. Option C (54) is area (9 × 6). Option D (27) is 9 × 3.

Question 14 Single-select geometry data

Six students scored the following on a math quiz: 72, 85, 90, 68, 85, 72. What is the mode of these scores?

A 68 B 72 and 85 C 78.67 D 80

Answer and explanation

Correct answer: 72 and 85

The mode is the value(s) that appear most frequently. Both 72 and 85 each appear twice, more than 68 or 90. This dataset has two modes (bimodal): 72 and 85. The mean (average) would be (72+85+90+68+85+72)/6 = 472/6 ≈ 78.67, which is C, not the mode.

Question 15 Numeric entry numbers operations

A paraeducator buys 3 notebooks at $2.75 each and 2 folders at $1.50 each. What is the total cost in dollars?

Type your answer

Answer and explanation

Correct answer: 11.25

Notebooks: 3 × $2.75 = $8.25. Folders: 2 × $1.50 = $3.00. Total: $8.25 + $3.00 = $11.25.

Question 16 Single-select numbers operations

Which of the following numbers is NOT a prime number?

A 11 B 17 C 21 D 23

Answer and explanation

Correct answer: 21

A prime number has exactly two factors: 1 and itself. 21 = 3 × 7, so it has four factors (1, 3, 7, 21), it is NOT prime. 11, 17, and 23 are all prime numbers (divisible only by 1 and themselves).

Question 17 Single-select geometry data

A bag contains 4 red marbles, 3 blue marbles, and 5 green marbles. If one marble is drawn at random, what is the probability of drawing a blue marble?

A 1/6 B 1/3 C 3/12 D 1/5

Answer and explanation

Correct answer: 3/12

Total marbles = 4 + 3 + 5 = 12. Blue marbles = 3. Probability = 3/12 (which simplifies to 1/4). A (1/6) would mean 2 blue out of 12. B (1/3) would mean 4 blue out of 12. D (1/5) would mean a total of 15 marbles. C correctly represents 3 blue out of 12 total.

Question 18 Single-select numbers operations

A school orders 48 boxes of crayons. Each box has 24 crayons. Which estimate is closest to the total number of crayons ordered?

A About 100 crayons B About 500 crayons C About 1,000 crayons D About 5,000 crayons

Answer and explanation

Correct answer: About 1,000 crayons

Estimate: 48 ≈ 50 and 24 ≈ 25. 50 × 25 = 1,250, which is closest to 1,000. The actual answer is 48 × 24 = 1,152. Options A (100) and B (500) are too low; option D (5,000) is too high.

Question 19 Single-select numbers operations

A student is struggling to understand that 1/2 and 2/4 are equal fractions. Which CONCRETE manipulative would best help demonstrate this concept?

A Show the student a number line with fractions labeled at equal intervals B Have the student fold a paper into halves, then fold another identical paper into fourths, and compare the shaded sections C Write the fractions on the board and explain that they are equivalent using cross-multiplication D Give the student a worksheet with 20 equivalent fraction problems to complete

Answer and explanation

Correct answer: Have the student fold a paper into halves, then fold another identical paper into fourths, and compare the shaded sections

The concrete manipulative approach (fold paper, shade, compare) gives the student a tangible, visual way to see that 1/2 and 2/4 cover the same area, building genuine conceptual understanding before the abstract notation. A number line (A) is semi-concrete but less tactile. Cross-multiplication (C) is an abstract procedure that doesn't build conceptual understanding. A worksheet (D) is practice, not initial instruction.

Question 20 Single-select geometry data

A pie chart shows how a classroom of 30 students spends free time. Reading: 30%, Gaming: 40%, Sports: 20%, Art: 10%. How many students chose Sports?

A 3 students B 6 students C 9 students D 12 students

Answer and explanation

Correct answer: 6 students

20% of 30 students chose Sports. 0.20 × 30 = 6 students. Reading: 0.30 × 30 = 9. Gaming: 0.40 × 30 = 12. Art: 0.10 × 30 = 3. Total: 9+12+6+3 = 30. ✓

Question 21 Single-select numbers operations

The temperature in a classroom was -3°F in the morning. By afternoon, the temperature dropped another 8 degrees. What is the temperature in the afternoon?

A -11°F B -5°F C 5°F D 11°F

Answer and explanation

Correct answer: -11°F

To find the new temperature, add the drop to the starting temperature: -3 + (-8) = -3 - 8 = -11°F. When adding a negative number, you move further left (lower) on the number line. Starting at -3 and moving 8 more units in the negative direction gives -11°F.

Question 22 Single-select numbers operations

A paraeducator is checking a student's work on the following expression. What is the correct value of (4 + 6) × 3 - 2²?

A 26 B 28 C 34 D 30

Answer and explanation

Correct answer: 26

Follow the order of operations (PEMDAS): Step 1, Parentheses: (4 + 6) = 10. Step 2, Exponents: 2² = 4. Step 3, Multiplication: 10 × 3 = 30. Step 4, Subtraction: 30 - 4 = 26. The correct answer is 26.

Question 23 Single-select numbers operations

A student is working on the equation 3x + 7 = 22. What is the value of x?

A 3 B 4 C 5 D 6

Answer and explanation

Correct answer: 5

Solve for x step by step: Step 1, Subtract 7 from both sides: 3x = 22 - 7 = 15. Step 2, Divide both sides by 3: x = 15 ÷ 3 = 5. Check: 3(5) + 7 = 15 + 7 = 22. Correct.

Question 24 Single-select numbers operations

A paraeducator asks a student to evaluate the expression 4² + 3³. What is the correct answer?

A 35 B 43 C 49 D 25

Answer and explanation

Correct answer: 43

Evaluate each exponent separately: Step 1, 4² means 4 × 4 = 16. Step 2, 3³ means 3 × 3 × 3 = 27. Step 3, Add the results: 16 + 27 = 43. The correct answer is 43.

Question 25 Numeric entry numbers operations

A reading table in the classroom is 5.5 feet long. How many inches long is the table? (There are 12 inches in 1 foot.)

Type your answer

Answer and explanation

Correct answer: 66

To convert feet to inches, multiply by 12 (since there are 12 inches in 1 foot): 5.5 feet × 12 inches/foot = 66 inches. The table is 66 inches long.

Question 26 Single-select numbers operations

A paraeducator is helping students practice adding mixed numbers. What is 2 3/4 + 1 2/4?

A 3 5/4 B 4 1/4 C 3 1/4 D 4 3/4

Answer and explanation

Correct answer: 4 1/4

Step 1, Add the whole numbers: 2 + 1 = 3. Step 2, Add the fractions: 3/4 + 2/4 = 5/4. Step 3, Convert the improper fraction: 5/4 = 1 1/4. Step 4, Add to the whole number total: 3 + 1 1/4 = 4 1/4. The answer is 4 1/4.

Question 27 Single-select numbers operations

A teacher asks students to divide 3/4 ÷ 1/2 as part of a fraction lesson. What is the correct answer?

A 3/8 B 1 1/4 C 1 1/2 D 2

Answer and explanation

Correct answer: 1 1/2

To divide fractions, multiply by the reciprocal of the divisor: Step 1, Find the reciprocal of 1/2, which is 2/1. Step 2, Multiply: 3/4 × 2/1 = 6/4. Step 3, Simplify: 6/4 = 3/2 = 1 1/2. The answer is 1 1/2.

Question 28 Single-select numbers operations

The school store sells a notebook for $40. The price increases by 15%. What is the new price of the notebook?

A $44.00 B $45.00 C $46.00 D $55.00

Answer and explanation

Correct answer: $46.00

Step 1, Find 15% of $40: 0.15 × 40 = $6.00. Step 2, Add the increase to the original price: $40.00 + $6.00 = $46.00. Alternatively, multiply directly: $40 × 1.15 = $46.00. The new price is $46.00.

Question 29 Single-select numbers operations

A school has 80 students enrolled in an after-school program. Due to schedule changes, 25% of the students transferred to a different program. How many students remain?

A 55 B 60 C 65 D 20

Answer and explanation

Correct answer: 60

Step 1, Find 25% of 80: 0.25 × 80 = 20 students transferred. Step 2, Subtract from the original: 80 - 20 = 60 students remain. Alternatively, since 25% left, 75% stayed: 0.75 × 80 = 60. The answer is 60 students.

Question 30 Single-select numbers operations

A paraeducator is teaching place value. In the number 4,752, what is the value of the digit 7?

A 7 B 70 C 700 D 7,000

Answer and explanation

Correct answer: 700

Identify each digit's place in 4,752: 4 is in the thousands place (value = 4,000), 7 is in the hundreds place (value = 700), 5 is in the tens place (value = 50), 2 is in the ones place (value = 2). The digit 7 is in the hundreds place, so its value is 700.

Question 31 Numeric entry numbers operations

Maria works as a paraeducator and earns $12.50 per hour. She works 6 hours on Monday and 4 hours on Wednesday. How many dollars does she earn in total? (Enter the number only.)

Type your answer

Answer and explanation

Correct answer: 125

Step 1, Find total hours worked: 6 + 4 = 10 hours. Step 2, Multiply total hours by the hourly rate: 10 × $12.50 = $125.00. Maria earns $125 in total.

Question 32 Single-select numbers operations

A student is practicing integer subtraction and needs to evaluate -8 - (-3). What is the correct result?

A -11 B -5 C 5 D 11

Answer and explanation

Correct answer: -5

Subtracting a negative number is the same as adding its opposite: -8 - (-3) = -8 + 3. Since the numbers have opposite signs, subtract the smaller absolute value from the larger: 8 - 3 = 5, then keep the sign of the number with the larger absolute value (negative): result = -5.

Question 33 Numeric entry numbers operations

Evaluate the expression: 18 ÷ (2 + 1) + 5²

Type your answer

Answer and explanation

Correct answer: 31

Follow the order of operations (PEMDAS): Step 1, Parentheses: (2 + 1) = 3. Step 2, Exponents: 5² = 25. Step 3, Division: 18 ÷ 3 = 6. Step 4, Addition: 6 + 25 = 31. The answer is 31.

Question 34 Single-select numbers operations

A paraeducator is modeling multiplication of mixed numbers for a student. What is 1 1/2 × 2 2/3?

A 3 B 3 1/2 C 4 D 4 1/3

Answer and explanation

Correct answer: 4

Step 1, Convert each mixed number to an improper fraction: 1 1/2 = 3/2, and 2 2/3 = 8/3. Step 2, Multiply the improper fractions: 3/2 × 8/3 = 24/6. Step 3, Simplify: 24/6 = 4. The answer is 4.

Question 35 Numeric entry numbers operations

On a classroom map, the scale is 1 inch = 25 miles. Two cities on the map are 3.5 inches apart. How many miles apart are the two cities in real life?

Type your answer

Answer and explanation

Correct answer: 87.5

Set up a proportion using the map scale: 1 inch / 25 miles = 3.5 inches / x miles. Cross-multiply: x = 3.5 × 25 = 87.5 miles. Alternatively, multiply the number of inches by the scale factor: 3.5 × 25 = 87.5. The two cities are 87.5 miles apart.

Question 36 Numeric entry geometry data

A paraeducator cuts out a triangular bulletin board decoration that has a base of 12 cm and a height of 8 cm. What is the area of the triangle in square centimeters?

Type your answer

Answer and explanation

Correct answer: 48

The formula for the area of a triangle is A = 1/2 × base × height. Substitute the values: A = 1/2 × 12 × 8. Multiply: 1/2 × 12 = 6, then 6 × 8 = 48. The area is 48 square centimeters.

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What's covered

What's actually on the Math subtest

36 questions, 60 minutes, calculator on for the whole thing. The questions split roughly evenly between Numbers and Operations (fractions, percentages, order of operations, word problems) and Geometry and Data (area, perimeter, charts, graphs, averages, basic measurement). The math itself is not advanced, this is paraeducator certification, not the SAT, but the time pressure and the calculator interface are what catch people off guard. Practice with our calculator at least twice before exam day so it feels familiar, not foreign.

Numbers & Operations

~18 questions · 50%

1Whole numbers, place value, ordering, rounding

2Fractions, add, subtract, multiply, divide

3Decimals, operations, place value, converting

4Percentages, percent of number, percent change

5Ratio and proportion

6Order of operations (PEMDAS)

7Linear equations, one variable

8Word problems, real classroom scenarios

Geometry, Measurement & Data

~18 questions · 50%

1Area and perimeter of rectangles, triangles

2Volume of rectangular prisms

3Circumference and area of circles

4Reading bar graphs, pie charts, line graphs

5Mean, median, mode, range

6Basic probability

7Unit conversions, metric and customary

8Reasonable estimation and measurement

FAQ

How the on-screen calculator works in ParaPathways Math

Does the real exam give you a calculator?+

Yes, an on-screen 4-function calculator is available for the entire Math subtest (ETS 5759). You cannot bring your own calculator. Our practice test includes the identical calculator interface with Transfer Display functionality.

What question types are on the Math subtest?+

Two formats: single-select (choose one answer A–D) and numeric entry (type a number into a blank box). The Transfer Display button copies the calculator result directly into the numeric entry field, just like the real exam.

Do I need to memorize formulas?+

No formula sheet is provided on the real exam. You need to know: area/perimeter of rectangles and triangles, circumference and area of circles, and volume of rectangular prisms. The calculator handles arithmetic, you supply the setup.

What is the passing score for Math?+

The recommended passing score is approximately 334 scaled (out of 350). Some states use 332. Check the state passing scores page for your specific state's requirement.

How it works

The two question formats you'll see, and which one trips people up

Math uses single-select with four answer choices like every other multiple-choice test, no surprises there. The other format is numeric entry: an empty rectangle, no options, just type the number. That's where the on-screen calculator earns its keep. After you punch in the equation, hit Transfer Display and the answer drops straight into the input field, no retyping. Honestly, the biggest mistake I see paraeducators make is doing arithmetic in their head to "save time," then losing points on the kind of careless errors the calculator was designed to eliminate. Use it on every step, even the easy ones. There's no bonus for mental math on this exam.

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Passing Score by State →

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Exam Day Guide →

What to bring, timing, and what to expect

ParaPathways vs ParaPro →

Which exam does your state require?

Question formats

The Math formats you will see in the practice test

The Math practice test mixes answer formats and topic formats. Learn what each one looks like first, then use the full quiz to build speed and accuracy.

Format · Single-select

Four answer choices, one correct answer.

This is the most familiar format. Read the question, solve before looking too hard at the choices, then use the choices to catch obvious mistakes.

Recognize it: answers are labeled A-D.
Best method: solve first, then match your result.
Watch for: distractors that use the right numbers in the wrong operation.

Example

A class of 25 students took a quiz. 60% passed. Solve 0.60 x 25 = 15, then choose the answer choice that matches 15.

Format · Numeric entry

No answer choices. Type the number yourself.

Numeric entry questions feel harder because there is no list of answers to reassure you. The key is writing a clean expression before typing anything.

Recognize it: the answer area is a blank input box.
Best method: set up the equation, calculate, then type only the final value.
Watch for: extra units, commas, or rounding that the prompt did not ask for.

Example

A bulletin board is 8 feet by 5 feet. Area is length x width, so 8 x 5 = 40. Type 40.

Format · Calculator transfer

Use the calculator display without retyping.

Some Math mistakes happen after the math is already solved. Transfer Display helps prevent copying the wrong digit into a numeric-entry field.

Recognize it: the answer is calculated, then typed into a box.
Best method: calculate once, transfer the display, then check the field.
Watch for: decimals and negative numbers.

Example

If the calculator shows 11.25 for a money problem, transfer or copy 11.25 exactly. Do not round unless the question asks for a whole number.

Format · Word problem

Classroom stories that hide a simple operation.

Word problems usually test whether you can turn a classroom situation into math. Underline the action: total, difference, each, left, more, fewer, percent, or ratio.

Recognize it: a student, teacher, class, recipe, bus, or school supply situation.
Best method: write the operation in words before calculating.
Watch for: answering the intermediate number instead of the final question.

Example

A student has $25 and buys items costing $9 and $5. The setup is money left = 25 - (9 + 5), not 25 + 14.

Format · Chart and data

Tables, graphs, averages, medians, and comparisons.

Data questions are often easier when you slow down. First identify what the chart is measuring, then find the exact row, bar, or value the question names.

Recognize it: table, graph, list of scores, votes, or measurements.
Best method: label the needed values before calculating.
Watch for: mean vs median vs mode.

Example

For 5, 22, 17, 3, 8, put the numbers in order first: 3, 5, 8, 17, 22. The median is the middle value, 8.

Format · Geometry and formulas

Area, perimeter, volume, circles, and measurement.

Formula questions are usually direct if you choose the right formula. The most common trap is using area when the question asks for perimeter, or perimeter when it asks for area.

Recognize it: shape, side length, radius, diameter, height, width, or unit conversion.
Best method: write the formula before substituting numbers.
Watch for: square units vs linear units.

Example

A rectangle that is 9 feet long and 6 feet wide has perimeter 2 x (9 + 6) = 30 feet. Area would be 54 square feet, but that answers a different question.