FTCE PreK–3
Math Exam
Study Guide –
Latest Version
2026
FTCE PreK–3 Mathematics (053) Exam Study Guide
100 Practice Questions & Answers
Domain 1: Number Sense and Operations
,1. A kindergarten student is counting a set of 12 objects. Which counting principle is the
student demonstrating when they say the last number name, "twelve," represents the total
number of objects?
A. Order Irrelevance Principle
B. Stable Order Principle
C. Cardinality Principle ✓
D. One-to-One Correspondence Principle
2. Which of the following is the best example of a teacher using a manipulative to develop the
concept of conservation of number?
A. Showing flash cards with numbers and pictures.
B. Having students count beads on a string.
C. Arranging 7 counters in a tight cluster and then spreading them out, asking if the number
changed. ✓
D. Having students write numbers in a workbook.
3. A student writes "51" for "fifteen." This error is most likely due to a misunderstanding of:
A. Multiplication facts.
B. Place value. ✓
C. Fraction equivalence.
D. Geometric shapes.
4. Which number is composite?
A. 17
B. 23
C. 31
D. 39 ✓
5. What is the prime factorization of 84?
A. 2 x 2 x 21
B. 2 x 3 x 14
C. 2² x 3 x 7 ✓
D. 4 x 3 x 7
6. A number is rounded to 3.8. What is the smallest possible value the original number could
have been?
A. 3.749
B. 3.75 ✓
C. 3.79
D. 3.84
,7. Which model is most appropriate for teaching the concept of fractions as parts of a whole?
A. A number line
B. A hundreds chart
C. A set of counting bears
D. A area model (e.g., a partitioned circle or rectangle) ✓
8. Which fraction is between 1/2 and 3/4?
A. 2/5
B. 5/8 ✓
C. 1/3
D. 7/10
9. A recipe calls for 2/3 cup of milk and 1/2 cup of oil. What is the total volume of liquid?
A. 3/5 cup
B. 7/6 cups ✓
C. 3/6 cup
D. 5/6 cup
10. What is 4.5% written as a decimal?
A. 0.045 ✓
B. 0.45
C. 4.5
D. 450
11. A teacher asks students to represent the number 5 in as many ways as possible. Which of
the following student responses shows a correct but non-standard representation?
A. 2 + 3
B. V (Roman numeral)
C. Five
D. A drawing of a hand ✓
12. Which operation should be used to solve the problem: "There are 6 boxes with 4 cookies
in each box. How many cookies are there in all?"
A. Addition
B. Subtraction
C. Multiplication ✓
D. Division
13. Using the distributive property, how can 6 x 8 be expressed?
A. (6 x 4) + (6 x 4) ✓
, B. (6 + 8) x (6 + 8)
C. (6 x 6) + (6 x 2)
D. 6 + 6 + 6 + 6 + 6 + 6 + 6 + 6
14. What is the greatest common factor (GCF) of 24 and 36?
A. 6
B. 12 ✓
C. 18
D. 24
15. What is the least common multiple (LCM) of 6 and 8?
A. 24 ✓
B. 48
C. 16
D. 32
Domain 2: Algebraic Reasoning
16. A repeating pattern using shapes is: Circle, Square, Triangle, Circle, Square, Triangle,
Circle... What is the next shape?
A. Circle
B. Square ✓
C. Triangle
D. Diamond
17. Which of the following is an example of a growing pattern?
A. A, B, C, A, B, C, A...
B. 2, 4, 6, 8, 10... ✓
C. Red, Blue, Red, Blue, Red...
D. 5, 3, 5, 3, 5, 3...
18. If □ + 7 = 15, what is the value of □?
A. 7
B. 8 ✓
C. 15
D. 22
19. A function rule is "multiply by 3 and then subtract 1." If the input is 4, what is the output?
A. 8
Math Exam
Study Guide –
Latest Version
2026
FTCE PreK–3 Mathematics (053) Exam Study Guide
100 Practice Questions & Answers
Domain 1: Number Sense and Operations
,1. A kindergarten student is counting a set of 12 objects. Which counting principle is the
student demonstrating when they say the last number name, "twelve," represents the total
number of objects?
A. Order Irrelevance Principle
B. Stable Order Principle
C. Cardinality Principle ✓
D. One-to-One Correspondence Principle
2. Which of the following is the best example of a teacher using a manipulative to develop the
concept of conservation of number?
A. Showing flash cards with numbers and pictures.
B. Having students count beads on a string.
C. Arranging 7 counters in a tight cluster and then spreading them out, asking if the number
changed. ✓
D. Having students write numbers in a workbook.
3. A student writes "51" for "fifteen." This error is most likely due to a misunderstanding of:
A. Multiplication facts.
B. Place value. ✓
C. Fraction equivalence.
D. Geometric shapes.
4. Which number is composite?
A. 17
B. 23
C. 31
D. 39 ✓
5. What is the prime factorization of 84?
A. 2 x 2 x 21
B. 2 x 3 x 14
C. 2² x 3 x 7 ✓
D. 4 x 3 x 7
6. A number is rounded to 3.8. What is the smallest possible value the original number could
have been?
A. 3.749
B. 3.75 ✓
C. 3.79
D. 3.84
,7. Which model is most appropriate for teaching the concept of fractions as parts of a whole?
A. A number line
B. A hundreds chart
C. A set of counting bears
D. A area model (e.g., a partitioned circle or rectangle) ✓
8. Which fraction is between 1/2 and 3/4?
A. 2/5
B. 5/8 ✓
C. 1/3
D. 7/10
9. A recipe calls for 2/3 cup of milk and 1/2 cup of oil. What is the total volume of liquid?
A. 3/5 cup
B. 7/6 cups ✓
C. 3/6 cup
D. 5/6 cup
10. What is 4.5% written as a decimal?
A. 0.045 ✓
B. 0.45
C. 4.5
D. 450
11. A teacher asks students to represent the number 5 in as many ways as possible. Which of
the following student responses shows a correct but non-standard representation?
A. 2 + 3
B. V (Roman numeral)
C. Five
D. A drawing of a hand ✓
12. Which operation should be used to solve the problem: "There are 6 boxes with 4 cookies
in each box. How many cookies are there in all?"
A. Addition
B. Subtraction
C. Multiplication ✓
D. Division
13. Using the distributive property, how can 6 x 8 be expressed?
A. (6 x 4) + (6 x 4) ✓
, B. (6 + 8) x (6 + 8)
C. (6 x 6) + (6 x 2)
D. 6 + 6 + 6 + 6 + 6 + 6 + 6 + 6
14. What is the greatest common factor (GCF) of 24 and 36?
A. 6
B. 12 ✓
C. 18
D. 24
15. What is the least common multiple (LCM) of 6 and 8?
A. 24 ✓
B. 48
C. 16
D. 32
Domain 2: Algebraic Reasoning
16. A repeating pattern using shapes is: Circle, Square, Triangle, Circle, Square, Triangle,
Circle... What is the next shape?
A. Circle
B. Square ✓
C. Triangle
D. Diamond
17. Which of the following is an example of a growing pattern?
A. A, B, C, A, B, C, A...
B. 2, 4, 6, 8, 10... ✓
C. Red, Blue, Red, Blue, Red...
D. 5, 3, 5, 3, 5, 3...
18. If □ + 7 = 15, what is the value of □?
A. 7
B. 8 ✓
C. 15
D. 22
19. A function rule is "multiply by 3 and then subtract 1." If the input is 4, what is the output?
A. 8
