Elementary Education K-6: Mathematics
3 free practice tests · 35 questions each · 1h 10min · No sign-up required
About This Exam
This is Subtest 4 of the FTCE Elementary Education K-6 exam. It covers mathematics content and mathematics instruction at the elementary level. You need to demonstrate both mathematical knowledge and the ability to teach mathematical concepts to K-6 students effectively.
What's Covered
- Number sense, operations, and proportionality — whole numbers, fractions, decimals, percentages, ratios, proportional reasoning, order of operations, and number properties
- Measurement, data analysis, and probability — units of measurement, conversions, perimeter, area, volume, reading and interpreting data displays, mean, median, mode, and basic probability
- Geometry — two-dimensional and three-dimensional shapes, properties of shapes, symmetry, transformations (translations, reflections, rotations), coordinate planes, and angles
- Algebraic thinking and the relationship between algebra and geometry — patterns, expressions, equations, inequalities, function tables, and connecting algebraic and geometric representations
- Mathematical instruction and assessment — concrete-representational-abstract (CRA) sequence, manipulatives, problem-solving strategies, mathematical discourse, and common student misconceptions
For the official exam description, see the official FTCE K-6 Mathematics page.
Study Tips
- Fractions and proportional reasoning are the most heavily tested content areas. Be able to add, subtract, multiply, and divide fractions fluently, and understand fraction models.
- Know the CRA (Concrete-Representational-Abstract) instructional sequence. The exam frequently asks which step comes next or which manipulative is appropriate for a concept.
- Measurement conversions within and between systems are commonly tested. Know the relationships between units (inches to feet, grams to kilograms, etc.).
- Geometry questions often require you to calculate area and perimeter of composite shapes. Practice decomposing shapes into rectangles and triangles.
- Read the pedagogy questions carefully — when two math strategies are both valid, the exam usually favors the one that builds conceptual understanding over rote procedure.
How to Register
Register at fl.nesinc.com. The exam costs $150 (for all four K-6 subtests taken together). A scaled score of 200 (scaled) is required to pass. Military personnel, veterans, and their spouses may be eligible for certification exam fee waivers through the Florida Department of Education.
About Our Practice Tests
All questions are original and written to match the difficulty, format, and topic coverage of the real exam based on official exam descriptions. We offer two modes: Practice Mode gives you instant feedback and explanations after each question, and Test Mode simulates the real exam with a timer and no feedback until you submit. Both modes are completely free with no account required.
Sample Practice Questions
Review these sample questions to get a feel for the exam. For the full interactive experience, use the Practice Tests above.
- A) 2 hundreds blocks, 3 tens rods, and 4 unit cubes
- B) 23 tens rods and 4 unit cubes
- C) 2 tens rods, 3 hundreds blocks, and 4 unit cubes
- D) 234 unit cubes only
View Answer & Explanation
Correct Answer:
A) 2 hundreds blocks, 3 tens rods, and 4 unit cubes
Explanation:
In base-ten representation, 234 = 2 hundreds (flats) + 3 tens (rods) + 4 ones (unit cubes). This models place value concretely: each position represents a power of 10. While choice D (234 unit cubes) has the correct total value, it doesn't demonstrate place value understanding.
- A) Commutative property
- B) Associative property
- C) Distributive property
- D) Identity property
View Answer & Explanation
Correct Answer:
C) Distributive property
Explanation:
The distributive property states that a(b + c) = ab + ac. Multiplying a number by a sum equals the sum of individual products. This property is fundamental in mental math and algebra. The commutative property involves order (ab = ba); associative involves grouping ((ab)c = a(bc)).
- A) tell the student the answer is wrong without explanation
- B) ask the student to use a multiplication check: 7 × 6 = 42, not 48, to identify the error
- C) move on to the next problem
- D) assign extra homework
View Answer & Explanation
Correct Answer:
B) ask the student to use a multiplication check: 7 × 6 = 42, not 48, to identify the error
Explanation:
Using the inverse relationship between multiplication and division teaches self-checking strategies. Having the student verify with 7 × 6 = 42 ≠ 48 reveals the error naturally. Then the student can find the correct answer: 48 ÷ 6 = 8, verified by 8 × 6 = 48.
- A) 15
- B) 21
- C) 23
- D) 27
View Answer & Explanation
Correct Answer:
C) 23
Explanation:
A prime number has exactly two factors: 1 and itself. 23 is divisible only by 1 and 23. 15 = 3 × 5 (composite); 21 = 3 × 7 (composite); 27 = 3 × 9 (composite). Prime numbers are fundamental in number theory and have exactly two distinct factors.
- A) Protractors
- B) Fraction circles or fraction bars that visually represent parts of a whole
- C) Calculators
- D) Rulers
View Answer & Explanation
Correct Answer:
B) Fraction circles or fraction bars that visually represent parts of a whole
Explanation:
Fraction circles and bars provide concrete, visual representations of fractions — showing that 1/4 means one of four equal parts. Students can physically compare fractions (seeing 1/2 > 1/4), find equivalents, and perform operations. Concrete manipulatives are essential for building fractional understanding before abstract procedures.