FTCE Middle Grades Mathematics 5-9 Exam Prep

FTCE Middle Grades Math Exam Overview

The Florida Teacher Certification Exam (FTCE) Middle Grades Mathematics 5-9 is a computer-based, 70-question FTCE test for prospective middle school math teachers in Florida. The FTCE Math 5-9 tests candidates on mathematical foundations taught at the middle school education level.

The test questions are all multiple choice with four response options (A-D), and there are five different question types: word problem, graphics, scenario, direct question, and command. The test makeup consists of ten tested competencies related to solving, analyzing, and understanding mathematical concepts, such as algebra, statistics, and geometry.

Test takers have 2 hours and 30 minutes to complete the exam. To pass the FTCE middle school math test, which is pass/fail, candidates must receive a scaled score of 200, which means candidates must correctly answer about 71% of the questions. This article will outline the FTCE Middle Grades Mathematics 5-9 tested topics, exam format, FTCE registration, testing policies, and preparation.

Practice tests give you a better idea of the topics you have mastered and those you should keep studying.

What is on the FTCE Middle Grades Math Exam?

The FTCE middle school math test is divided into ten tested competencies, with each competency further broken down into various skills. The content of these FTCE competencies and percentage of the test is listed here:

Competency 1: Problem-Solving and Reasoning Skills (13%)

Competency 1 covers eight skills:

  1. Apply mathematical equations to real-world scenarios.
  2. Solve multi-step problems.
  3. Assess result validity from the original problem.
  4. Solve various problems utilizing mathematical concepts.
  5. Validate or invalidate mathematical arguments.
  6. Compose educated conclusions from various statements.
  7. Implement teaching strategies for problem-solving for students.
  8. Understand the difference between deductive and inductive reasoning.

Competency 2: Mathematical Manipulatives and models, and instructional technology (6%)

Competency 2 encompasses four skills:

  1. Display knowledge of different mathematical representations.
  2. Analyze mathematical concepts through varying representations.
  3. Identify technology, resources, and manipulatives that help teach mathematics.
  4. Identify technology, resources, and manipulatives that help teach a group of students with varying learning styles.

Competency 3: Mathematics Assessments (9%)

Competency 3 outlines six skills:

  1. Utilize various methods to assess student learning progress.
  2. Analyze students' learning needs through work samples.
  3. Utilize technology to assess students' performance.
  4. Tailor classroom instruction based on student performance data.
  5. Review questioning strategies, interpreting their level of cognitive complexity.
  6. Identify assessment types that use multiple levels of cognitive complexity.

Competency 4: Connections among Mathematical Concepts (7%)

Competency 4 covers five skills:

  1. Identify multiple topics' prerequisite skills.
  2. Identify common math misconceptions.
  3. Find relationships between mathematical concepts.
  4. Assess math errors.
  5. Explain middle grades to postsecondary education mathematical foundational concepts.

Competency 5: Number Sense, Operations, and Proportionality (9%)

Competency 5 includes six skills:

  1. Compare number sizes when numbers are in various formats such as fractions and decimals.
  2. Conduct mental estimation.
  3. Display prime factorization proficiency.
  4. Display proficiency utilizing Greatest Common Factor (GCF) and Least Common Multiple (LCM).
  5. Solve mathematical problems by using ratios and proportions.
  6. Analyze mathematical problems and choose the best operation to solve them.

Competency 6: Foundations of Algebra (14%)

Competency 6 encompasses 11 skills:

  1. Analyze patterns to find missing terms.
  2. Understand the relationships between tables, graphs, and equations.
  3. Simplify expressions, both rational and irrational.
  4. Utilizing the exponential properties, simplify expressions that include radicals and rational exponents.
  5. Evaluate one-variable equations and inequalities.
  6. Assess one-variable graphs of inequalities.
  7. Assess two-variable graphs of linear equations or inequalities.
  8. Utilizing a graph, table, or equation, find the slope and intercept.
  9. Find the equation of a line.
  10. Display proficiency in finding square roots.
  11. Display proficiency in properties of operations.

Competency 7: Algebraic Thinking (11%)

Competency 7 presents nine skills:

  1. Display knowledge of linear and nonlinear functions.
  2. Given a line, choose the equation that represents a perpendicular or parallel line.
  3. Display knowledge of polynomials.
  4. Utilizing graphs, substitution, or elimination, solve two-variable linear equation systems.
  5. Find the solution set of two-variable system linear inequalities.
  6. Evaluate mathematical problems using quadratic equations.
  7. Display knowledge of quadratic function graphs.
  8. Utilizing square roots, complete equations that include radicals.
  9. Display knowledge of the laws of exponents.

Competency 8: Data Analysis, Statistics, and Probability (7%)

Competency 8 tests on six skills:

  1. Apply the most appropriate measure of center given various situations.
  2. Identify and assess data ranges and distribution.
  3. Utilize univariate and bivariate data to analyze graphical information.
  4. Choose the best-fitting graph type based on given data.
  5. Display sample population proficiency.
  6. Utilize probabilities to make educated predictions.

Competency 9: Two-Dimensional Geometry (15%)

Competency 9 incorporates 12 skills:

  1. Define line, segment, ray, or distances based on undefined points, lines, or planes.
  2. Display knowledge of angle properties.
  3. Find angle measurements based on polygon properties.
  4. Utilizing triangle properties, assess proofs.
  5. Assess proofs utilizing triangle inequality theorems.
  6. Display proficiency using the SAS, ASA, and SSS postulates in analyzing triangle relationships.
  7. Evaluate right triangle mathematical problems using various theorems.
  8. Evaluate right triangle mathematical problems by applying trigonometric ratios.
  9. Display knowledge of quadrilateral properties.
  10. Utilize distance and midpoint formulas on the coordinate plane.
  11. Identify transformation types of geometric figures.
  12. Display knowledge of circle properties.

Competency 10: Measurement and Spatial Sense (9%)

Competency 10 incorporates six skills:

  1. Convert measuring units.
  2. Solve problems to find the area, volume, circumference, and other measurements.
  3. Explain the relationship between dimensions and other measurements.
  4. Name 3D figure characteristics.
  5. Find the net of 3D figures.
  6. Given a 3D object, find the 2D view.

FTCE Math 5-9 Exam Format

The FTCE Middle Grades 5-9 exam is a computer-based test taken at testing centers in various FTCE testing locations nationwide. The exam consists of approximately 70 multiple-choice questions, consisting of the ten tested competencies listed in the above section. The questions consist of five question types: word problem, graphics, scenario, direct question, and command.

Candidates have 2 hours and 30 minutes to complete the FTCE Math 5-9 exam. Test-takers should expect to spend a little over three hours at the testing site. Candidates must show up 30 minutes before the test time for the testing center to verify their identification, conduct a security screening, and perform other administrative tasks. FTCE Middle School Math test-takers do not receive any scheduled breaks during this FTCE test. There is no formula sheet provided for the test, but a Texas Instruments TI-30X IIS scientific calculator is supplied.

How to Register for the FTCE Middle School Math Exam

There are four simple steps to register for the FTCE Middle Grades Math 5-9 exam:

  1. Create an FTCE/FELE account on the official website or log in to a pre-existing FTCE/FELE account.
  2. Under the "Register for the FTCE/FELE" tab, choose "FTCE Middle Grades Mathematics 5-9." In this step, candidates answer a few questions and agree to test policies.
  3. Under "Open Registrations/Schedule," select desired testing center location, time, and date.
  4. Once all info is verified, pay the $150 registration fee and confirm the FTCE registration.

After registering for the FTCE Math 5-9, candidates have one year to take the exam or they will have to re-register and pay another $150 for the FTCE test cost.

Information & Policies for Test Day

On testing day, candidates report to the testing center 30 minutes before the FTCE Math 5-9 exam start time. Once there, staff will verify their identification, conduct security screens, and complete other administrative tasks. Candidates must bring two valid forms of identification to the testing site, such as a driver's license, passport, etc. The photo identification must be the official card or document. No digital versions or copies will be accepted.

Candidates are not allowed to bring electronics of any sort or most personal items into the test room. Most testing centers in FTCE testing locations provide secure lockers for test-takers to place their personal items. For the FTCE Math 5-9, candidates are not allowed to bring personal calculators nor references of any type, such as a pre-made FTCE Math 5-9 formula sheet. The testing center will provide candidates with a Texas Instruments TI-30X IIS scientific calculator - the reference material allowed inside the test room.

FTCE Math 5-9 Scoring

To pass the FTCE Middle Grades Mathematics 5-9, candidates must receive a scaled score of 200, which is equivalent to 71%, meaning: test-takers need to answer approximately 50 questions correctly out of the 70 total questions. Since the FTCE Math 5-9 is an all multiple-choice exam, candidates will receive immediate unofficial results after taking the test (as long as the test is not currently undergoing revisions.)

Candidates receive their official results within four weeks of the exam date and will be able to check their score status on the FTCE/FELE website. If candidates do not meet the FTCE passing score for the FTCE Middle School Math test, they can retest, paying the full $150 registration fee again. Retests must be after 31 calendar days after the last test date. If the candidate passed the test but still wish to retake, the FTCE retake policy requires them to wait three years.

The FTCE does not have a maximum number of retakes allowed. Candidates can continue to retake the FTCE Middle Grades Math 5-9 until they obtain the required FTCE scores as long as they re-register each time, pay the $150 fee, and follow the guidelines listed above.

Preparing for the Middle Grades Mathematics (5-9) Exam

Candidates should create their own FTCE study guide and study schedules to prepare for the FTCE Middle School Math. Candidates should begin their FTCE prep with understanding the general overview of the exam, test format and logistics. Then they should create an individualized FTCE Math 5-9 study guide to cover all the tested skills and competencies.

Although candidates are not authorized to use an FTCE Math 5-9 formula sheet on the exam, candidates should make one for their studies. Candidates can reference the sheet, add new formulas, and ultimately decide which formulas are critical for them to remember for the test.

Multiple times during their studies candidates should take practice tests. The FTCE/FELE website offers a practice test with 30 multiple-choice questions that can be timed to mimic the actual exam. These Florida Teacher Certification Exam sample questions cover each competency and question type. Once candidates take the practice test, they can assess areas they need to study more.


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Exam Instructions:

Complete the practice test below to test your knowledge.
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  1. Estimate the square root of 21 to the nearest tenth.

    • Correct Answer
  2. Simplify the expression 7g (6 - 4m).

    • Correct Answer
  3. What is the angle of rotational symmetry for an octagon?

    • Correct Answer
  4. The bar graph below shows the type of girl scout cookies and the amount that was sold this year. Which girl scout cookie had the 3rd most sales?

    • Correct Answer

  5. Use the coordinate plane to answer the following question: In which quadrants do points A, B, C, and D appear in respectively?

    • Correct Answer
  6. Multiply and simplify the following rational expressions:

    {eq}\dfrac{x+1}{x^2 - 3x + 2} \times \dfrac{x^2 + 2x - 3}{x^2 + 2x + 1} {/eq}

    • Correct Answer
  7. How many diagonals can be drawn in the following hexagon?



    • Correct Answer
  8. What is the factored form of the following quadratic equation?

    {eq}x^2 - 3x - 54 = 0 {/eq}

    • Correct Answer
  9. Evaluate the function below when x = 2 and y = -1.

    • Correct Answer

  10. What is shown in the figure?

    • Correct Answer
  11. Which of the following is a correct logical disjunction formed with these two phrases?

    Jim enjoys reading books.

    Jim enjoys running outside.

    • Correct Answer
  12. What will be the ordered pair of this function when the input is {eq}x = 5 {/eq}?

    {eq}f(x) = -2x\sqrt{x^2 - 16} + 3x^2\log(x^3 - 25) {/eq}

    • Correct Answer
  13. Which of the following types of questions bring verbal reasoning to math assessments?

    • Correct Answer

  14. Use the table to answer the question: Which test has a higher average score? What is the mean of this test?

    • Correct Answer
  15. What is the GCF of 54 and 63?

    • Correct Answer