The FTCE Middle Grades Mathematics 5–9 examination (test code 025) is the Florida subject area examination for certification to teach mathematics in grades 5 through 9. It is a computer-based test (CBT) of approximately 50 multiple-choice questions in 2 hours and 30 minutes, weighted 30 percent to algebra and 20 percent to student reasoning and instructional practice, with an on-screen scientific calculator provided during the test. The passing score, in the Florida Department of Education’s published form, is: A scaled score of at least 200. The FLDOE/Pearson examination fee is $150.
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The examination at a glance
| Item | Verified position |
|---|---|
| Examination | FTCE Middle Grades Mathematics 5–9 — Florida Teacher Certification Examinations, test code 025 |
| Certification | Subject area examination for Florida’s Mathematics (5-9) certificate — teaching mathematics in grades 5–9 |
| Format | Computer-based test (CBT) with approximately 50 multiple-choice questions; each question has four response options (A, B, C, D). Tests may include questions being evaluated for future administrations that do not affect the score |
| Length | 2 hours and 30 minutes of testing time; total appointment time is longer, and any time taken for breaks is considered part of the available testing time |
| Content | Five competencies under the official Test Information Guide: Algebra 30%; Geometry 20%; Student Reasoning and Instructional Practice 20%; Number Sense, Operations, and Proportionality 15%; Data Analysis, Statistics, and Probability 15% — percentages are the guide’s approximate percentages of total test questions |
| Passing score | A scaled score of at least 200 |
| Examination fee | FLDOE/Pearson fee: $150 |
| Reference materials | An on-screen scientific calculator will be provided during the test; examinees may not bring their own calculator. A reference sheet is not provided for this test. Hand-held calculators may be available upon request |
| Delivery and scores | By appointment, year-round, at computer-based test sites throughout Florida and nationwide. On-site score reports are typically provided immediately after testing; all official score reports are released within 4 weeks of testing |
| Administrator | The Florida Department of Education (FLDOE) owns the FTCE program; Pearson administers the examinations. PassProfessor is independent and is not affiliated with FLDOE or Pearson |
The FTCE Middle Grades Mathematics 5–9 examination measures the knowledge of a beginning Florida middle grades mathematics teacher across the span that defines the assignment: the arithmetic students arrive with, the algebra and geometry they are travelling toward, the data literacy the modern curriculum asks of them, and — at a fifth of the paper — the teacher’s own reasoning about student thinking. Read the blueprint’s architecture before its contents: one dominant competency (algebra, 30 percent), two at 20 percent (geometry, and student reasoning and instructional practice), and two at 15 percent (number sense and proportionality; data analysis, statistics, and probability). That architecture, not any textbook’s table of contents, is the syllabus. This guide treats all five competencies at their published weights, skill by skill, because the Test Information Guide’s forty-seven skills are the finest-grained public statement of what can be asked.
Reading the verified facts
Every fact in the table above is stated as the administering program states it in its own publications, because candidates for this examination are ill-served by the approximations that circulate about it — and this examination attracts more than most, for a specific reason: its blueprint has been redeveloped. The current Test Information Guide organises the examination into five competencies. Older outlines — still reproduced across third-party material — divide it into ten, with different names and weights, and carry topics the current guide does not name. Three reading disciplines govern this guide. First, the figures given are the program’s figures, reproduced from the official test page and the current Test Information Guide named in this file’s INTERNAL section; where those documents do not publish a figure, this guide prints none rather than borrowing one. Second, the passing standard is given only in FLDOE’s published form — a scaled score of at least 200. FLDOE publishes a “Maximum Percentages Needed” table as a guideline for interpreting scaled scores; it is not a passing score, it does not convert 200 into a share of questions answered correctly, and third parties who present a percentage as this examination’s cut score are misreading it. Third, the competency percentages are the Test Information Guide’s approximate percentages of total test questions — planning weights, not a published count of questions per competency, and this guide does not convert them into one. Finally: the companion PassProfessor program is in the works and unbuilt — nothing in this guide describes a question bank, a course, or an enrollment that exists today.
The route, step by step
Step 1 — Confirm the examination with the Bureau
The Florida Bureau of Educator Certification decides which tests you need, after you apply for certification. Confirm that the FTCE Middle Grades Mathematics 5–9 examination (025) is the subject area examination required on your file. Two confusions live at this step and both are expensive: FLDOE’s certification page styles the certificate “Mathematics (5-9),” but the examination’s own published name is Middle Grades Mathematics 5–9 — search and register under the test name; and the grades 5–9 examination (025) is not the Mathematics 6–12 examination (026), a different instrument for a different grade band. A candidate who prepares for the wrong mathematics examination has spent the fee and the season on the wrong blueprint.
Step 2 — Prepare from the official guide
The program publishes a Test Information Guide for this examination: the test design, the competencies and skills with the blueprint percentages, sample test questions with their keyed responses, a section on the question formats in use, and a bibliography. It also publishes a tutorial for the computer-based test experience. Work from the guide’s skills as your syllabus — each of the forty-seven skills is a statement of something the examination may ask, phrased in the program’s own verbs — and work from the current guide: the redeveloped five-competency version is the operative one. Note FLDOE’s own position, stated on the program’s resource pages, when you weigh any outside material including this guide: the Department does not endorse third-party FTCE preparation materials and recommends its own Test Information Guides and resources.
Step 3 — Register and schedule
Registration runs through the official FTCE program site. Tests are by appointment, year-round; you schedule your test during registration, based on available dates, at computer-based test sites throughout Florida and nationwide. The FLDOE/Pearson examination fee is $150. When you register you must agree to abide by all testing rules and policies — the program asks you to read them at registration, and the break policy in particular deserves the reading: any time taken for breaks is considered part of your available testing time.
Step 4 — Sit the examination
Arrive for an appointment longer than the 2 hours and 30 minutes of testing time it contains. The examination is approximately 50 multiple-choice questions, each with four response options, delivered as a computer-based test (CBT). The reference-materials position for this test is specific, and it is stated here in full because partial versions of it circulate: an on-screen scientific calculator will be provided during the test; examinees may not bring their own calculator; a reference sheet is not provided for this test; hand-held calculators may be available upon request. Two consequences follow. The calculator you will use is the on-screen one, so its operation — exponent and radical entry, grouping — is part of the instrument to rehearse, not a detail to meet on the day. And every formula named across the geometry skills must be known outright: there is no sheet to consult. The test may include questions being evaluated for future administrations that do not affect your score; they cannot be identified, so the only sound strategy is full effort on every item.
Step 5 — Read the result in the program’s terms
On-site score reports are typically provided immediately after testing — the program’s own caveat is that on-site reporting may not be available for tests being redeveloped or revised — and all official score reports are released within 4 weeks of testing. Read the result against the published standard and in the published form: a scaled score of at least 200. If the sitting did not clear the standard, the rebuild begins from the blueprint, not from a percentage: work the competencies in weight order, and let the heaviest — algebra — set the calendar.
The blueprint in full
Competency 1: Knowledge of Number Sense, Operations, and Proportionality — 15% (9 skills)
Skill 1 examines comparing and converting between rational numbers represented in various ways — fractions, terminating and repeating decimals, percentages, the number line — examined as fluency between representations, not as four separate topics. Skill 2 examines performing operations with rational numbers, using estimates and algorithms, and evaluating multi-step expressions using the order of operations, including integer exponents, multiple levels of grouping symbols, and absolute value: the competency’s computational core. Skill 3 examines estimating irrational numbers, including square roots, and comparing them to rational numbers. Skill 4 examines representing and performing operations with real number approximations in scientific notation, with attention to significant digits. Skill 5 examines applying factors of whole numbers to arithmetic operations — common factors, least common denominator, greatest common measure. Skill 6 examines solving problems involving ratios and proportions, the guide’s examples running to mixtures, comparisons, rates, measurement conversions, graphs, percent growth, taxes, and depreciation: proportionality is the middle grades’ signature idea, and its applications list is correspondingly wide. Skill 7 examines applying the properties of operations — associative, commutative, distributive, inverse relationships — in multi-step arithmetic with rational numbers. Skill 8 examines operating with numbers involving radicals and with rational numbers with rational exponents, under the laws of exponents. Skill 9 examines interpreting operations on rational numbers and radicals within mathematical and real-world contexts — the competency closing, as it opened, on meaning rather than mechanics alone. The guide treats this competency as the paper’s foundation to be made automatic: its operations are the substrate inside algebra and data items across the rest of the examination.
Competency 2: Knowledge of Algebra — 30% (10 skills)
Skill 1 examines identifying and applying numerical and algebraic patterns using tables, graphs, written descriptions, and formulas — four representations, one pattern. Skill 2 examines evaluating a function at a given input value, determining whether a relationship presented in various forms — tables, written descriptions, function notation — represents a function, and determining its type: linear, quadratic, cubic, exponential growth and decay, absolute value, square root, cube root. This is the blueprint’s taxonomy skill, and it is examined as recognition across forms. Skill 3 examines applying operations with exponents and radicals to generate equivalent expressions — polynomials, radical expressions, rational expressions. Skill 4 examines solving linear and absolute value equations and inequalities with one or two variables, representing solutions algebraically or graphically, and interpreting the key features — vertex, line of symmetry — of an absolute value function in real-world and mathematical contexts. Skill 5 examines identifying the slope and intercepts of a line from a graph, table, or equation, and determining the equation of a line: through two given points, through one given point, perpendicular to a given line, parallel to a given line, with a given slope. Skill 6 examines solving and interpreting systems of two-variable linear equations and inequalities, algebraically, graphically, and in real-world contexts — three methods, and items can demand the interpretation, not only the solution. Skill 7 examines identifying and interpreting the x-intercepts, y-intercept, vertex, line of symmetry, and concavity of a quadratic function in real-world and mathematical situations. Skill 8 examines analyzing key features of quadratic functions and solving by a variety of methods — factoring, the quadratic formula, completing the square, graphing — so the candidate must hold all four methods and choose among them. Skill 9 examines determining and selecting graphical representations of exponential functions in the forms the guide specifies, representing growth and decay — depreciation, compound interest, population growth. Skill 10 examines determining the impacts of shifting and scaling transformations on the formulas for linear, quadratic, and absolute value functions. The guide teaches this competency as one subject — the function, in its families and forms: representation, feature-reading, solving, and transformation, applied family by family.
Competency 3: Knowledge of Geometry — 20% (11 skills)
Skill 1 examines classifying triangles, quadrilaterals, and solids based on their defining attributes. Skill 2 examines applying formulas for the area of a triangle and composite figures — rectangles, trapezoids, parallelograms, rhombi are the guide’s examples — where composite figures test decomposition, not recall alone. Skill 3 examines applying formulas for volume and surface area of solids: right solids, Cavalieri’s principle, and nets for non-right solids. Skill 4 generalises the measurement strand: solving mathematical and real-world problems involving perimeter, circumference, and area of two-dimensional figures and surface area and volume of three-dimensional figures. Skill 5 examines solving problems using the coordinate plane — geometry’s meeting point with algebra’s graphs. Skill 6 examines proportional relationships between similar two- and three-dimensional figures, geometry’s share of the proportionality theme. Skill 7 examines the Triangle Inequality Theorem, the Pythagorean Theorem, and the Pythagorean Theorem converse — note the converse is named separately, because recognising when a triangle must be right is a different act from using that one is. Skill 8 examines the formula for the sum of interior angles of polygons, the Triangle Sum Theorem, properties of angles, parallel lines cut by a transversal, and relationships between angles of triangles. Skill 9 examines applying translations, rotations, reflections, and scaling transformations, based on the relationship between a figure and its pre-image, to demonstrate congruence and similarity. Skill 10 examines applying the Side-Side-Side, Side-Angle-Side, Angle-Side-Angle, Angle-Angle-Side, Angle-Angle, and Hypotenuse-Leg criteria to prove pairs of triangles congruent or similar, and using the concepts of congruence and similarity to solve problems: the blueprint’s proof skill, with all six criteria named. Skill 11 examines determining the center, radius, and equation of a circle and selecting graphical representations of a circle on a coordinate plane. The guide teaches the competency in its two strands — measurement fluency and deductive structure — with formulas carried in memory, since the sitting provides no reference sheet.
Competency 4: Knowledge of Data Analysis, Statistics, and Probability — 15% (9 skills)
Skill 1 examines identifying and determining measures of central tendency and measures of variation of a numerical data set. Skill 2 examines interpreting information and patterns from a numerical data display and from the shape of its distribution — symmetry, gaps, clusters, outliers, mode, range — the reading of a distribution as a shape with features, not only as numbers. Skill 3 examines identifying displays for univariate numerical and categorical data: histograms, box plots, bar charts, frequency tables. Skill 4 examines determining estimates for a population total, mean, and percentage using data from a survey — inference from sample to population in its applied form. Skill 5 examines identifying statistical questions and samples to draw inferences about a population: the design judgement beneath Skill 4’s arithmetic. Skill 6 examines determining the properties of correlations in bivariate data displayed in scatter plots and frequency tables representing real-world situations. Skill 7 examines selecting linear functions that fit real-world bivariate numerical data suggesting a possible linear association, and interpreting the x- and y-intercepts — data’s bridge back to algebra’s lines, with the intercepts read for meaning. Skill 8 examines determining theoretical probabilities of outcomes and events in simple and repeated experiments — the guide’s examples are rolling a 3 on a standard six-sided die, and drawing two red balls in a row with replacement. Skill 9 examines determining and comparing experimental and theoretical probabilities to make predictions and draw conclusions about real-world situations. The guide treats the competency as a single arc — describe, display, infer, and only then predict — because its probability skills assume the statistical judgement the earlier skills build.
Competency 5: Knowledge of Student Reasoning and Instructional Practice — 20% (8 skills)
Skill 1 examines analyzing real-world contexts across subject areas to represent them with appropriate mathematical expressions and equations — modelling, framed as a teaching knowledge: choosing the representation a student will meet. Skill 2 examines identifying appropriate methods to facilitate instruction in using mathematical strategies, concepts, and procedures with mathematical fluency to solve problems in various contexts. Skill 3 examines identifying opportunities for students to evaluate the reasonableness of their results, and assessing the validity of students’ mathematical arguments — the examination asking the teacher to do, professionally, what its own items do: judge reasoning, not only answers. Skill 4 examines identifying patterns to make mathematical connections between problems across subject areas, and analyzing a sequence of concepts for mathematical continuity within and across grade levels. Skill 5 examines selecting appropriate mathematical representations — verbal statements, pictures, graphs, algebraic expressions — and instructional tools for teaching concepts to all students. Skill 6 examines analyzing learning progressions, demonstrating how students’ knowledge and skills develop over time among concrete, representational, and abstract modes of understanding. Skill 7 examines analyzing and interpreting individual student mathematics assessment data, using a variety of assessment formats, to guide instructional decisions and differentiate instruction. Skill 8 examines analyzing students’ mathematical misconceptions, errors, and gaps in knowledge and choosing instructional approaches to promote student achievement. The guide treats this competency as examinable professional knowledge with its own methods — the scenario is its native item form, in which a described student’s work is the stimulus and the keyed response is the diagnosis or the next instructional move — and as the competency candidates most often underprepare, assuming strong content knowledge covers it. It does not.
The sitting itself: format, tools, scoring, and what follows
The Test Information Guide names the question formats in use: Scenario items, which present a situation, problem, or case study and ask for a diagnosis or a recommended course of action; Direct Questions; Command items; Graphics items, built on a number line, a geometric figure, graphs of lines or curves, a table, or a chart; and Word Problems, applying mathematical principles to a real-world problem. Read that list against the blueprint and the paper’s character resolves: the scenario format is Competency 5’s natural vehicle, graphics items run through geometry and data, and word problems carry proportionality and algebra into context. A preparation diet of bare computation rehearses only part of the announced format list.
The arithmetic of the sitting is the first discipline. Approximately 50 questions in 150 minutes allows three minutes an item on average — a misleading average. A classification or feature-identification item may take a minute, while a multi-step system, a composite-volume problem, or a misconception scenario legitimately takes five, because the stimulus — a student’s worked solution, a figure, a data display — must be read before the question behind it can be. Work steadily, mark the items consuming a second item’s time, and return to them with the faster marks banked. Answer every item: the test may contain questions being evaluated for future administrations that do not affect your score, they cannot be identified, and no blank can earn anything.
The clock has one further property candidates plan around too late: it does not pause. Any time taken for breaks is considered part of the available testing time, per the official test page, so a break is a spending decision, not a rest — take one if it buys back more concentration than it costs minutes, and know the price before you stand up.
The tools deserve their own paragraph, because this examination’s provision is specific and differs across the FTCE family: an on-screen scientific calculator is provided, your own calculator may not be brought, no reference sheet is provided, and hand-held calculators may be available upon request. Practise accordingly — calculator fluency on the provided instrument for the exponent, radical, and multi-step work the skills name, and formula knowledge held outright, because there is no sheet and no personal device to fall back on.
Scoring is reported in the program’s own terms, and this guide keeps them. The standard is a scaled score of at least 200. A scaled score is not a percentage and does not disclose one: FLDOE does not publish a conversion from the scaled standard to a share of questions answered correctly for this examination, and its “Maximum Percentages Needed” table — a guideline that circulates widely in third-party material, sometimes presented as if it were the passing score — is not the standard. On-site score reports are typically provided immediately after testing, with the redevelopment caveat noted in the route section; official reports follow within 4 weeks.
What this examination is for
A note on this page’s place in the PassProfessor catalog, stated plainly: the catalog’s FTCE coverage spans the General Knowledge Test, the Professional Education Test, and subject area examinations including Elementary Education K–6 and Exceptional Student Education K–12. The FTCE Middle Grades Mathematics 5–9 examination had no program of its own in that coverage. This guide and its companion program page close that gap, covering this examination’s blueprint, route, and standard — and nothing borrowed from neighbouring examinations’ blueprints, including Mathematics 6–12.
Preparation errors this guide is written to prevent
The recurring errors are structural, and they repeat across sittings. Candidates study to the wrong blueprint — and for this examination the trap is precise: the superseded ten-competency outline still circulates in third-party material, with weights and topics the current five-competency guide does not publish, so a candidate can study diligently for a paper that no longer exists. Candidates study evenly across an uneven paper, giving a 15 percent competency the hours algebra’s 30 percent needed. Candidates prepare as mathematicians only, rehearsing content for a paper a fifth of which examines student reasoning and misconceptions. Candidates prepare for recognition when the skills demand operation — solving, proving, interpreting, diagnosing. Candidates meet the on-screen calculator for the first time at the sitting, and carry formulas they expected a reference sheet to hold. And candidates carry a percentage in their heads as the passing standard, because a third-party page printed one. Every section of this guide is aimed at one of those errors.
After the examination
Passing the FTCE Middle Grades Mathematics 5–9 examination satisfies the subject area examination requirement attached to Florida’s Mathematics (5-9) certificate. It is one component of a certification file administered by the Bureau of Educator Certification. Keep the official score report, and note the standard you were measured against in the form it was published — a scaled score of at least 200 — since a scaled result cannot be reconstructed from memory or from a percentage someone else attached to it. The credential it supports is the middle grades one described in the companion program page: a teacher certified for the grades where arithmetic becomes algebra.
A preparation plan that respects the blueprint
Build the plan on the blueprint’s weights, not on habit or on the order of a textbook. Open with algebra — 30 percent, the sitting’s centre — and work it as the guide organises it: patterns and function recognition first, then equivalent expressions, equations and systems, and the quadratic and exponential families with their transformations, converting every skill into worked items early and rehearsing the multi-form movement — table to graph to formula and back. Then take student reasoning and instructional practice at its full 20 percent, as a discipline of its own: work described student errors until the diagnosis comes before the options are read. Work geometry next at 20 percent, formulas to automaticity — there is no reference sheet — and the congruence criteria as proof instruments. Close with number sense and data analysis at 15 percent each, treating number sense as speed work and data as the describe-display-infer-predict arc. Practise throughout with an on-screen scientific calculator, because that is the provided instrument. Reserve complete timed sittings — approximately 50 questions inside 2 hours and 30 minutes, breaks counted as the real sitting counts them — for the plan’s final stage. Keep a running record, competency by competency, of where practice performance is thin, and let it set the final week’s work. The companion FTCE Middle Grades Mathematics 5–9 Exam Preparation page describes the preparation program itself, which is in the works; this guide stands on its own as the route and blueprint reference for the FTCE Middle Grades Mathematics 5–9 examination.
Frequently asked questions
Why does algebra carry nearly a third of the examination?
Because algebra is where middle grades mathematics is heading. The certificate covers the grades in which students move from arithmetic to algebra, and the blueprint weights the destination accordingly — 30 percent on patterns, functions, equations, systems, and the quadratic and exponential families.
Why is there no percentage for the passing score?
Because the program does not publish one as the standard. The passing score for the FTCE Middle Grades Mathematics 5–9 examination is published as: a scaled score of at least 200. FLDOE’s “Maximum Percentages Needed” table is a guideline for interpreting scores, not a passing score, and any percentage presented by a third party as this examination’s cut score misstates the standard.
What calculator will I use, and can I bring my own?
An on-screen scientific calculator will be provided during the test, and examinees may not bring their own calculator. Hand-held calculators may be available upon request. No reference sheet is provided, so formulas must be known outright.
What kinds of questions appear on the examination?
The Test Information Guide names the formats: Scenario items (a situation, problem, or case study, followed by a diagnosis or a recommended course of action), Direct Questions, Command items, Graphics items built on number lines, geometric figures, graphs, tables, or charts, and Word Problems applying mathematical principles to real-world problems. Each question has four response options.
Is the examination the same as Mathematics 6–12?
No. That is a separate examination (code 026), on its own blueprint, for the secondary grade band. The FTCE Middle Grades Mathematics 5–9 examination is code 025. Names, grade bands, and blueprints all differ; preparation for one does not substitute for the other.
Does the clock stop for breaks?
No. The official test page states that any time taken for breaks is considered part of your available testing time. Plan breaks as spending from the same 2 hours and 30 minutes.
What is the student reasoning competency really testing?
The teaching of mathematics, examined directly: representing real-world contexts for students, facilitating instruction with fluency, judging the reasonableness of students’ results and the validity of their arguments, selecting representations and tools, reading learning progressions and assessment data, and — its capstone skill — analyzing students’ misconceptions, errors, and gaps and choosing the instructional approach that addresses them.
How should the 2 hours and 30 minutes be paced?
At an average of three minutes an item, treated as a budget rather than a metronome: bank the fast identification items, mark and move past any multi-step computation or scenario consuming a second item’s time, and return with the paper complete. Full-length timed practice at the real shape — approximately 50 items, 150 minutes, breaks on the clock, on-screen calculator only — is how the pace becomes automatic.
Where do this guide’s facts come from?
From the program’s own publications — the official test page for Middle Grades Mathematics 5–9 (test code 025) and the official Test Information Guide’s competencies, skills, and blueprint, in its current redeveloped five-competency form — recorded in this file’s INTERNAL section. Facts that could not be verified from those sources were omitted rather than borrowed.