Coverage by content domain
Lessons and questions are organized around the exam’s content areas so your preparation reflects the structure of the assessment.
Why Test Alignment Matters for Your FTCE Middle Grades Mathematics 5–9 Study Guide
Certification test standards are broad, but the exam questions are very specific. Our team of curriculum experts uses the 240 Study Guide Creation Process to ensure the most aligned, specific content for your FTCE Middle Grades Mathematics 5–9 (025) test — so you are not wasting time on broad subject review that may not show up on exam day.
Why 240 is the best choice for the FTCE 025 study guide
- Built around the official exam framework
- Organized by the competencies actually used on the exam
- Shows exactly what is covered and where depth is partial
- Includes aligned questions, flashcards, study materials, and videos
- Helps candidates study what is actually tested instead of broad generic content
Transparent coverage is a strength. We show where the guide is strong, where depth is partial, and where a gap has been identified so you can make an informed study decision.
How to Read This Alignment Review
5Domains
47Competencies reviewed
99%Test-aligned
46Covered
1Partially covered
0Gaps
- CoveredCompetency is comprehensively supported by the guide.
- Partially coveredCore content is covered, but some depth gaps remain.
- Coverage gap identifiedA content gap has been identified.
This study guide is based on the current official exam framework. We review and update alignment whenever the official framework changes so candidates are always studying current, accurate material.
Knowledge of number sense, operations, and proportionality (Domain 1)Partially covered
545 questions · 30 materials · 66 cards · 19 videosPartially covered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| 1. Compare and convert between rational numbers represented in various ways (i.e., fractions, terminating and repeating decimals, percentages, number line). | M.Fraction, Decimal, Percentage Conversions; M.Comparing Fractions | Covered | 56 | 2 | 11 | 2 | Covered by 2 topics (56 questions, 2 materials, 11 cards, 2 videos). |
| 2. Solve problems by performing operations with rational numbers, using estimates and algorithms, and evaluate multi-step expressions using order of operations (e.g., expressions with integer exponents, multiple levels of grouping symbols, and absolute value). | M.Operations and Rational and Irrational Numbers; M.Operational Algorithm Relationships; M.Order of Operations; M.Order of Operations - Grouping; M.Order Real Numbers by Magnitude | Covered | 78 | 5 | 16 | 3 | Covered by 5 topics (78 questions, 5 materials, 16 cards, 3 videos). |
| 3. Estimate irrational numbers, including square roots, and compare them to rational numbers. | M.Square Roots and Radicals; M.Radicals and Exponents | Covered | 14 | 2 | 4 | 1 | Covered by 2 topics (14 questions, 2 materials, 4 cards, 1 videos). |
| 4. Represent and perform operations with real number approximations with scientific notation, giving attention to significant digits. | M.Exponential and Scientific Notation; M.Scientific Notation Operations | Covered | 19 | 2 | 2 | 2 | Covered by 2 topics (19 questions, 2 materials, 2 cards, 2 videos). |
| 5. Apply factors of whole numbers to arithmetic operations (e.g., common factors, LCD, GCM). | M.Prime and Composite Numbers; M.Factors; M.Prime Factorization; M.Mental Math and Estimation; M.Structure of Number Systems | Covered | 101 | 5 | 22 | 4 | Covered by 5 topics (101 questions, 5 materials, 22 cards, 4 videos). |
| 6. Solve problems involving ratios and proportions (e.g., mixtures, comparisons, rates, measurement conversions, graphs, percent growth, taxes, depreciation). | M.Representations of Fractions in Word Problems; M.Ratios; M.Unit Rates; M.Ratios, Proportions, Percents; M.Converting Units - Proportional Reasoning; M.Converting Units - Dimensional Analysis; M.Proportional Reasoning - Word Problems | Covered | 160 | 7 | 7 | 6 | Covered by 7 topics (160 questions, 7 materials, 7 cards, 6 videos). |
| 7. Apply properties of operations (i.e., associative, commutative, distributive, inverse relationships between operations) in performing multi-step arithmetic operations with rational numbers. | M.Operational Properties; M.Identities; M.Inverse Operations | Covered | 62 | 3 | 8 | 1 | Covered by 3 topics (62 questions, 3 materials, 8 cards, 1 videos). |
| 8. Solve problems by performing operations with numbers involving radicals and with rational numbers with rational exponents, making use of the laws of exponents. | M.Properties of Exponents; M.Properties of Exponents - Applying Multiple Properties; M.Radicals and Exponents; M.Simplifying Radicals | Covered | 53 | 4 | 4 | 1 | Covered by 4 topics (53 questions, 4 materials, 4 cards, 1 videos). |
| 9. Interpret operations on rational numbers and radicals within mathematical and real-world contexts. | M.Operations with Radicals | Partially covered | 7 | 1 | 2 | 0 | Partial coverage by 1 topic (7 questions, 1 materials, 2 cards, 0 videos); limited supporting content. |
Knowledge of algebra (Domain 2)Covered
528 questions · 42 materials · 67 cards · 14 videosCovered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| 1. Identify and apply numerical and algebraic patterns, using tables, graphs, written descriptions, and formulas. | M.Types of Sequences; M.Patterns - Developing an Expression; M.Patterns - Developing a Linear Formula; M.Creating Formulas for Patterns - Arithmetic and Geometric | Covered | 79 | 4 | 9 | 3 | Covered by 4 topics (79 questions, 4 materials, 9 cards, 3 videos). |
| 2. Evaluate a function at a given value of its input to determine whether a relationship presented in various forms (e.g., tables, written descriptions, function notation) represents a function and to determine its type (i.e., linear, quadratic, cubic, exponential growth and decay, absolute value, square root, cube root). | M.Relation and Function Representations | Covered | 39 | 1 | 4 | 0 | Covered by 1 topic (39 questions, 1 materials, 4 cards, 0 videos). |
| 3. Apply operations with exponents and radicals to generate equivalent expressions (e.g., polynomials, radical expressions, rational expressions). | M.Polynomials; M.Equivalence of Expressions - To Simplify; M.Equivalence of Expressions - To Expand; M.Advanced Equivalence of Expressions - To Simplify; M.Linear Expression Evaluation; M.Verbal to Symbolic Expression - Basic; M.Symbolic to Verbal | Covered | 118 | 7 | 20 | 4 | Covered by 7 topics (118 questions, 7 materials, 20 cards, 4 videos). |
| 4. Solve linear and absolute value equations or inequalities with one or two variables, representing solutions algebraically or graphically, and interpret the key features (vertex, line of symmetry) of an absolute value function within real-world or mathematical contexts. | M.Interpreting Inequalities; M.Solving Linear Inequalities; M.Solve Linear Inequalities - Graphically; M.Absolute Value Inequalities; M.Absolute Value Functions | Covered | 34 | 5 | 8 | 2 | Covered by 5 topics (34 questions, 5 materials, 8 cards, 2 videos). |
| 5. Identify the slope and intercepts of a line using a graph, table, or equation, and determine the equation of a line (i.e., passes through two given points, through one given point, perpendicular to a given line, parallel to a given line, has a given slope). | M.Linear Equations - Rearrange to Slope-Intercept Form; M.Understanding Linear Equations and Their Properties | Covered | 30 | 2 | 2 | 0 | Covered by 2 topics (30 questions, 2 materials, 2 cards, 0 videos). |
| 6. Solve and interpret systems of two-variable linear equations and inequalities, algebraically, graphically, and in real-world contexts. | M.Solving Systems of Linear Equations; M.Solving Systems of Linear Equations - Word Problems; M.Solve for x - Linear; M.Solve for x - Radical; M.Forms of Equations | Covered | 57 | 5 | 9 | 3 | Covered by 5 topics (57 questions, 5 materials, 9 cards, 3 videos). |
| 7. Identify and interpret the x-intercepts, y-intercept, vertex, line of symmetry, and concavity of a quadratic function representing real-world and mathematical situations. | M.Quadratic Equations; M.Sketch a Quadratic - Standard Form; M.Sketch a Quadratic - Vertex Form | Covered | 34 | 3 | 5 | 2 | Covered by 3 topics (34 questions, 3 materials, 5 cards, 2 videos). |
| 8. Analyze key features of quadratic functions presented in mathematical and real-world contexts, and solve using a variety of methods (e.g., factoring, quadratic formula, completing the square, graphing). | M.Quadratic Equation - Solve via Graphing; M.Quadratic Equation - Solve via Factoring; M.Quadratic Equation - Solve via Complete the Square; M.Quadratic Equation - Solve via Quadratic Formula; M.Advanced Quadratic Equation - Real World Problems; M.Quadratic Equations - Forms | Covered | 33 | 6 | 6 | 0 | Covered by 6 topics (33 questions, 6 materials, 6 cards, 0 videos). |
| 9. Determine and select graphical representations of exponential functions in the form abx and a(1 + r)x that represent real-world problems of exponential growth and decay (e.g., problems about depreciation, compound interest, population growth). | M.Exponential Functions - Real World Problems - Compound Interest; M.Exponential Functions - Real World Problems - Annuities; M.Exponential Functions; M.Exponential Functions - Real World Problems | Covered | 44 | 4 | 8 | 0 | Covered by 4 topics (44 questions, 4 materials, 8 cards, 0 videos). |
| 10. Determine the impacts of shifting and scaling transformations on the formulas for linear, quadratic, and absolute value functions. | M.Parent Functions; M.Functional Transformations - Linear and Quadratic; M.Functional Transformations - Absolute Value; M.Functional Transformations - Radical; M.Functional Transformations - Exponential | Covered | 60 | 5 | 6 | 0 | Covered by 5 topics (60 questions, 5 materials, 6 cards, 0 videos). |
Knowledge of geometry (Domain 3)Covered
516 questions · 36 materials · 111 cards · 17 videosCovered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| 1. Classify triangles, quadrilaterals, and solids based on their defining attributes. | M.Attributes of Polygons - Irregular Shapes; M.Attributes of Three Dimensional Figures; M.Angles and Measurements in Polygons; M.Points, Lines, Planes, Angles; M.Attributes of Polygons - Advanced | Covered | 57 | 5 | 50 | 2 | Covered by 5 topics (57 questions, 5 materials, 50 cards, 2 videos). |
| 2. Apply formulas for the area of a triangle and composite figures to find solutions for various shapes (e.g., rectangles, trapezoids, parallelograms, rhombi). | M.Area and Perimeter of Rectangles and Triangles; M.Area and Perimeter of Polygons; M.Area and Perimeter of Polygons - Irregular Shapes | Covered | 69 | 3 | 2 | 1 | Covered by 3 topics (69 questions, 3 materials, 2 cards, 1 videos). |
| 3. Apply formulas for volume and surface area of solids (i.e., right solids, Cavalieri’s principle, nets for non-right solids). | M.Nets; M.Pyramids and Prisms; M.Types of Prisms; M.Surface Area in 3D; M.Volume in 3D; M.Volume of Box | Covered | 91 | 6 | 13 | 5 | Covered by 6 topics (91 questions, 6 materials, 13 cards, 5 videos). |
| 4. Solve mathematical and real-world problems involving formulas for the perimeter, circumference, and area of 2D figures and the surface area and volume of 3D figures. | M.Solving with Shapes - Rectangles and Squares; M.Solving with Shapes - Quadrilaterals; M.Dimensional Changes Affecting Area and Volume | Covered | 41 | 3 | 0 | 0 | Covered by 3 topics (41 questions, 3 materials, 0 cards, 0 videos). |
| 5. Solve mathematical and real-world problems using the coordinate plane. | M.Coordinate Geometry; M.The Coordinate Plane; M.Slope, Midpoint, and Distance; M.Parallel and Perpendicular Lines and Formulas | Covered | 64 | 4 | 8 | 3 | Covered by 4 topics (64 questions, 4 materials, 8 cards, 3 videos). |
| 6. Solve mathematical and real-world problems involving proportional relationships between similar 2D and 3D figures. | M.Proportional Reasoning - 2D Shapes; M.Advanced Similar Shapes; M.Proportional Reasoning - Scale Drawings; M.Proportional Reasoning - 3D Figures | Covered | 45 | 4 | 11 | 2 | Covered by 4 topics (45 questions, 4 materials, 11 cards, 2 videos). |
| 7. Solve mathematical and real-world problems using the Triangle Inequality Theorem, the Pythagorean Theorem, and the Pythagorean Theorem converse. | M.Pythagorean Theorem; M.Apply Triangle Properties; M.Apply Triangle Inequalities; M.Angles in Triangles; M.Measurements in Circles | Covered | 70 | 5 | 16 | 3 | Covered by 5 topics (70 questions, 5 materials, 16 cards, 3 videos). |
| 8. Solve mathematical and real-world problems involving 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. | M.Solving with Points, Lines, Planes, Angles | Covered | 27 | 1 | 6 | 1 | Covered by 1 topic (27 questions, 1 materials, 6 cards, 1 videos). |
| 9. Apply translations, rotations, reflections, and scaling transformations based on the relationship between a 2D geometric figure and its pre-image to demonstrate congruence and similarity. | M.Rigid Transformations; M.Non-Rigid Transformations | Covered | 22 | 2 | 8 | 0 | Covered by 2 topics (22 questions, 2 materials, 8 cards, 0 videos). |
| 10. Apply Side-Side-Side, Side-Angle-Side, Angle-Side-Angle, Angle-Angle-Side, Angle-Angle, and Hypotenuse-Leg criteria to prove pairs of triangles are congruent or similar, including the concepts of congruence and similarity of triangles to solve mathematical and real-world problems. | M.Advanced Geometric Constructions - Triangles; M.Prove Theorems - Triangles | Covered | 20 | 2 | 5 | 0 | Covered by 2 topics (20 questions, 2 materials, 5 cards, 0 videos). |
| 11. Determine the center, the radius, and the equation of a circle, and select graphical representations of a circle on a coordinate plane. | M.Circles and Ellipses | Covered | 10 | 1 | 6 | 0 | Covered by 1 topic (10 questions, 1 materials, 6 cards, 0 videos). |
Knowledge of data analysis, statistics, and probability (Domain 4)Covered
332 questions · 19 materials · 66 cards · 7 videosCovered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| 1. Identify and determine measures of central tendency and measures of variation of a numerical data set. | M.Measures of Center and Range | Covered | 56 | 1 | 4 | 1 | Covered by 1 topic (56 questions, 1 materials, 4 cards, 1 videos). |
| 2. Interpret information and patterns from a numerical data display and from the shape of its distribution (i.e., symmetry, gaps, clusters, outliers, mode, range). | M.Normal Distribution; M.Advanced Measures of Center and Range | Covered | 35 | 2 | 11 | 0 | Covered by 2 topics (35 questions, 2 materials, 11 cards, 0 videos). |
| 3. Identify displays for univariate numerical and categorical data (e.g., histograms, box plots, bar charts, frequency tables). | M.Graphs and Plots; M.Boxplots; M.Choosing a Graph or Plot; M.Data Analysis and Interpretation | Covered | 86 | 4 | 17 | 3 | Covered by 4 topics (86 questions, 4 materials, 17 cards, 3 videos). |
| 4. Determine estimates for a population total, mean, and percentage using data from a survey. | M.Observations, Conclusions, and Relationships | Covered | 11 | 1 | 10 | 0 | Covered by 1 topic (11 questions, 1 materials, 10 cards, 0 videos). |
| 5. Identify statistical questions and samples to draw inferences about a population. | M.Surveys; M.Sampling Methods | Covered | 22 | 2 | 7 | 0 | Covered by 2 topics (22 questions, 2 materials, 7 cards, 0 videos). |
| 6. Determine the properties of correlations in bivariate data displayed in scatter plots and frequency tables, representing real-world situations. | M.Bivariate Data Analysis | Covered | 17 | 1 | 7 | 1 | Covered by 1 topic (17 questions, 1 materials, 7 cards, 1 videos). |
| 7. Select linear functions that fit to real-world bivariate numerical data and that suggest a possible linear association, and interpret the x- and y-intercepts. | M.Line of Best Fit; M.Calculating Linear Regression | Covered | 14 | 2 | 3 | 0 | Covered by 2 topics (14 questions, 2 materials, 3 cards, 0 videos). |
| 8. Determine the theoretical probabilities of outcomes (e.g., rolling a 3 on a standard 6-sided die) and events (e.g., drawing two red balls in a row when drawing with replacement from a bag containing a given number of red and green balls) in simple and repeated experiments. | M.Probability; M.Simple and Compound Events; M.Compound Probabilities (OR); M.Probability Models | Covered | 73 | 4 | 11 | 2 | Covered by 4 topics (73 questions, 4 materials, 11 cards, 2 videos). |
| 9. Determine and compare experimental and theoretical probabilities to make predictions and draw conclusions about real-world situations. | M.Probability Simulations; M.Statistical Experiments | Covered | 18 | 2 | 4 | 0 | Covered by 2 topics (18 questions, 2 materials, 4 cards, 0 videos). |
Knowledge of student reasoning and instructional practice (Domain 5)Covered
247 questions · 23 materials · 43 cards · 6 videosCovered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| 1. Analyze real-world contexts across subject areas to represent them with appropriate mathematical expressions and equations. | M.Modeling and Evaluating Real-World Situations; M.Real-World Applications; M.Selecting Appropriate Solution Strategies; M.Using Structure to Analyze Complex Problems | Covered | 49 | 4 | 0 | 0 | Covered by 4 topics (49 questions, 4 materials, 0 cards, 0 videos). |
| 2. Identify appropriate methods to facilitate instruction in using mathematical strategies, concepts, and procedures with mathematical fluency to solve problems in various real-world or mathematical contexts. | M.Backward Design; M.Major Math Instructional Theories; M.Variety of Representations | Covered | 24 | 3 | 18 | 2 | Covered by 3 topics (24 questions, 3 materials, 18 cards, 2 videos). |
| 3. Identify opportunities for students to evaluate the reasonableness of their results, and assess the validity of students’ mathematical arguments. | M.Conclusions from Premises; M.Formal Conclusions from Premises; M.Inductive vs Deductive Reasoning; M.Reasonableness of Results; M.Teaching Mathematical Reasoning for Older Children | Covered | 46 | 5 | 3 | 0 | Covered by 5 topics (46 questions, 5 materials, 3 cards, 0 videos). |
| 4. Identify patterns to make mathematical connections between different mathematical and real-world problems across subject areas, and analyze a sequence of concepts for mathematical continuity within and across grade levels. | M.Mathematical Connections; M.Interdisciplinary Connections | Covered | 12 | 2 | 0 | 0 | Covered by 2 topics (12 questions, 2 materials, 0 cards, 0 videos). |
| 5. Select appropriate mathematical representations (e.g., verbal statements, pictures, graphs, algebraic expressions) and instructional tools for teaching mathematical concepts to all students. | M.Manipulatives for Older Children; M.Variety of Representations; M.Variety of Representations for Older Children | Covered | 16 | 3 | 16 | 0 | Covered by 3 topics (16 questions, 3 materials, 16 cards, 0 videos). |
| 6. Analyze learning progressions to demonstrate how students’ mathematical knowledge and skills develop over time among concrete, representational, and abstract modes of understanding. | M.Learning Progressions in Math | Covered | 19 | 1 | 3 | 1 | Covered by 1 topic (19 questions, 1 materials, 3 cards, 1 videos). |
| 7. Analyze and interpret individual student mathematics assessment data using a variety of assessment formats to guide instructional decisions and differentiate instruction. | M.Types of Assessment - Math; M.Using Assessment to Adjust Instruction; M.Authentic Assessment; M.Assessment Terminology; M.Use Variety in Problem Structure | Covered | 51 | 5 | 14 | 2 | Covered by 5 topics (51 questions, 5 materials, 14 cards, 2 videos). |
| 8. Analyze students' mathematical misconceptions, errors, and gaps in knowledge and choose instructional approaches to promote student achievement. | M.Evaluate Student Solutions | Covered | 40 | 1 | 0 | 1 | Covered by 1 topic (40 questions, 1 materials, 0 cards, 1 videos). |
How 240 Creates The FTCE Middle Grades Mathematics 5–9 (025) Study Guide
Every 240 study guide starts with the official exam framework. From there, we organize lessons, practice, and study tools around the categories the exam uses to measure candidate knowledge.
Review the official exam framework
We begin with the standards, domains, competencies, objectives, or content categories published by the testing authority.
Map the tested categories
We map every major area the exam is designed to cover so the guide reflects the real structure of the test.
Build lessons around tested content
We create study materials to support the official blueprint, not broad filler content.
Cross-check practice against exam expectations
We review practice content against the framework and real exam patterns so preparation stays targeted.
Review and update as standards change
When official frameworks change, we review guides and update alignment as needed.
Reviewed by subject-matter experts and maintained to reflect current standards.
Why 240 Is Better Than Other Generic Study Guides
Not all study guides are built the same way. Here is what separates a test-aligned guide from a generic one — and why it matters when you are preparing for the FTCE Middle Grades Mathematics 5–9.
Generic prep
- Covers broad subject areas without structure
- No clear connection to the official exam framework
- Practice questions may not reflect the real test format
- May not update when official standards change
- Can be helpful for quick, broad review
240 test-aligned FTCE 025 prep
- Every lesson maps to an official domain or competency
- Built directly from the official exam framework
- Practice questions aligned to what the exam actually measures
- A clear study path by tested category
- Study smarter and enter test day more prepared
FAQs About the FTCE Middle Grades Mathematics 5–9 Study Guide
The questions teacher candidates ask us most often about the FTCE Middle Grades Mathematics 5–9 study guide.
Is 240 a good study guide for FTCE Middle Grades Mathematics 5–9?
240 is a strong option because the guide is built around the official exam framework and shows detailed alignment by SMR and competency.
How closely does 240 align to the FTCE 025 exam?
This guide is 99% aligned based on a competency-by-competency review of the official framework and the study resources included in the guide.
Does 240 cover every competency?
This page shows coverage transparently across covered, partially covered, and identified gaps so candidates can see exactly how the guide maps to the exam.
What does “partially covered” mean?
Partially covered means the guide addresses the core parts of a competency, but some depth or subtopics may still be limited.