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 MTTC Mathematics (Elementary) 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 MTTC Mathematics (Elementary) (089) 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 MTTC 089 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
4Domains
119Competencies reviewed
93%Test-aligned
104Covered
13Partially covered
2Gaps
- 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.
MATHEMATICAL PROCESSES AND NUMBER CONCEPTS (Domain I)Partially covered
SMR I.001 · Understand principles of mathematical reasoning and techniques for communicating mathematical ideas.106 questions · 14 materials · 35 cards · 2 videosPartially covered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| a. analyzing the nature and purpose of axiomatic systems (e.g., understanding the relationships among theorems, postulates, definitions, and undefined terms) | M.Proofs | Covered | 8 | 1 | 3 | 0 | Covered by 1 topic (8 questions, 1 materials, 3 cards, 0 videos). |
| b. using inductive and deductive logic to develop and validate conjectures | M.Inductive vs Deductive Reasoning | Covered | 10 | 1 | 3 | 0 | Covered by 1 topic (10 questions, 1 materials, 3 cards, 0 videos). |
| c. applying the laws of deductive logic to draw valid conclusions | M.Conclusions from Premises; M.Formal Conclusions from Premises; M.Proofs | Covered | 24 | 3 | 3 | 0 | Covered by 3 topics (24 questions, 3 materials, 3 cards, 0 videos). |
| d. developing counterexamples to a conjecture | M.Advanced Abstract and Quantitative Reasoning | Covered | 7 | 1 | 4 | 0 | Covered by 1 topic (7 questions, 1 materials, 4 cards, 0 videos). |
| e. developing and evaluating direct and indirect proofs | M.Indirect Proofs | Covered | 9 | 1 | 1 | 0 | Covered by 1 topic (9 questions, 1 materials, 1 cards, 0 videos). |
| f. using appropriate mathematical terminology | M.Diversity and Engagement - ELL; M.Teaching Mathematical Vocabulary; M.Teaching Mathematical Reasoning for Older Children | Covered | 23 | 3 | 2 | 1 | Covered by 3 topics (23 questions, 3 materials, 2 cards, 1 videos). |
| g. translating common language into symbols and vice versa | M.Teaching Mathematical Vocabulary; M.Symbolic to Verbal | Covered | 21 | 2 | 6 | 1 | Covered by 2 topics (21 questions, 2 materials, 6 cards, 1 videos). |
| h. using a variety of numeric, symbolic, and graphic methods to communicate mathematical ideas and concepts | M.Multimodal Teaching - Math; M.Variety of Representations; M.Variety of Representations for Older Children | Covered | 18 | 3 | 18 | 0 | Covered by 3 topics (18 questions, 3 materials, 18 cards, 0 videos). |
| i. making connections among numeric, symbolic, graphic, and verbal representations | M.Alternate Representations of Problems | Partially covered | 5 | 1 | 0 | 0 | Partial coverage by 1 topic (5 questions, 1 materials, 0 cards, 0 videos); limited supporting content. |
SMR I.002 · Understand problem-solving strategies, connections among different mathematical ideas, and the use of mathematical modeling to solve real-world problems.154 questions · 17 materials · 31 cards · 3 videosCovered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| a. devising, carrying out, and evaluating a problem-solving plan | M.Selecting Appropriate Solution Strategies; M.Sense Making and Perseverance | Covered | 17 | 2 | 0 | 0 | Covered by 2 topics (17 questions, 2 materials, 0 cards, 0 videos). |
| b. evaluating the reasonableness of a solution | M.Reasonableness of Results; M.Evaluating Truth of Statements | Covered | 19 | 2 | 1 | 0 | Covered by 2 topics (19 questions, 2 materials, 1 cards, 0 videos). |
| c. applying a range of strategies (e.g., drawing a diagram, working backwards, creating a simpler problem) to solve problems | M.Selecting Appropriate Solution Strategies; M.Prioritizing Relevant and Missing Information; M.Using Structure to Analyze Complex Problems; M.Properties of Equality; M.Geometric Constructions; M.Combine and Dissect 2D Figures | Covered | 57 | 6 | 7 | 1 | Covered by 6 topics (57 questions, 6 materials, 7 cards, 1 videos). |
| d. analyzing problems that have multiple solutions | M.Prioritizing Relevant and Missing Information; M.Sense Making and Perseverance | Covered | 15 | 2 | 1 | 0 | Covered by 2 topics (15 questions, 2 materials, 1 cards, 0 videos). |
| e. selecting an appropriate tool or technology to solve a given problem | M.Manipulatives for Young Children; M.Informal vs Formal Measurement; M.Integrating Digital Technology | Covered | 28 | 3 | 14 | 2 | Covered by 3 topics (28 questions, 3 materials, 14 cards, 2 videos). |
| f. recognizing connections among two or more mathematical concepts (e.g., area as a quadratic function) | M.Mathematical Connections | Covered | 9 | 1 | 0 | 0 | Covered by 1 topic (9 questions, 1 materials, 0 cards, 0 videos). |
| g. exploring the relationship between geometry and algebra | M.Solving with Matrix Transformations | Covered | 8 | 1 | 0 | 0 | Covered by 1 topic (8 questions, 1 materials, 0 cards, 0 videos). |
| h. applying mathematics across the curriculum and in everyday contexts | M.Real-World Applications; M.Interdisciplinary Connections; M.Financial Literacy | Covered | 29 | 3 | 9 | 0 | Covered by 3 topics (29 questions, 3 materials, 9 cards, 0 videos). |
SMR I.003 · Understand and apply concepts of proportional reasoning.206 questions · 14 materials · 29 cards · 8 videosPartially covered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| a. analyzing connections between fraction concepts and ratios and proportions | M.Ratios; M.Unit Rates; M.Ratios, Proportions, Percents; M.Percent Change | Covered | 79 | 4 | 5 | 3 | Covered by 4 topics (79 questions, 4 materials, 5 cards, 3 videos). |
| b. describing the relationship between proportions and direct and inverse variation | M.Graphs of Proportional Relationships; M.Inversely Proportional vs Directly Proportional; M.Constants of Proportionality | Covered | 6 | 3 | 3 | 0 | Covered by 3 topics (6 questions, 3 materials, 3 cards, 0 videos). |
| c. analyzing and applying the relationship between proportions and similar figures | M.Proportional Reasoning - 2D Shapes; M.Proportional Reasoning - Scale Drawings; M.Proportional Reasoning - 3D Figures | Covered | 34 | 3 | 3 | 2 | Covered by 3 topics (34 questions, 3 materials, 3 cards, 2 videos). |
| d. applying connections among proportions, probability, and sampling | M.Expressing Probabilities | Partially covered | 3 | 1 | 3 | 0 | Partial coverage by 1 topic (3 questions, 1 materials, 3 cards, 0 videos); limited supporting content. |
| e. analyzing a variety of representations of proportional relationships | M.Graphs and Plots | Covered | 32 | 1 | 9 | 1 | Covered by 1 topic (32 questions, 1 materials, 9 cards, 1 videos). |
| f. modeling and solving problems involving ratios and proportions | M.Fraction, Decimal, Percentage Conversions; M.Ratios; M.Proportional Reasoning - Word Problems | Covered | 64 | 3 | 10 | 2 | Covered by 3 topics (64 questions, 3 materials, 10 cards, 2 videos). |
SMR I.004 · Understand number systems and equivalent ways of representing numbers.305 questions · 15 materials · 43 cards · 8 videosCovered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| a. applying place value concepts to numeration systems | M.Place Value; M.Rounding; M.Compare Places on a Number Line; M.Order Real Numbers by Magnitude | Covered | 83 | 4 | 6 | 3 | Covered by 4 topics (83 questions, 4 materials, 6 cards, 3 videos). |
| b. identifying characteristics and relationships among natural, whole, integer, rational, irrational, and real numbers | M.Structure of Number Systems; M.Characteristics of Rational Numbers | Covered | 19 | 2 | 12 | 1 | Covered by 2 topics (19 questions, 2 materials, 12 cards, 1 videos). |
| c. using a variety of equivalent representations of numbers (e.g., ½ = 0.5 = 50% = √¼) | M.Comparing Fractions | Covered | 41 | 1 | 4 | 1 | Covered by 1 topic (41 questions, 1 materials, 4 cards, 1 videos). |
| d. applying properties of number operations (e.g., commutative, distributive) | M.Operational Properties; M.Identities | Covered | 55 | 2 | 7 | 1 | Covered by 2 topics (55 questions, 2 materials, 7 cards, 1 videos). |
| e. applying order relations to numbers | M.Order of Operations; M.Order of Operations - Grouping; M.Fraction Operations - Multiply and Divide; M.Fraction Operations - Mixed Numbers | Covered | 75 | 4 | 14 | 2 | Covered by 4 topics (75 questions, 4 materials, 14 cards, 2 videos). |
| f. using set operations (e.g., union, intersection, complement) | M.Diagrams | Covered | 16 | 1 | 2 | 0 | Covered by 1 topic (16 questions, 1 materials, 2 cards, 0 videos). |
| g. using manipulatives, verbal expressions, and geometric models to represent numbers | M.Manipulatives for Young Children | Covered | 16 | 1 | 4 | 0 | Covered by 1 topic (16 questions, 1 materials, 4 cards, 0 videos). |
SMR I.005 · Understand number theory and operations on number systems.319 questions · 29 materials · 59 cards · 11 videosCovered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| a. analyzing properties of prime numbers, factors, multiples, and divisibility | M.Prime and Composite Numbers; M.Factors; M.Prime Factorization; M.Composition and Decomposition of Multi-Digit Numbers; M.Euclidean Algorithm; M.Interpreting Remainders; M.Square Roots and Radicals; M.Simplifying Radicals; M.Divisibility Rules; M.Fraction Operations - Add and Subtract | Covered | 151 | 10 | 18 | 4 | Covered by 10 topics (151 questions, 10 materials, 18 cards, 4 videos). |
| b. applying number properties to manipulate and simplify algebraic expressions | M.Rational Expressions; M.Equivalence of Expressions - To Simplify; M.Advanced Equivalence of Expressions - To Simplify; M.Linear Expression Evaluation; M.Quadratic Expression Evaluation; M.Linear Expression Addition and Subtraction | Covered | 65 | 6 | 8 | 2 | Covered by 6 topics (65 questions, 6 materials, 8 cards, 2 videos). |
| c. using scientific notation to compute with very large and very small numbers | M.Exponential and Scientific Notation; M.Radicals and Exponents | Covered | 17 | 2 | 3 | 2 | Covered by 2 topics (17 questions, 2 materials, 3 cards, 2 videos). |
| d. comparing and contrasting models of operations across number systems (e.g., using a rectangular array to model multiplication of whole numbers and fractions) | M.Models for Multiplication and Division; M.Matrices and Addition Subtraction; M.Matrices and Scalar Multiplication; M.Matrices and Multiplication | Covered | 21 | 4 | 8 | 1 | Covered by 4 topics (21 questions, 4 materials, 8 cards, 1 videos). |
| e. using manipulatives, verbal expressions, and geometric models to represent number operations | M.Connecting Situations with Operations | Covered | 9 | 1 | 0 | 0 | Covered by 1 topic (9 questions, 1 materials, 0 cards, 0 videos). |
| f. applying and evaluating mental mathematics and estimation strategies | M.Mental Math and Estimation | Covered | 24 | 1 | 7 | 0 | Covered by 1 topic (24 questions, 1 materials, 7 cards, 0 videos). |
| g. analyzing standard and nonstandard computational algorithms | M.Euclidean Algorithm; M.Operational Algorithm Relationships; M.Operation and Algorithm Connections | Covered | 25 | 3 | 14 | 0 | Covered by 3 topics (25 questions, 3 materials, 14 cards, 0 videos). |
| h. solving a variety of problems using number operations | M.Whole Number Operations on a Number Line; M.Inverse Operations; M.Representations of Fractions in Word Problems | Covered | 23 | 3 | 4 | 2 | Covered by 3 topics (23 questions, 3 materials, 4 cards, 2 videos). |
PATTERNS, ALGEBRAIC RELATIONSHIPS, AND FUNCTIONS (Domain II)Partially covered
SMR II.006 · Describe, analyze, and generalize mathematical patterns.85 questions · 7 materials · 15 cards · 3 videosPartially covered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| b. recognizing and extending numerical and geometric patterns | M.Patterns - Developing an Expression | Covered | 19 | 1 | 1 | 1 | Covered by 1 topic (19 questions, 1 materials, 1 cards, 1 videos). |
| c. exploring and describing symmetric and spatial patterns (e.g., fractals, tessellations) | M.Tessellations | Partially covered | 4 | 1 | 1 | 0 | Partial coverage by 1 topic (4 questions, 1 materials, 1 cards, 0 videos); limited supporting content. |
| d. analyzing and generalizing sequences, series, and recursive patterns | M.Patterns - Developing a Linear Formula; M.Creating Formulas for Patterns - Arithmetic and Geometric; M.Concepts of Series and Sequence; M.Diverge or Converge | Covered | 54 | 4 | 11 | 2 | Covered by 4 topics (54 questions, 4 materials, 11 cards, 2 videos). |
| e. using patterns to make inferences, predictions, and decisions | M.Patterns - Developing a Linear Formula; M.Creating Formulas for Patterns - Arithmetic and Geometric; M.Mathematical Induction for Creating Formulas | Covered | 54 | 3 | 6 | 2 | Covered by 3 topics (54 questions, 3 materials, 6 cards, 2 videos). |
SMR II.007 · Use variables and symbolic expressions to describe and analyze patterns of change and functional relationships.145 questions · 16 materials · 38 cards · 3 videosPartially covered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| a. representing situations using variables and expressions | M.Dependent and Independent Variables; M.Verbal to Symbolic Linear Equations | Covered | 30 | 2 | 7 | 1 | Covered by 2 topics (30 questions, 2 materials, 7 cards, 1 videos). |
| b. exploring patterns of change characteristic of families of functions (e.g., linear, quadratic, exponential) | M.Quadratic Equations | Covered | 15 | 1 | 3 | 1 | Covered by 1 topic (15 questions, 1 materials, 3 cards, 1 videos). |
| c. translating among verbal, graphic, tabular, and symbolic representations of functions | M.Relation and Function Representations; M.Line of Best Fit; M.Parent Functions; M.Exponential Functions - Asymptotes | Covered | 58 | 4 | 8 | 0 | Covered by 4 topics (58 questions, 4 materials, 8 cards, 0 videos). |
| d. distinguishing between relations and functions | M.Forms of Equations; M.Relation and Function Representations | Covered | 46 | 2 | 13 | 1 | Covered by 2 topics (46 questions, 2 materials, 13 cards, 1 videos). |
| e. analyzing functions in terms of range, domain, and intercepts | M.Domain and Range - Discrete; M.Domain and Range - Continuous; M.Advanced Domain and Range of Functions; M.Domain and Range - Set Notation | Covered | 13 | 4 | 10 | 0 | Covered by 4 topics (13 questions, 4 materials, 10 cards, 0 videos). |
| f. using piecewise functions | M.Piecewise Functions; M.Solving Piecewise Functions | Partially covered | 6 | 2 | 1 | 0 | Partial coverage by 2 topics (6 questions, 2 materials, 1 cards, 0 videos); limited supporting content. |
| g. analyzing the relationship among the graphs of f(x) and transformations [e.g., f(x ± c), f(x) ± c, c f(x), one over f parentheses x end parentheses1⁄f(x)] | M.Functional Transformations - Linear and Quadratic | Covered | 14 | 1 | 6 | 0 | Covered by 1 topic (14 questions, 1 materials, 6 cards, 0 videos). |
| h. using graphing calculators and utilities to analyze properties of functions | M.Basics of Graphing Calculators | Partially covered | 2 | 1 | 0 | 0 | Partial coverage by 1 topic (2 questions, 1 materials, 0 cards, 0 videos); limited supporting content. |
SMR II.008 · Understand properties and applications of linear functions, and solve related equations and inequalities.163 questions · 16 materials · 20 cards · 7 videosCovered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| a. describing properties of slope and intercepts | M.Parallel and Perpendicular Lines and Formulas; M.Linear Equation Word Problems - More Slope; M.Understanding Linear Equations and Their Properties | Covered | 48 | 3 | 4 | 1 | Covered by 3 topics (48 questions, 3 materials, 4 cards, 1 videos). |
| b. analyzing the relationship between a linear equation and its graph | M.Linear Equations - Rearrange to Slope-Intercept Form; M.Linear Equation Word Problems; M.Linear Equations - Standard Form; M.Linear Equations - Point-Slope Form | Covered | 35 | 4 | 2 | 1 | Covered by 4 topics (35 questions, 4 materials, 2 cards, 1 videos). |
| c. determining the equation of a line in a variety of situations | M.Linear Equation Word Problems; M.Linear Equation Word Problems - More Slope | Covered | 19 | 2 | 0 | 1 | Covered by 2 topics (19 questions, 2 materials, 0 cards, 1 videos). |
| d. modeling problems using linear equations and inequalities | M.Linear Equation Word Problems; M.Linear Equation Word Problems - More Slope; M.Interpreting Inequalities; M.Compound Inequalities on Number Line | Covered | 31 | 4 | 7 | 3 | Covered by 4 topics (31 questions, 4 materials, 7 cards, 3 videos). |
| e. solving linear systems using a variety of methods (e.g., using substitution, using graphs, using matrices) | M.Solve for x - Linear; M.Solving Systems of Linear Equations; M.Solve Linear Inequalities - Graphically; M.Solving Linear Inequalities; M.Solving Systems of Linear Inequalities; M.Matrices - Determinant and Inverse; M.Matrices to Solve Systems of Equations | Covered | 68 | 7 | 8 | 3 | Covered by 7 topics (68 questions, 7 materials, 8 cards, 3 videos). |
SMR II.009 · Understand properties and applications of quadratic functions, and solve related equations and inequalities.89 questions · 13 materials · 22 cards · 2 videosCovered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| a. solving quadratic equations, inequalities, and systems using a variety of methods (e.g., graphical, analytical) | M.Solving Systems of Quadratic Equations; M.Solve Quadratic Inequalities - Algebraically; M.Solve Quadratic Inequalities - Graphically; M.Quadratic Inequalities - Create Shaded Graph; M.Solving Systems of Quadratic Inequalities; M.Quadratic Equations; M.Quadratic Equation - Solve via Quadratic Formula; M.Quadratic Equation - Solve via Complete the Square; M.Quadratic Equation - Solve via Factoring; M.Quadratic Equation - Solve via Graphing | Covered | 57 | 10 | 8 | 1 | Covered by 10 topics (57 questions, 10 materials, 8 cards, 1 videos). |
| b. exploring the zeros, turning point (vertex), and symmetry of a quadratic function | M.Quadratic Equation - Solve via Quadratic Formula; M.Advanced Quadratic Equation - Real World Problems; M.Sketch a Quadratic - Standard Form | Covered | 21 | 3 | 3 | 1 | Covered by 3 topics (21 questions, 3 materials, 3 cards, 1 videos). |
| c. analyzing how changing the coefficients of a quadratic function changes its graph | M.Sketch a Quadratic - Standard Form | Covered | 9 | 1 | 1 | 1 | Covered by 1 topic (9 questions, 1 materials, 1 cards, 1 videos). |
| d. using quadratic functions to model and solve problems, including maximum and minimum problems | M.Quadratic Equations; M.Advanced Quadratic Equation - Real World Problems; M.Conjectures from Graphs; M.Higher Order Derivatives and Slopes | Covered | 38 | 3 | 16 | 1 | Covered by 4 topics (38 questions, 3 materials, 16 cards, 1 videos). |
SMR II.010 · Understand properties and applications of nonlinear functions and the conceptual foundations of calculus.269 questions · 32 materials · 61 cards · 0 videosPartially covered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| a. using exponential functions to model and solve real-world problems | M.Exponential Functions; M.Exponential Functions - Reflections; M.Exponential Functions - Real World Problems | Covered | 30 | 3 | 5 | 0 | Covered by 3 topics (30 questions, 3 materials, 5 cards, 0 videos). |
| b. recognizing the relationship between inverse variation and rational functions | M.Function Composition and Inversion; M.Determine the Validity of an Inverse; M.Direct and Indirect Variation | Covered | 26 | 3 | 7 | 0 | Covered by 3 topics (26 questions, 3 materials, 7 cards, 0 videos). |
| c. exploring the properties and graphs of polynomial, rational, radical, exponential, logarithmic, and trigonometric (i.e., sine, cosine, tangent) functions | M.Properties of Logarithms; M.Operations with Radicals; M.Polynomials; M.Advanced Factoring Polynomials; M.Rational Functions; M.Exponential Functions; M.Logarithmic Functions; M.Logarithmic Functions - Change Base; M.Solve for x - Radical; M.Sketch a Polynomial - From Roots; M.Trigonometric Ratio Graphs; M.Trigonometric Ratio Graphs - Real Word Problems; M.Functional Transformations - Exponential; M.Functional Transformations - Radical | Covered | 143 | 14 | 27 | 0 | Covered by 14 topics (143 questions, 14 materials, 27 cards, 0 videos). |
| d. using graphing calculators to solve systems of equations involving these functions | M.Basics of Graphing Calculators; M.Technology and Trigonometric Function Problems | Partially covered | 4 | 2 | 0 | 0 | Partial coverage by 2 topics (4 questions, 2 materials, 0 cards, 0 videos); limited supporting content. |
| e. analyzing the relationships among the graph, slope of the secant line, and the derivative of a function | M.Rates of Change - Average vs Instantaneous; M.Derivatives and Slopes | Covered | 26 | 2 | 10 | 0 | Covered by 2 topics (26 questions, 2 materials, 10 cards, 0 videos). |
| f. recognizing the relationship between the area under a curve and integration | M.Integration | Covered | 8 | 1 | 4 | 0 | Covered by 1 topic (8 questions, 1 materials, 4 cards, 0 videos). |
| g. describing how calculus is used to solve problems involving dynamic change | M.Calculus Connections to Formulas; M.Accumulations; M.Distance by Integration; M.Calculus - Rates; M.Calculus - Velocity and Acceleration; M.Calculus - Work; M.Calculus - Center of Mass; M.Foundational Theorems of Calculus | Covered | 44 | 8 | 16 | 0 | Covered by 8 topics (44 questions, 8 materials, 16 cards, 0 videos). |
MEASUREMENT AND GEOMETRY (Domain III)Partially covered
SMR III.011 · Understand attributes of measurement and measuring units.145 questions · 8 materials · 29 cards · 5 videosPartially covered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| a. selecting appropriate units (standard and nonstandard) to estimate and record measurements of angle (degree and radian), length, area, volume, mass, temperature, and time | None | Coverage gap identified | 0 | 0 | 0 | 0 | No matching topic found in the study guide. |
| b. identifying tools for performing measurements | M.Measurement Tools; M.Advanced Measurement Principles; M.Choosing Appropriate Units | Covered | 43 | 3 | 16 | 2 | Covered by 3 topics (43 questions, 3 materials, 16 cards, 2 videos). |
| c. converting measurements within measurement systems | M.Metric System; M.Converting Units - Proportional Reasoning | Covered | 39 | 2 | 5 | 2 | Covered by 2 topics (39 questions, 2 materials, 5 cards, 2 videos). |
| d. analyzing how changes in the measurement of one attribute relate to changes in others | M.Dimensional Changes Affecting Area and Volume | Covered | 23 | 1 | 0 | 0 | Covered by 1 topic (23 questions, 1 materials, 0 cards, 0 videos). |
| e. using dimensional analysis to solve problems | M.Converting Units - Dimensional Analysis | Covered | 29 | 1 | 1 | 1 | Covered by 1 topic (29 questions, 1 materials, 1 cards, 1 videos). |
| f. solving problems involving density, pressure, rates of change, and other derived units | M.Converting Units - Dimensional Analysis | Covered | 29 | 1 | 1 | 1 | Covered by 1 topic (29 questions, 1 materials, 1 cards, 1 videos). |
| g. evaluating precision, accuracy, measurement errors, and percent error | M.Measurement Principles | Covered | 11 | 1 | 9 | 0 | Covered by 1 topic (11 questions, 1 materials, 9 cards, 0 videos). |
SMR III.012 · Apply measurement principles to analyze the spatial characteristics of two- and three-dimensional shapes.230 questions · 15 materials · 33 cards · 5 videosCovered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| a. deriving and applying formulas for the perimeter, area, surface area, or volume of two- and three-dimensional composite figures | M.Area and Perimeter of Polygons; M.Derivation of Geometric Equations; M.Generating Formulas for Shapes; M.Surface Area in 3D; M.Volume in 3D; M.Area and Perimeter of Rectangles and Triangles; M.Area and Perimeter of Polygons - Irregular Shapes | Covered | 129 | 7 | 7 | 3 | Covered by 7 topics (129 questions, 7 materials, 7 cards, 3 videos). |
| b. exploring scale factors for the area and volume of similar figures | M.Advanced Similar Shapes | Covered | 11 | 1 | 10 | 0 | Covered by 1 topic (11 questions, 1 materials, 10 cards, 0 videos). |
| c. applying right triangle trigonometry and the Pythagorean theorem to solve problems (e.g., problems involving indirect measurements) | M.Pythagorean Theorem; M.Apply Triangle Properties; M.Trigonometric Ratios; M.Inverse Trigonometric Ratios | Covered | 54 | 4 | 12 | 2 | Covered by 4 topics (54 questions, 4 materials, 12 cards, 2 videos). |
| d. interpreting three-dimensional drawings of objects | M.Convert Between Surface Area and Volume | Covered | 9 | 1 | 0 | 0 | Covered by 1 topic (9 questions, 1 materials, 0 cards, 0 videos). |
| e. analyzing cross sections and nets of three-dimensional figures | M.Conic Sections; M.Nets | Covered | 27 | 2 | 5 | 0 | Covered by 2 topics (27 questions, 2 materials, 5 cards, 0 videos). |
SMR III.013 · Apply geometric principles of points, lines, angles, planes, congruence, and similarity to analyze the formal characteristics of two- and three-dimensional shapes.166 questions · 15 materials · 69 cards · 5 videosPartially covered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| a. determining necessary and sufficient conditions for the existence of a particular shape | M.Attributes of Two-Dimensional Shapes | Covered | 18 | 1 | 19 | 0 | Covered by 1 topic (18 questions, 1 materials, 19 cards, 0 videos). |
| b. applying properties of parallel and perpendicular lines and angles to analyze shapes | M.Angles in Triangles; M.Measurements Inside Triangles | Covered | 21 | 2 | 10 | 1 | Covered by 2 topics (21 questions, 2 materials, 10 cards, 1 videos). |
| c. comparing and analyzing shapes and formally establishing the relationships among them (e.g., congruence, similarity) | M.Measurements in Circles; M.Measurements in Circles Advanced; M.Pyramids and Prisms; M.Types of Prisms; M.Apply Triangle Inequalities; M.Solving with Shapes - Quadrilaterals; M.Attributes of Two-Dimensional Shapes | Covered | 89 | 7 | 38 | 3 | Covered by 7 topics (89 questions, 7 materials, 38 cards, 3 videos). |
| d. using geometric principles to prove theorems | M.Prove Theorems - Lines and Angles; M.Prove Theorems - Triangles; M.Prove Theorems - Parallelograms | Covered | 28 | 3 | 19 | 0 | Covered by 3 topics (28 questions, 3 materials, 19 cards, 0 videos). |
| e. applying properties of two-dimensional shapes to analyze three-dimensional shapes | M.Attributes of Three Dimensional Figures; M.2D of 3D shape | Covered | 23 | 2 | 7 | 1 | Covered by 2 topics (23 questions, 2 materials, 7 cards, 1 videos). |
| f. recognizing the uses of dynamic geometry software in making conjectures and investigating properties of shapes | M.Using Calculators to Check Math | Partially covered | 5 | 1 | 1 | 0 | Partial coverage by 1 topic (5 questions, 1 materials, 1 cards, 0 videos); limited supporting content. |
SMR III.014 · Apply properties of geometric transformations and coordinate geometry to describe geometric objects in two and three dimensions.125 questions · 8 materials · 33 cards · 4 videosCovered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| a. analyzing figures in terms of translations, reflections, rotations, dilations, and contractions | M.Non-Rigid Transformations; M.Rigid Transformations | Covered | 22 | 2 | 8 | 0 | Covered by 2 topics (22 questions, 2 materials, 8 cards, 0 videos). |
| b. applying transformations to explore the concepts of congruence and similarity | M.Non-Rigid Transformations; M.Rigid Transformations | Covered | 22 | 2 | 8 | 0 | Covered by 2 topics (22 questions, 2 materials, 8 cards, 0 videos). |
| c. using transformations to characterize the symmetry of an object | M.Multiple Transformations | Covered | 18 | 1 | 2 | 0 | Covered by 1 topic (18 questions, 1 materials, 2 cards, 0 videos). |
| d. locating objects in terms of their position using rectangular coordinate systems | M.Coordinate Geometry; M.The Coordinate Plane | Covered | 29 | 2 | 5 | 1 | Covered by 2 topics (29 questions, 2 materials, 5 cards, 1 videos). |
| e. locating and describing the locus of points that satisfy a given condition | M.Points, Lines, Planes, Angles; M.Solving with Points, Lines, Planes, Angles | Covered | 40 | 2 | 18 | 2 | Covered by 2 topics (40 questions, 2 materials, 18 cards, 2 videos). |
| f. applying concepts of slope, distance, midpoint, and parallel and perpendicular lines to determine the geometric and algebraic properties of figures in the coordinate plane | M.Slope, Midpoint, and Distance | Covered | 16 | 1 | 0 | 1 | Covered by 1 topic (16 questions, 1 materials, 0 cards, 1 videos). |
DATA ANALYSIS, STATISTICS, PROBABILITY, AND DISCRETE MATHEMATICS (Domain IV)Partially covered
SMR IV.015 · Understand methods of organizing, displaying, analyzing, and interpreting data.245 questions · 15 materials · 52 cards · 5 videosPartially covered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| a. organizing data using tables and spreadsheets | M.Spreadsheet Fields | Partially covered | 1 | 1 | 1 | 0 | Partial coverage by 1 topic (1 questions, 1 materials, 1 cards, 0 videos); limited supporting content. |
| b. creating a variety of charts to display data (e.g., pie charts, box plots, stem and leaf plots, scatter plots, frequency histograms) | M.Graphs and Plots; M.Boxplots | Covered | 43 | 2 | 17 | 1 | Covered by 2 topics (43 questions, 2 materials, 17 cards, 1 videos). |
| c. evaluating the source, organization, and presentation of data | M.Data Analysis and Interpretation; M.Appropriate vs Inappropriate Representations of Data; M.Bivariate Data Analysis; M.Advanced Bivariate Data Analysis; M.Choosing a Graph or Plot | Covered | 81 | 5 | 23 | 3 | Covered by 5 topics (81 questions, 5 materials, 23 cards, 3 videos). |
| d. applying and interpreting measures of central tendency (e.g., mean, median, mode) and spread (e.g., range, standard deviation) | M.Measures of Center and Range; M.Advanced Measures of Center and Range; M.Describing Data Patterns and Outliers | Covered | 80 | 3 | 15 | 1 | Covered by 3 topics (80 questions, 3 materials, 15 cards, 1 videos). |
| e. analyzing the effects of data transformations on measures of central tendency and spread | M.Effect of Change in Data on Measures of Center and Range | Covered | 16 | 1 | 3 | 0 | Covered by 1 topic (16 questions, 1 materials, 3 cards, 0 videos). |
| f. using appropriate technology to analyze and manipulate data | M.Calculating Linear Regression; M.Probability Simulations | Covered | 13 | 2 | 5 | 0 | Covered by 2 topics (13 questions, 2 materials, 5 cards, 0 videos). |
| g. evaluating the validity of statistical arguments | M.Statistical Questions | Covered | 11 | 1 | 1 | 0 | Covered by 1 topic (11 questions, 1 materials, 1 cards, 0 videos). |
SMR IV.016 · Understand methods of collecting data and making predictions and inferences based on data.51 questions · 6 materials · 17 cards · 0 videosPartially covered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| a. applying appropriate techniques for collecting data | M.Sampling Methods | Covered | 12 | 1 | 5 | 0 | Covered by 1 topic (12 questions, 1 materials, 5 cards, 0 videos). |
| b. analyzing factors that may affect the validity of a survey, including bias | M.Surveys | Covered | 10 | 1 | 3 | 0 | Covered by 1 topic (10 questions, 1 materials, 3 cards, 0 videos). |
| c. using simulations and sampling to test inferences | M.Probability Simulations; M.Sampling Methods | Covered | 19 | 2 | 8 | 0 | Covered by 2 topics (19 questions, 2 materials, 8 cards, 0 videos). |
| d. applying principles of interpolation and extrapolation | M.Interpolation of Data | Partially covered | 1 | 1 | 1 | 0 | Partial coverage by 1 topic (1 questions, 1 materials, 1 cards, 0 videos); limited supporting content. |
| e. analyzing linear regression lines and correlation coefficients | M.Calculating Linear Regression | Partially covered | 6 | 1 | 2 | 0 | Partial coverage by 1 topic (6 questions, 1 materials, 2 cards, 0 videos); limited supporting content. |
| f. analyzing the relationship between sample size and width of confidence interval | M.Level of Confidence | Covered | 15 | 1 | 4 | 0 | Covered by 1 topic (15 questions, 1 materials, 4 cards, 0 videos). |
| g. employing confidence intervals in making predictions and inferences based on data | M.Level of Confidence | Covered | 15 | 1 | 4 | 0 | Covered by 1 topic (15 questions, 1 materials, 4 cards, 0 videos). |
SMR IV.017 · Understand the theory of probability and probability distributions.159 questions · 13 materials · 47 cards · 5 videosPartially covered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| a. enumerating the sample space of an event | M.Sample Spaces to Determine Probabilities | Partially covered | 4 | 1 | 1 | 1 | Partial coverage by 1 topic (4 questions, 1 materials, 1 cards, 1 videos); limited supporting content. |
| b. determining simple and compound probabilities | M.Simple and Compound Events | Covered | 11 | 1 | 1 | 1 | Covered by 1 topic (11 questions, 1 materials, 1 cards, 1 videos). |
| c. determining conditional probabilities | M.Probability; M.Fundamental Counting Principle | Covered | 57 | 2 | 9 | 2 | Covered by 2 topics (57 questions, 2 materials, 9 cards, 2 videos). |
| d. finding the probability of dependent and independent events | M.Probability; M.Probability Models | Covered | 58 | 2 | 9 | 1 | Covered by 2 topics (58 questions, 2 materials, 9 cards, 1 videos). |
| e. calculating expected values | M.Chi-Square Test | Covered | 6 | 1 | 7 | 0 | Covered by 1 topic (6 questions, 1 materials, 7 cards, 0 videos). |
| f. using simulations and sampling to determine experimental probabilities | M.Observations, Conclusions, and Relationships; M.Statistical Experiments | Covered | 22 | 2 | 11 | 0 | Covered by 2 topics (22 questions, 2 materials, 11 cards, 0 videos). |
| g. solving problems using geometric probability (e.g., ratio of two areas) | M.Fundamental Counting Principle; M.Geometric Probability | Covered | 13 | 2 | 2 | 2 | Covered by 2 topics (13 questions, 2 materials, 2 cards, 2 videos). |
| h. applying probability distributions (e.g., binomial, normal) to solve problems | M.Probability Distributions; M.Normal Distribution; M.Using Distributions; M.Uniform Distributions | Covered | 45 | 4 | 17 | 0 | Covered by 4 topics (45 questions, 4 materials, 17 cards, 0 videos). |
| i. modeling and solving real-world problems using probability concepts | M.Probability; M.Sample Spaces to Determine Probabilities | Covered | 51 | 2 | 9 | 2 | Covered by 2 topics (51 questions, 2 materials, 9 cards, 2 videos). |
SMR IV.018 · Understand principles of discrete mathematics.55 questions · 6 materials · 18 cards · 0 videosPartially covered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| a. solving counting problems using permutations and combinations | M.Combinations and Permutations | Covered | 20 | 1 | 2 | 0 | Covered by 1 topic (20 questions, 1 materials, 2 cards, 0 videos). |
| b. using sets and set relations to represent algebraic and geometric concepts | None | Coverage gap identified | 0 | 0 | 0 | 0 | No matching topic found in the study guide. |
| c. using finite graphs and trees to model problem situations | M.Diagrams | Covered | 16 | 1 | 2 | 0 | Covered by 1 topic (16 questions, 1 materials, 2 cards, 0 videos). |
| d. employing recursion and iteration methods to model problems | M.Recursion and Iteration | Partially covered | 3 | 1 | 1 | 0 | Partial coverage by 1 topic (3 questions, 1 materials, 1 cards, 0 videos); limited supporting content. |
| e. describing and analyzing efficient algorithms to accomplish a task or solve a problem in a variety of contexts (e.g., practical and computer-related situations) | M.Operational Algorithm Relationships; M.Operation and Algorithm Connections | Covered | 9 | 2 | 13 | 0 | Covered by 2 topics (9 questions, 2 materials, 13 cards, 0 videos). |
| f. using linear programming to model and solve problems | M.Calculus Connections to Formulas | Partially covered | 7 | 1 | 0 | 0 | Partial coverage by 1 topic (7 questions, 1 materials, 0 cards, 0 videos); limited supporting content. |
How 240 Creates The MTTC Mathematics (Elementary) (089) 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 MTTC Mathematics (Elementary).
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 MTTC 089 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 MTTC Mathematics (Elementary) Study Guide
The questions teacher candidates ask us most often about the MTTC Mathematics (Elementary) study guide.
Is 240 a good study guide for MTTC Mathematics (Elementary)?
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 MTTC 089 exam?
This guide is 93% 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.