240's TExES Math 7-12 Study Guide Is 91% Test-Aligned
240's TExES Math 7-12 study guide is built around the official exam framework so you can study what is actually tested. This page shows exactly how the guide maps to the real exam — SMR by SMR and competency by competency — so you can see where coverage is strongest, where some depth gaps remain, and how each part of the guide supports your prep.
91%
test-aligned
119
Fully covered
21
Partially covered
3
Coverage gap
Based on a competency-by-competency review of the official framework and the lessons, practice questions, flashcards, videos, and study materials included in this guide.
2817
Practice Questions
564
Flashcards
267
Study Materials
63
Videos
Why Test Alignment Matters for Your TExES Math 7-12 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 TExES Math 7-12 (235) 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 TExES 235 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
6 domains · 143 competencies reviewed · 91% test-aligned
Covered— competency is comprehensively supported by the guide
Partially covered— core content is covered, but some depth gaps remain
Coverage gap identified— a 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.
NUMBER CONCEPTS (DOMAIN I)
Partially covered
SMR I.001 The teacher understands the real number system and its structure, operations, algorithms and representations.
194 Qs13 Materials45 Cards6 VideosPartially covered
| Official Competency | Matching 240 Topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| A. Understands the concepts of place value, number base and decimal representations of real numbers. | M.Place Value | Covered | 33 | 1 | 2 | 1 | Covered by 1 topic (33 questions, 1 materials, 2 cards, 1 videos). |
| B. Understands the algebraic structure and properties of the real number system and its subsets (e.g., real numbers as a field, integers as an additive group). | M.Structure of Number Systems; M.Group, Ring, and Field Theory | Covered | 17 | 2 | 17 | 1 | Covered by 2 topics (17 questions, 2 materials, 17 cards, 1 videos). |
| C. Describes and analyzes properties of subsets of the real numbers (e.g., closure, identities). | M.Characteristics of Rational Numbers; M.Operational Properties; M.Identities | Covered | 63 | 3 | 10 | 1 | Covered by 3 topics (63 questions, 3 materials, 10 cards, 1 videos). |
| D. Selects and uses appropriate representations of real numbers (e.g., fractions, decimals, percents, roots, exponents, scientific notation) for particular situations. | M.Representations of Fractions in Word Problems; M.Exponential and Scientific Notation; M.Properties of Exponents | Covered | 48 | 3 | 4 | 2 | Covered by 3 topics (48 questions, 3 materials, 4 cards, 2 videos). |
| E. Uses a variety of models (e.g., geometric, symbolic) to represent operations, algorithms and real numbers. | M.Fraction, Decimal, Percentage Conversions; M.Operational Algorithm Relationships | Covered | 20 | 2 | 20 | 1 | Covered by 2 topics (20 questions, 2 materials, 20 cards, 1 videos). |
| F. Uses real numbers to model and solve a variety of problems. | None | Coverage gap identified | 0 | 0 | 0 | 0 | No matching topic found in the study guide. |
| G. Uses deductive reasoning to simplify and justify algebraic processes. | M.Inductive vs Deductive Reasoning | Covered | 10 | 1 | 3 | 0 | Covered by 1 topic (10 questions, 1 materials, 3 cards, 0 videos). |
| H. Demonstrates how some problems that have no solution in the integer or rational number systems have solutions in the real number system. | M.Operations and Rational and Irrational Numbers | Partially covered | 3 | 1 | 0 | 0 | Partial coverage by 1 topic (3 questions, 1 materials, 0 cards, 0 videos); limited supporting content. |
SMR I.002 The teacher understands the complex number system and its structure, operations, algorithms and representations.
74 Qs9 Materials26 Cards2 VideosPartially covered
| Official Competency | Matching 240 Topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| A. Demonstrates how some problems that have no solution in the real number system have solutions in the complex number system. | M.Imaginary and Complex Numbers | Covered | 10 | 1 | 10 | 1 | Covered by 1 topic (10 questions, 1 materials, 10 cards, 1 videos). |
| B. Understands the properties of complex numbers (e.g., complex conjugate, magnitude/modulus, multiplicative inverse). | M.Complex Numbers and Their Conjugates; M.Complex Numbers - Inverses; M.Complex Numbers - Modulus | Covered | 23 | 3 | 7 | 0 | Covered by 3 topics (23 questions, 3 materials, 7 cards, 0 videos). |
| C. Understands the algebraic structure of the complex number system and its subsets (e.g., complex numbers as a field, complex addition as vector addition). | M.Complex Numbers - Distance | Partially covered | 4 | 1 | 3 | 0 | Partial coverage by 1 topic (4 questions, 1 materials, 3 cards, 0 videos); limited supporting content. |
| D. Selects and uses appropriate representations of complex numbers (e.g., vector, ordered pair, polar, exponential) for particular situations. | M.Complex Numbers and the Complex Plane; M.Different Representations of Complex Numbers; M.Polar Coordinates | Covered | 23 | 3 | 7 | 0 | Covered by 3 topics (23 questions, 3 materials, 7 cards, 0 videos). |
| E. Describes complex number operations (e.g., addition, multiplication, roots) using symbolic and geometric representations. | M.Operations with Complex Numbers | Covered | 14 | 1 | 2 | 1 | Covered by 1 topic (14 questions, 1 materials, 2 cards, 1 videos). |
SMR I.003 The teacher understands number theory concepts and principles and uses numbers to model and solve problems in a variety of situations.
280 Qs19 Materials43 Cards6 VideosCovered
| Official Competency | Matching 240 Topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| A. Applies ideas from number theory (e.g., prime numbers and factorization, the Euclidean algorithm, divisibility, congruence classes, modular arithmetic, the fundamental theorem of arithmetic) to solve problems. | M.Prime and Composite Numbers; M.Factors; M.Prime Factorization; M.Euclidean Algorithm; M.Congruence Classes and Modular Arithmetic | Covered | 91 | 5 | 16 | 3 | Covered by 5 topics (91 questions, 5 materials, 16 cards, 3 videos). |
| B. Applies number theory concepts and principles to justify and prove number relationships. | M.Justify and Prove Number Relationships | Covered | 12 | 1 | 2 | 0 | Covered by 1 topic (12 questions, 1 materials, 2 cards, 0 videos). |
| C. Compares and contrasts properties of vectors and matrices with properties of number systems (e.g., existence of inverses, non-commutative operations). | M.Matrices and Addition Subtraction; M.Matrices and Multiplication; M.Properties of Matrices; M.Vectors and Scalars | Covered | 21 | 4 | 9 | 0 | Covered by 4 topics (21 questions, 4 materials, 9 cards, 0 videos). |
| D. Uses properties of numbers (e.g., fractions, decimals, percents, ratios, proportions) to model and solve real-world problems. | M.Ratios; M.Fraction Operations - Mixed Numbers; M.Ratios, Proportions, Percents; M.Constants of Proportionality; M.Percent Change; M.Proportional Reasoning - Scale Drawings | Covered | 96 | 6 | 10 | 3 | Covered by 6 topics (96 questions, 6 materials, 10 cards, 3 videos). |
| E. Applies counting techniques such as permutations and combinations to quantify situations and solve problems. | M.Combinations and Permutations | Covered | 20 | 1 | 2 | 0 | Covered by 1 topic (20 questions, 1 materials, 2 cards, 0 videos). |
| F. Uses estimation techniques to solve problems and judges the reasonableness of solutions. | M.Reasonableness of Results; M.Mental Math and Estimation | Covered | 40 | 2 | 7 | 0 | Covered by 2 topics (40 questions, 2 materials, 7 cards, 0 videos). |
PATTERNS AND ALGEBRA (DOMAIN II)
Partially covered
SMR II.004 The teacher uses patterns to model and solve problems and formulate conjectures.
139 Qs13 Materials27 Cards3 VideosPartially covered
| Official Competency | Matching 240 Topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| A. Recognizes and extends patterns and relationships in data presented in tables, sequences or graphs. | M.Patterns - Developing a Linear Formula; M.Creating Formulas for Patterns - Arithmetic and Geometric | Covered | 46 | 2 | 4 | 2 | Covered by 2 topics (46 questions, 2 materials, 4 cards, 2 videos). |
| B. Uses methods of recursion and iteration to model and solve 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. |
| C. Uses the principle of mathematical induction. | M.Creating Formulas for Patterns - Arithmetic and Geometric; M.Mathematical Induction for Creating Formulas | Covered | 37 | 2 | 4 | 1 | Covered by 2 topics (37 questions, 2 materials, 4 cards, 1 videos). |
| D. Analyzes the properties of sequences and series (e.g., Fibonacci, arithmetic, geometric) and uses them to solve problems involving finite and infinite processes. | M.Types of Sequences; M.Patterns - Developing an Expression; M.Fibonacci Sequences; M.Teaching the Concept of Limits in Sequences and Series; M.Concepts of Series and Sequence; M.Find Sum of Series | Covered | 50 | 6 | 16 | 1 | Covered by 6 topics (50 questions, 6 materials, 16 cards, 1 videos). |
| E. Understands how sequences and series are applied to solve problems in the mathematics of finance (e.g., simple, compound and continuous interest rates; annuities). | M.Exponential Functions - Real World Problems; M.Exponential Functions - Real World Problems - Compound Interest; M.Exponential Functions - Real World Problems - Annuities | Covered | 32 | 3 | 8 | 0 | Covered by 3 topics (32 questions, 3 materials, 8 cards, 0 videos). |
SMR II.005 The teacher understands attributes of functions, relations and their graphs.
114 Qs11 Materials22 Cards0 VideosPartially covered
| Official Competency | Matching 240 Topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| A. Understands when a relation is a function. | M.Relation and Function Representations | Covered | 39 | 1 | 4 | 0 | Covered by 1 topic (39 questions, 1 materials, 4 cards, 0 videos). |
| B. Identifies the mathematical domain and range of functions and relations and determines reasonable domains for given situations. | M.Domain and Range - Discrete; M.Domain and Range - Continuous; M.Domain and Range - Set Notation | Covered | 8 | 3 | 6 | 0 | Covered by 3 topics (8 questions, 3 materials, 6 cards, 0 videos). |
| C. Understands that a function represents a dependence of one quantity on another and can be represented in a variety of ways (e.g., concrete models, tables, graphs, diagrams, verbal descriptions, symbols). | M.Relation and Function Representations | Covered | 39 | 1 | 4 | 0 | Covered by 1 topic (39 questions, 1 materials, 4 cards, 0 videos). |
| D. Identifies and analyzes even and odd functions, one-to-one functions, inverse functions and their graphs. | M.Surjective vs Injective; M.Function Composition and Inversion; M.Even and Odd Functions | Covered | 39 | 3 | 6 | 0 | Covered by 3 topics (39 questions, 3 materials, 6 cards, 0 videos). |
| E. Applies basic transformations [e.g., k f(x), f(x) + k, f(x – k), f(kx), |f(x)|] to a parent function, f, and describes the effects on the graph of y = 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). |
| F. Performs operations (e.g., sum, difference, composition) on functions, finds inverse relations and describes results symbolically and graphically. | M.Function Composition and Inversion; M.Advanced Domain and Range of Functions - Composition; M.Linear Expression Addition and Subtraction | Covered | 28 | 3 | 2 | 0 | Covered by 3 topics (28 questions, 3 materials, 2 cards, 0 videos). |
| G. Uses graphs of functions to formulate conjectures of identities [e.g., y = x2 − 1 and y = (x – 1)(x + 1), y = log x3 and y = 3 log x, y = sin(x + ) and y = cos x]. | M.Parent Functions | Partially covered | 7 | 1 | 1 | 0 | Partial coverage by 1 topic (7 questions, 1 materials, 1 cards, 0 videos); limited supporting content. |
SMR II.006 The teacher understands linear and quadratic functions, analyzes their algebraic and graphical properties and uses them to model and solve problems.
212 Qs27 Materials22 Cards8 VideosCovered
| Official Competency | Matching 240 Topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| A. Understands the concept of slope as a rate of change and interprets the meaning of slope and intercept in a variety of situations. | M.Linear Equation Word Problems | Covered | 15 | 1 | 0 | 1 | Covered by 1 topic (15 questions, 1 materials, 0 cards, 1 videos). |
| B. Writes equations of lines given various characteristics (e.g., two points, a point and slope, slope and y-intercept). | M.Linear Equations - Rearrange to Slope-Intercept Form; M.Linear Equation Word Problems - More Slope; M.Linear Equations - Standard Form; M.Linear Equations - Point-Slope Form | Covered | 24 | 4 | 2 | 0 | Covered by 4 topics (24 questions, 4 materials, 2 cards, 0 videos). |
| C. Applies techniques of linear and matrix algebra to represent and solve problems involving linear systems. | M.Solving Systems of Linear Equations; M.Solving Systems of Linear Inequalities; M.Matrices to Solve Systems of Equations | Covered | 23 | 3 | 1 | 1 | Covered by 3 topics (23 questions, 3 materials, 1 cards, 1 videos). |
| D. Analyzes the zeros (real and complex) of quadratic functions. | M.Quadratic Equations; M.Quadratic Equations with Complex Roots; M.Sketch a Polynomial - From Roots | Covered | 33 | 3 | 5 | 1 | Covered by 3 topics (33 questions, 3 materials, 5 cards, 1 videos). |
| E. Makes connections between the y = ax2 + bx + c and the y = a(x – h)2 + k representations of a quadratic function and its graph. | M.Sketch a Quadratic - Standard Form; M.Sketch a Quadratic - Vertex Form | Covered | 19 | 2 | 2 | 1 | Covered by 2 topics (19 questions, 2 materials, 2 cards, 1 videos). |
| F. Solves problems involving quadratic functions using a variety of methods (e.g., factoring, completing the square, using the quadratic formula, using a graphing calculator). | 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 | Covered | 31 | 5 | 3 | 0 | Covered by 5 topics (31 questions, 5 materials, 3 cards, 0 videos). |
| G. Models and solves problems involving linear and quadratic equations and inequalities using a variety of methods, including technology. | M.Solve for x - Linear; M.Solve for x - Linear (Multiple Variables); M.Interpreting Inequalities; M.Solve Linear Inequalities - Graphically; M.Solve Quadratic Inequalities - Algebraically; M.Solve Quadratic Inequalities - Graphically; M.Quadratic Inequalities - Create Shaded Graph; M.Absolute Value Inequalities; M.Solve for x - Nonlinear | Covered | 67 | 9 | 9 | 4 | Covered by 9 topics (67 questions, 9 materials, 9 cards, 4 videos). |
SMR II.007 The teacher understands polynomial, rational, radical, absolute value and piecewise functions, analyzes their algebraic and graphical properties and uses them to model and solve problems.
136 Qs19 Materials39 Cards2 VideosPartially covered
| Official Competency | Matching 240 Topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| A. Recognizes and translates among various representations (e.g., written, tabular, graphical, algebraic) of polynomial, rational, radical, absolute value and piecewise functions. | M.Polynomials; M.Advanced Factoring Polynomials; M.Absolute Value Functions; M.Piecewise Functions; M.Functional Transformations - Absolute Value; M.Solve for x - Radical | Covered | 55 | 6 | 9 | 0 | Covered by 6 topics (55 questions, 6 materials, 9 cards, 0 videos). |
| B. Describes restrictions on the domains and ranges of polynomial, rational, radical, absolute value and piecewise functions. | M.Advanced Domain and Range of Functions; M.Advanced Domain and Range of Functions - Piecewise | Covered | 6 | 2 | 7 | 0 | Covered by 2 topics (6 questions, 2 materials, 7 cards, 0 videos). |
| C. Makes and uses connections among the significant points (e.g., zeros, local extrema, points where a function is not continuous or not differentiable) of a function, the graph of the function and the function’s symbolic representation. | M.Conjectures from Graphs | Partially covered | 0 | 0 | 0 | 0 | Partial coverage by 1 topic (0 questions, 0 materials, 0 cards, 0 videos); limited supporting content. |
| D. Analyzes functions in terms of vertical, horizontal and slant asymptotes. | M.Rational Functions | Partially covered | 4 | 1 | 6 | 0 | Partial coverage by 1 topic (4 questions, 1 materials, 6 cards, 0 videos); limited supporting content. |
| E. Analyzes and applies the relationship between inverse variation and rational functions. | M.Determine the Validity of an Inverse; M.Direct and Indirect Variation | Covered | 5 | 2 | 5 | 0 | Covered by 2 topics (5 questions, 2 materials, 5 cards, 0 videos). |
| F. Solves equations and inequalities involving polynomial, rational, radical, absolute value and piecewise functions using a variety of methods (e.g., tables, algebraic methods, graphs, use of a graphing calculator) and evaluates the reasonableness of solutions. | M.Square Roots and Radicals; M.Radicals and Exponents; M.Simplifying Radicals; M.Solving Piecewise Functions; M.Advanced Equivalence of Expressions - To Simplify; M.Equivalence of Expressions - To Expand; M.Equivalence of Expressions - To Simplify | Covered | 64 | 7 | 13 | 2 | Covered by 7 topics (64 questions, 7 materials, 13 cards, 2 videos). |
| G. Models situations using polynomial, rational, radical, absolute value and piecewise functions and solves problems using a variety of methods, including technology. | 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 The teacher understands exponential and logarithmic functions, analyses their algebraic and graphical properties and uses them to model and solve problems.
84 Qs9 Materials17 Cards0 VideosPartially covered
| Official Competency | Matching 240 Topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| A. Recognizes and translates among various representations (e.g., written, numerical, tabular, graphical, algebraic) of exponential and logarithmic functions. | M.Exponential Functions - Reflections; M.Logarithmic Functions | Covered | 9 | 2 | 3 | 0 | Covered by 2 topics (9 questions, 2 materials, 3 cards, 0 videos). |
| B. Recognizes and uses connections among significant characteristics (e.g., intercepts, asymptotes) of a function involving exponential or logarithmic expressions, the graph of the function and the function’s symbolic representation. | M.Exponential Functions - Asymptotes; M.Logarithmic Functions | Covered | 12 | 2 | 3 | 0 | Covered by 2 topics (12 questions, 2 materials, 3 cards, 0 videos). |
| C. Understands the relationship between exponential and logarithmic functions and uses the laws and properties of exponents and logarithms to simplify expressions and solve problems. | M.Properties of Logarithms; M.Exponential Functions; M.Logarithmic Functions | Covered | 41 | 3 | 11 | 0 | Covered by 3 topics (41 questions, 3 materials, 11 cards, 0 videos). |
| D. Uses a variety of representations and techniques (e.g., numerical methods, tables, graphs, analytic techniques, graphing calculators) to solve equations, inequalities and systems involving exponential and logarithmic functions. | M.Exponential Functions - Asymptotes; M.Logarithmic Functions - Graph | Covered | 10 | 2 | 2 | 0 | Covered by 2 topics (10 questions, 2 materials, 2 cards, 0 videos). |
| E. Models and solves problems involving exponential growth and decay. | M.Exponential Functions | Covered | 12 | 1 | 3 | 0 | Covered by 1 topic (12 questions, 1 materials, 3 cards, 0 videos). |
| F. Uses logarithmic scales (e.g., Richter, decibel) to describe phenomena and solve problems. | M.Logarithmic Phenomena | Partially covered | 4 | 1 | 2 | 0 | Partial coverage by 1 topic (4 questions, 1 materials, 2 cards, 0 videos); limited supporting content. |
| G. Uses exponential and logarithmic functions to model and solve problems involving the mathematics of finance (e.g., compound interest). | M.Exponential Functions - Real World Problems | Covered | 17 | 1 | 5 | 0 | Covered by 1 topic (17 questions, 1 materials, 5 cards, 0 videos). |
| H. Uses the exponential function to model situations and solve problems in which the rate of change of a quantity is proportional to the current amount of the quantity [i.e.,]. | M.Exponential Functions - Real World Problems - Compound Interest | Covered | 11 | 1 | 4 | 0 | Covered by 1 topic (11 questions, 1 materials, 4 cards, 0 videos). |
SMR II.009 The teacher understands trigonometric and circular functions, analyzes their algebraic and graphical properties and uses them to model and solve problems.
89 Qs11 Materials5 Cards0 VideosPartially covered
| Official Competency | Matching 240 Topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| A. Analyzes the relationships among the unit circle in the coordinate plane, circular functions and the trigonometric functions. | M.The Unit Circle | Covered | 9 | 1 | 0 | 0 | Covered by 1 topic (9 questions, 1 materials, 0 cards, 0 videos). |
| B. Recognizes and translates among various representations (e.g., written, numerical, tabular, graphical, algebraic) of trigonometric functions and their inverses. | M.Trigonometric Ratio Graphs - Real Word Problems | Partially covered | 7 | 1 | 0 | 0 | Partial coverage by 1 topic (7 questions, 1 materials, 0 cards, 0 videos); limited supporting content. |
| C. Recognizes and uses connections among significant properties (e.g., zeros, axes of symmetry, local extrema) and characteristics (e.g., amplitude, frequency, phase shift) of a trigonometric function, the graph of the function and the function’s symbolic representation. | M.Trigonometric Ratio Graphs | Covered | 19 | 1 | 3 | 0 | Covered by 1 topic (19 questions, 1 materials, 3 cards, 0 videos). |
| D. Understands the relationships between trigonometric functions and their inverses and uses these relationships to solve problems. | M.Laws of Sines and Cosines; M.Inverse Trigonometric Ratios | Covered | 19 | 2 | 2 | 0 | Covered by 2 topics (19 questions, 2 materials, 2 cards, 0 videos). |
| E. Uses trigonometric identities to simplify expressions and solve equations. | M.Advanced Trigonometric Identities - Special Triangles; M.Advanced Trigonometric Identities - Quotient and Reciprocal; M.Advanced Trigonometric Identities - Pythagorean Identities; M.Advanced Trigonometric Identities - More | Covered | 22 | 4 | 0 | 0 | Covered by 4 topics (22 questions, 4 materials, 0 cards, 0 videos). |
| F. Models and solves a variety of problems (e.g., analyzing periodic phenomena) using trigonometric functions. | M.Analyze and Solve Trigonometric Functions | Covered | 11 | 1 | 0 | 0 | Covered by 1 topic (11 questions, 1 materials, 0 cards, 0 videos). |
| G. Uses graphing calculators to analyze and solve problems involving trigonometric functions. | M.Trigonometric Ratio Graphs; M.Trigonometric Ratio Graphs - Real Word Problems; M.Technology and Trigonometric Function Problems | Covered | 28 | 3 | 3 | 0 | Covered by 3 topics (28 questions, 3 materials, 3 cards, 0 videos). |
SMR II.010 The teacher understands and solves problems using differential and integral calculus.
101 Qs13 Materials27 Cards0 VideosCovered
| Official Competency | Matching 240 Topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| A. Understands the concept of limit and the relationship between limits and continuity. | M.Calculus Connections to Formulas; M.Limits and Continuity; M.Limits and Continuity - Asymptote Equations; M.Limits That Do Not Exist | Covered | 41 | 4 | 6 | 0 | Covered by 4 topics (41 questions, 4 materials, 6 cards, 0 videos). |
| B. Relates the concept of average rate of change to the slope of the secant line and relates the concept of instantaneous rate of change to the slope of the tangent line. | M.Derivatives and Slopes; M.Rates of Change - Average vs Instantaneous | Covered | 26 | 2 | 10 | 0 | Covered by 2 topics (26 questions, 2 materials, 10 cards, 0 videos). |
| C. Uses the first and second derivatives to analyze the graph of a function (e.g., local extrema, concavity, points of inflection). | M.Derivatives and Slopes | Covered | 15 | 1 | 7 | 0 | Covered by 1 topic (15 questions, 1 materials, 7 cards, 0 videos). |
| D. Understands and applies the fundamental theorem of calculus and the relationship between differentiation and integration. | M.Foundational Theorems of Calculus | Covered | 8 | 1 | 5 | 0 | Covered by 1 topic (8 questions, 1 materials, 5 cards, 0 videos). |
| E. Models and solves a variety of problems (e.g., velocity, acceleration, optimization, related rates, work, center of mass) using differential and integral calculus. | M.Calculus Connections to Formulas; M.Derivatives and Slopes; M.Calculus - Rates; M.Calculus - Velocity and Acceleration; M.Integration; M.Calculus - Work; M.Calculus - Center of Mass | Covered | 47 | 7 | 18 | 0 | Covered by 7 topics (47 questions, 7 materials, 18 cards, 0 videos). |
| F. Analyzes how technology can be used to solve problems and illustrate concepts involving differential and integral calculus. | M.Derivatives and Slopes; M.Technology and Calculus Problems | Covered | 16 | 2 | 7 | 0 | Covered by 2 topics (16 questions, 2 materials, 7 cards, 0 videos). |
GEOMETRY AND MEASUREMENT (DOMAIN III)
Partially covered
SMR III.011 The teacher understands measurement as a process.
266 Qs16 Materials21 Cards7 VideosPartially covered
| Official Competency | Matching 240 Topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| A. Applies dimensional analysis to derive units and formulas in a variety of situations (e.g., rates of change of one variable with respect to another) and to find and evaluate solutions to problems. | M.Rearranging Formulas; M.Metric System; M.Converting Units - Dimensional Analysis | Covered | 57 | 3 | 5 | 2 | Covered by 3 topics (57 questions, 3 materials, 5 cards, 2 videos). |
| B. Applies formulas for perimeter, area, surface area and volume of geometric figures and shapes (e.g., polygons, pyramids, prisms, cylinders, cones, spheres) to solve problems. | M.Area and Perimeter of Polygons; M.Surface Area in 3D; M.Volume in 3D; M.Convert Between Surface Area and Volume | Covered | 108 | 4 | 7 | 2 | Covered by 4 topics (108 questions, 4 materials, 7 cards, 2 videos). |
| C. Recognizes the effects on length, area or volume when the linear dimensions of plane figures or solids are changed. | M.Dimensional Changes Affecting Area and Volume | Covered | 23 | 1 | 0 | 0 | Covered by 1 topic (23 questions, 1 materials, 0 cards, 0 videos). |
| D. Applies the Pythagorean theorem, proportional reasoning and right triangle trigonometry to solve measurement problems. | M.Pythagorean Theorem; M.Trigonometric Ratios; M.Proportional Reasoning - 2D Shapes; M.Attributes of Polygons - Similar vs Congruent | Covered | 50 | 4 | 5 | 3 | Covered by 4 topics (50 questions, 4 materials, 5 cards, 3 videos). |
| E. Relates the concept of area under a curve to the limit of a Riemann sum. | M.Riemann Sums | Partially covered | 6 | 1 | 1 | 0 | Partial coverage by 1 topic (6 questions, 1 materials, 1 cards, 0 videos); limited supporting content. |
| F. Uses integral calculus to compute various measurements associated with curves and regions (e.g., area, arc length) in the plane, and measurements associated with curves, surfaces and regions in three-space. | M.Areas by Integration; M.Volumes by Integration; M.Distance by Integration | Covered | 22 | 3 | 4 | 0 | Covered by 3 topics (22 questions, 3 materials, 4 cards, 0 videos). |
SMR III.012 The teacher understands geometries, in particular Euclidian geometry, as axiomatic systems.
145 Qs12 Materials38 Cards5 VideosPartially covered
| Official Competency | Matching 240 Topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| A. Understands axiomatic systems and their components (e.g., undefined terms, defined terms, theorems, examples, counterexamples). | M.Proofs | Covered | 8 | 1 | 3 | 0 | Covered by 1 topic (8 questions, 1 materials, 3 cards, 0 videos). |
| B. Uses properties of points, lines, planes, angles, lengths and distances to solve problems. | M.Coordinate Geometry; M.The Coordinate Plane; M.Solving with Points, Lines, Planes, Angles; M.Slope, Midpoint, and Distance; M.Points, Lines, Planes, Angles | Covered | 85 | 5 | 23 | 4 | Covered by 5 topics (85 questions, 5 materials, 23 cards, 4 videos). |
| C. Applies the properties of parallel and perpendicular lines to solve problems. | M.Parallel and Perpendicular Lines and Formulas | Covered | 19 | 1 | 3 | 1 | Covered by 1 topic (19 questions, 1 materials, 3 cards, 1 videos). |
| D. Uses properties of congruence and similarity to explore geometric relationships, justify conjectures and prove theorems. | M.Proofs | Covered | 8 | 1 | 3 | 0 | Covered by 1 topic (8 questions, 1 materials, 3 cards, 0 videos). |
| E. Describes and justifies geometric constructions made using compass and straightedge, reflection devices and other appropriate technologies. | M.Geometric Constructions; M.Advanced Geometric Constructions - Lines; M.Advanced Geometric Constructions - Shapes | Covered | 25 | 3 | 2 | 0 | Covered by 3 topics (25 questions, 3 materials, 2 cards, 0 videos). |
| F. Demonstrates an understanding of the use of appropriate software to explore attributes of geometric figures and to make and evaluate conjectures about geometric relationships. | None | Coverage gap identified | 0 | 0 | 0 | 0 | No matching topic found in the study guide. |
| G. Compares and contrasts the axioms of Euclidean geometry with those of non-Euclidean geometry (i.e., hyperbolic and elliptic geometry). | M.Euclidean Versus Non-Euclidean Geometry; M.Taxicab Measurements | Covered | 8 | 2 | 7 | 0 | Covered by 2 topics (8 questions, 2 materials, 7 cards, 0 videos). |
SMR III.013 The teacher understands the results, uses and applications of Euclidian geometry.
263 Qs19 Materials85 Cards6 VideosPartially covered
| Official Competency | Matching 240 Topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| A. Analyzes the properties of polygons and their components. | M.Angles in Triangles; M.Angles and Measurements in Polygons; M.Attributes of Polygons - Advanced | Covered | 41 | 3 | 35 | 1 | Covered by 3 topics (41 questions, 3 materials, 35 cards, 1 videos). |
| B. Analyzes the properties of circles and the lines that intersect them. | M.Measurements in Circles; M.Measurements in Circles Advanced | Covered | 40 | 2 | 12 | 1 | Covered by 2 topics (40 questions, 2 materials, 12 cards, 1 videos). |
| C. Uses geometric patterns and properties (e.g., similarity, congruence) to make generalizations about two- and three-dimensional figures and shapes (e.g., relationships of sides, angles). | M.Advanced Similar Shapes; M.Pyramids and Prisms; M.Apply Triangle Properties; M.Apply Triangle Inequalities; M.Measurements Inside Triangles; M.Proportional Reasoning - 3D Figures | Covered | 62 | 6 | 35 | 1 | Covered by 6 topics (62 questions, 6 materials, 35 cards, 1 videos). |
| D. Computes the perimeter, area and volume of figures and shapes created by subdividing and combining other figures and shapes (e.g., arc length, area of sectors). | M.Area and Perimeter of Polygons; M.Surface Area in 3D; M.Combine and Dissect 2D Figures | Covered | 74 | 3 | 6 | 1 | Covered by 3 topics (74 questions, 3 materials, 6 cards, 1 videos). |
| E. Analyzes cross-sections and nets of three-dimensional shapes. | M.Nets | Covered | 17 | 1 | 1 | 0 | Covered by 1 topic (17 questions, 1 materials, 1 cards, 0 videos). |
| F. Uses top, front, side and corner views of three-dimensional shapes to create complete representations and solve problems. | M.Attributes of Three Dimensional Figures; M.2D of 3D shape; M.Rotating 3D Objects | Covered | 27 | 3 | 8 | 1 | Covered by 3 topics (27 questions, 3 materials, 8 cards, 1 videos). |
| G. Applies properties of two- and three-dimensional shapes to solve problems across the curriculum and in everyday life. | M.Types of Prisms | Partially covered | 2 | 1 | 5 | 1 | Partial coverage by 1 topic (2 questions, 1 materials, 5 cards, 1 videos); limited supporting content. |
SMR III.014 The teacher understands coordinate, transformational and vector geometry and their connections.
97 Qs8 Materials17 Cards2 VideosPartially covered
| Official Competency | Matching 240 Topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| A. Identifies transformations (i.e., reflections, translations, glide-reflections, rotations, dilations) and explores their properties. | 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. Uses the properties of transformations and their compositions to solve problems. | M.Multiple Transformations | Covered | 18 | 1 | 2 | 0 | Covered by 1 topic (18 questions, 1 materials, 2 cards, 0 videos). |
| C. Uses transformations to explore and describe reflectional, rotational and translational symmetry. | M.Rigid Transformations | Covered | 16 | 1 | 4 | 0 | Covered by 1 topic (16 questions, 1 materials, 4 cards, 0 videos). |
| D. Applies transformations in the coordinate plane. | M.Rigid Transformations | Covered | 16 | 1 | 4 | 0 | Covered by 1 topic (16 questions, 1 materials, 4 cards, 0 videos). |
| E. Applies concepts and properties of slope, midpoint, parallelism, perpendicularity and distance to explore properties of geometric figures and solve problems in the coordinate plane. | M.Parallel and Perpendicular Lines and Formulas; M.Slope, Midpoint, and Distance | Covered | 35 | 2 | 3 | 2 | Covered by 2 topics (35 questions, 2 materials, 3 cards, 2 videos). |
| F. Uses coordinate geometry to derive and explore the equations, properties and applications of conic sections (i.e., lines, circles, hyperbolas, ellipses, parabolas). | M.Derivation of Geometric Equations; M.Conic Sections | Covered | 14 | 2 | 4 | 0 | Covered by 2 topics (14 questions, 2 materials, 4 cards, 0 videos). |
| G. Relates geometry and algebra by representing transformations as matrices and uses this relationship to solve problems. | M.Solving with Matrix Transformations | Covered | 8 | 1 | 0 | 0 | Covered by 1 topic (8 questions, 1 materials, 0 cards, 0 videos). |
| H. Explores the relationship between geometric and algebraic representations of vectors and uses this relationship to solve problems. | None | Coverage gap identified | 0 | 0 | 0 | 0 | No matching topic found in the study guide. |
PROBABILITY AND STATISTICS (DOMAIN IV)
Partially covered
SMR IV.015 The teacher understands how to use appropriate graphical and numerical techniques to explore data, characterize patterns and describe departures from patterns.
202 Qs11 Materials41 Cards3 VideosPartially covered
| Official Competency | Matching 240 Topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| A. Selects and uses an appropriate measurement scale (i.e., nominal, ordinal, interval, ratio) to answer research questions and analyze data. | M.Selecting Measurement Scales | Partially covered | 2 | 1 | 4 | 0 | Partial coverage by 1 topic (2 questions, 1 materials, 4 cards, 0 videos); limited supporting content. |
| B. Organizes, displays and interprets data in a variety of formats (e.g., tables, frequency distributions, scatter plots, stem-and-leaf plots, box-and-whisker plots, histograms, pie charts). | M.Graphs and Plots; M.Boxplots; M.Data Analysis and Interpretation | Covered | 71 | 3 | 17 | 2 | Covered by 3 topics (71 questions, 3 materials, 17 cards, 2 videos). |
| C. Applies concepts of center, spread, shape and skewness to describe a data distribution. | M.Describing Data Patterns and Outliers | Covered | 5 | 1 | 11 | 0 | Covered by 1 topic (5 questions, 1 materials, 11 cards, 0 videos). |
| D. Understands measures of central tendency (i.e., mean, median, mode) and dispersion (i.e., range, interquartile range, variance, standard deviation). | M.Measures of Center and Range; M.Advanced Measures of Center and Range | Covered | 75 | 2 | 12 | 1 | Covered by 2 topics (75 questions, 2 materials, 12 cards, 1 videos). |
| E. Applies linear transformations (i.e., translating, stretching, shrinking) to convert data and describes the effect of linear transformations on measures of central tendency and dispersion. | M.Linear Data Transformations; M.Effect of Change in Data on Measures of Center and Range | Covered | 18 | 2 | 4 | 0 | Covered by 2 topics (18 questions, 2 materials, 4 cards, 0 videos). |
| F. Analyzes connections among concepts of center and spread, data clusters and gaps, data outliers and measures of central tendency and dispersion. | 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). |
| G. Supports arguments, makes predictions and draws conclusions using summary statistics and graphs to analyze and interpret one-variable data. | M.Level of Confidence | Covered | 15 | 1 | 4 | 0 | Covered by 1 topic (15 questions, 1 materials, 4 cards, 0 videos). |
SMR IV.016 The teacher understands concepts and applications of probability.
139 Qs16 Materials35 Cards4 VideosPartially covered
| Official Competency | Matching 240 Topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| A. Understands how to explore concepts of probability through sampling, experiments and simulations and generates and uses probability models to represent situations. | M.Probability Models; M.Probability Simulations; M.Sampling Methods; M.Probability Distributions - From Simulation | Covered | 30 | 4 | 9 | 0 | Covered by 4 topics (30 questions, 4 materials, 9 cards, 0 videos). |
| B. Uses the concepts and principles of probability to describe the outcomes of simple and compound events. | M.Expressing Probabilities; M.Simple and Compound Events | Covered | 14 | 2 | 4 | 1 | Covered by 2 topics (14 questions, 2 materials, 4 cards, 1 videos). |
| C. Determines probabilities by constructing sample spaces to model situations. | M.Diagrams; M.Sample Spaces to Determine Probabilities; M.Fundamental Counting Principle | Covered | 30 | 3 | 4 | 2 | Covered by 3 topics (30 questions, 3 materials, 4 cards, 2 videos). |
| D. Solves a variety of probability problems using combinations and permutations. | M.Combinations and Permutations | Covered | 20 | 1 | 2 | 0 | Covered by 1 topic (20 questions, 1 materials, 2 cards, 0 videos). |
| E. Solves a variety of probability problems using ratios of areas of geometric regions. | M.Geometric Probability | Partially covered | 3 | 1 | 1 | 1 | Partial coverage by 1 topic (3 questions, 1 materials, 1 cards, 1 videos); limited supporting content. |
| F. Calculates probabilities using the axioms of probability and related theorems and concepts such as the addition rule, multiplication rule, conditional probability and independence. | M.Tables to Determine Independence | Covered | 8 | 1 | 2 | 0 | Covered by 1 topic (8 questions, 1 materials, 2 cards, 0 videos). |
| G. Understands expected value, variance and standard deviation of probability distributions (e.g., binomial, geometric, uniform, normal). | M.Probability Distributions; M.Comparing to Probability Distribution | Covered | 16 | 2 | 10 | 0 | Covered by 2 topics (16 questions, 2 materials, 10 cards, 0 videos). |
| H. Applies concepts and properties of discrete and continuous random variables to model and solve a variety of problems involving probability and probability distributions (e.g., binomial, geometric, uniform, normal). | M.Using Distributions; M.Uniform Distributions | Covered | 18 | 2 | 8 | 0 | Covered by 2 topics (18 questions, 2 materials, 8 cards, 0 videos). |
SMR IV.017 The teacher understands the relationships among probability theory, sampling and statistical inference and how statistical inference is used in making and evaluating predictions.
133 Qs13 Materials54 Cards1 VideosPartially covered
| Official Competency | Matching 240 Topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| A. Applies knowledge of designing, conducting, analyzing and interpreting statistical experiments to investigate real-world problems. | M.Statistical Questions; M.Statistical Experiments | Covered | 22 | 2 | 2 | 0 | Covered by 2 topics (22 questions, 2 materials, 2 cards, 0 videos). |
| B. Analyzes and interprets statistical information (e.g., the results of polls and surveys) and recognizes misleading as well as valid uses of statistics. | M.Surveys | Covered | 10 | 1 | 3 | 0 | Covered by 1 topic (10 questions, 1 materials, 3 cards, 0 videos). |
| C. Understands random samples and sample statistics (e.g., the relationship between sample size and confidence intervals, biased or unbiased estimators). | M.Observations, Conclusions, and Relationships; M.Level of Confidence | Covered | 26 | 2 | 13 | 0 | Covered by 2 topics (26 questions, 2 materials, 13 cards, 0 videos). |
| D. Makes inferences about a population using binomial, normal and geometric distributions. | M.Using Distributions | Covered | 13 | 1 | 4 | 0 | Covered by 1 topic (13 questions, 1 materials, 4 cards, 0 videos). |
| E. Describes and analyzes bivariate data using various techniques (e.g., scatterplots, regression lines, outliers, residual analysis, correlation coefficients). | M.Bivariate Data Analysis; M.Advanced Bivariate Data Analysis; M.Calculating Linear Regression | Covered | 35 | 3 | 15 | 1 | Covered by 3 topics (35 questions, 3 materials, 15 cards, 1 videos). |
| F. Understands how to transform nonlinear data into linear form to apply linear regression techniques to develop exponential, logarithmic and power regression models | M.Linear Regression with Non-Linear Data | Partially covered | 3 | 1 | 4 | 0 | Partial coverage by 1 topic (3 questions, 1 materials, 4 cards, 0 videos); limited supporting content. |
| G. Uses the law of large numbers and the central limit theorem in the process of statistical inference. | M.Central Limit Theorem and Large Numbers | Partially covered | 2 | 1 | 2 | 0 | Partial coverage by 1 topic (2 questions, 1 materials, 2 cards, 0 videos); limited supporting content. |
| H. Estimates parameters (e.g., population mean and variance) using point estimators (e.g., sample mean and variance). | M.Advanced Measures of Center and Range | Covered | 19 | 1 | 9 | 0 | Covered by 1 topic (19 questions, 1 materials, 9 cards, 0 videos). |
| I. Understands principles of hypotheses testing. | M.Hypothesis Testing | Partially covered | 3 | 1 | 5 | 0 | Partial coverage by 1 topic (3 questions, 1 materials, 5 cards, 0 videos); limited supporting content. |
MATHEMATICAL PROCESSES AND PERSPECTIVES (DOMAIN V)
Partially covered
SMR V.018 The teacher understands mathematical reasoning and problem solving.
137 Qs16 Materials16 Cards1 VideosCovered
| Official Competency | Matching 240 Topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| A. Understands the nature of proof, including indirect proof, in mathematics. | M.Indirect Proofs; M.Proofs | Covered | 17 | 2 | 4 | 0 | Covered by 2 topics (17 questions, 2 materials, 4 cards, 0 videos). |
| B. Applies correct mathematical reasoning to derive valid conclusions from a set of premises. | M.Conclusions from Premises; M.Formal Conclusions from Premises | Covered | 16 | 2 | 0 | 0 | Covered by 2 topics (16 questions, 2 materials, 0 cards, 0 videos). |
| C. Uses inductive reasoning to make conjectures and uses deductive methods to evaluate the validity of conjectures. | M.Inductive vs Deductive Reasoning; M.Advanced Abstract and Quantitative Reasoning; M.Evaluating Truth of Statements | Covered | 20 | 3 | 8 | 0 | Covered by 3 topics (20 questions, 3 materials, 8 cards, 0 videos). |
| D. Uses formal and informal reasoning to justify mathematical ideas. | M.Formal vs Informal Reasoning; M.Formal Reasoning Rules | Covered | 6 | 2 | 3 | 1 | Covered by 2 topics (6 questions, 2 materials, 3 cards, 1 videos). |
| E. Understands the problem-solving process (i.e., recognizing that a mathematical problem can be solved in a variety of ways, selecting an appropriate strategy, evaluating the reasonableness of a solution). | M.Selecting Appropriate Solution Strategies; M.Selecting Appropriate Solution Strategies - Look for a Pattern; M.Prioritizing Relevant and Missing Information; M.Using Structure to Analyze Complex Problems; M.Reasonableness of Results | Covered | 50 | 5 | 1 | 0 | Covered by 5 topics (50 questions, 5 materials, 1 cards, 0 videos). |
| F. Evaluates how well a mathematical model represents a real-world situation. | M.Modeling and Evaluating Real-World Situations; M.Spatial Reasoning | Covered | 28 | 2 | 1 | 0 | Covered by 2 topics (28 questions, 2 materials, 1 cards, 0 videos). |
SMR V.019 The teacher understands mathematical connections both within and outside of mathematics and how to communicate mathematical ideas and concepts.
54 Qs7 Materials32 Cards2 VideosPartially covered
| Official Competency | Matching 240 Topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| A. Recognizes and uses multiple representations of a mathematical concept (e.g., a point and its coordinates, the area of a circle as a quadratic function of the radius, probability as the ratio of two areas, area of a plane region as a definite integral). | M.Multiple Interpretations of Math Concepts; M.Variety of Representations for Older Children | Covered | 5 | 1 | 9 | 0 | Covered by 2 topics (5 questions, 1 materials, 9 cards, 0 videos). |
| B. Understands how mathematics is used to model and solve problems in other disciplines (e.g., art, music, science, social science, business). | M.Interdisciplinary Connections; M.Financial Literacy | Covered | 14 | 2 | 9 | 0 | Covered by 2 topics (14 questions, 2 materials, 9 cards, 0 videos). |
| C. Translates mathematical ideas between verbal and symbolic forms. | M.Symbolic to Verbal | Covered | 10 | 1 | 5 | 1 | Covered by 1 topic (10 questions, 1 materials, 5 cards, 1 videos). |
| D. Communicates mathematical ideas using a variety of representations (e.g., numeric, verbal, graphical, pictorial, symbolic, concrete). | 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. |
| E. Understands the use of visual media, such as graphs, tables, diagrams and animations, to communicate mathematical information. | M.Choosing a Graph or Plot | Covered | 15 | 1 | 9 | 1 | Covered by 1 topic (15 questions, 1 materials, 9 cards, 1 videos). |
| F. Uses appropriate mathematical terminology to express mathematical ideas. | M.Assessment Terminology | Partially covered | 5 | 1 | 0 | 0 | Partial coverage by 1 topic (5 questions, 1 materials, 0 cards, 0 videos); limited supporting content. |
MATHEMATICAL LEARNING, INSTRUCTION AND ASSESSMENT (DOMAIN VI)
Partially covered
SMR VI.020 The teacher understands how children learn mathematics and plans, organizes and implements instruction using knowledge of students, subject matter and statewide curriculum (Texas Essential Knowledge and Skills [TEKS]).
101 Qs13 Materials28 Cards4 VideosPartially covered
| Official Competency | Matching 240 Topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| A. Applies research-based theories of learning mathematics to plan appropriate instructional activities for all students. | M.Major Math Instructional Theories | Covered | 5 | 1 | 5 | 1 | Covered by 1 topic (5 questions, 1 materials, 5 cards, 1 videos). |
| B. Understands how students differ in their approaches to learning mathematics. | M.Planning for Group Experiences; M.Multimodal Teaching - Math | Covered | 17 | 2 | 8 | 1 | Covered by 2 topics (17 questions, 2 materials, 8 cards, 1 videos). |
| C. Uses students’ prior mathematical knowledge to build conceptual links to new knowledge and plans instruction that builds on students’ strengths and addresses students’ needs. | M.Authentic Assessment | Partially covered | 6 | 1 | 1 | 0 | Partial coverage by 1 topic (6 questions, 1 materials, 1 cards, 0 videos); limited supporting content. |
| D. Understands how learning may be enhanced through the use of manipulatives, technology and other tools (e.g., stop watches, rulers). | M.Using Calculators to Check Math; M.Manipulatives for Older Children | Covered | 8 | 2 | 4 | 0 | Covered by 2 topics (8 questions, 2 materials, 4 cards, 0 videos). |
| E. Understands how to provide instruction along a continuum from concrete to abstract. | M.Learning Progressions in Math; M.Learning Progressions in Geometry | Covered | 26 | 2 | 8 | 1 | Covered by 2 topics (26 questions, 2 materials, 8 cards, 1 videos). |
| F. Understands a variety of instructional strategies and tasks that promote students’ abilities to do the mathematics described in the TEKS. | M.Planning from TEKS | Partially covered | 6 | 1 | 1 | 0 | Partial coverage by 1 topic (6 questions, 1 materials, 1 cards, 0 videos); limited supporting content. |
| G. Understands how to create a learning environment that provides all students, including English-language learners, with opportunities to develop and improve mathematical skills and procedures. | M.Diversity and Engagement - ELL | Covered | 8 | 1 | 1 | 1 | Covered by 1 topic (8 questions, 1 materials, 1 cards, 1 videos). |
| H. Understands a variety of questioning strategies to encourage mathematical discourse and to help students analyze and evaluate their mathematical thinking. | M.Teaching Mathematical Reasoning for Older Children | Partially covered | 4 | 1 | 0 | 0 | Partial coverage by 1 topic (4 questions, 1 materials, 0 cards, 0 videos); limited supporting content. |
| I. Understands how to relate mathematics to students’ lives and to a variety of careers and professions. | M.Real-World Applications; M.Careers | Covered | 21 | 2 | 0 | 0 | Covered by 2 topics (21 questions, 2 materials, 0 cards, 0 videos). |
SMR VI.021 The teacher understands assessment and uses a variety of formal and informal assessment techniques to monitor and guide mathematics instruction and to evaluate student progress.
87 Qs5 Materials19 Cards4 VideosCovered
| Official Competency | Matching 240 Topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| A. Understands the purpose, characteristics and uses of various assessments in mathematics, including formative and summative assessments. | M.Types of Assessment - Math | Covered | 20 | 1 | 13 | 1 | Covered by 1 topic (20 questions, 1 materials, 13 cards, 1 videos). |
| B. Understands how to select and develop assessments that are consistent with what is taught and how it is taught. | M.Using Assessment to Adjust Instruction | Covered | 15 | 1 | 3 | 1 | Covered by 1 topic (15 questions, 1 materials, 3 cards, 1 videos). |
| C. Understands how to develop a variety of assessments and scoring procedures consisting of worthwhile tasks that assess mathematical understanding, common misconceptions and error patterns. | M.Use Variety in Problem Structure; M.Evaluate Student Solutions; M.Fair Assessment | Covered | 52 | 3 | 6 | 2 | Covered by 3 topics (52 questions, 3 materials, 6 cards, 2 videos). |
| D. Understands the relationship between assessment and instruction and knows how to evaluate assessment results to design, monitor and modify instruction to improve mathematical learning for all students, including English-language learners. | M.Types of Assessment - Math; M.Using Assessment to Adjust Instruction | Covered | 35 | 2 | 13 | 2 | Covered by 2 topics (35 questions, 2 materials, 13 cards, 2 videos). |
How 240 Creates The TExES Math 7-12 (235) Study Guide
Learn more →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.
1
Review the official exam framework
We begin with the standards, domains, competencies, objectives, or content categories published by the testing authority.
2
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.
3
Build lessons around tested content
We create study materials to support the official blueprint, not broad filler content.
4
Cross-check practice against exam expectations
We review practice content against the framework and real exam patterns so preparation stays targeted.
5
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.
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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 TExES Math 7-12.
Generic
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
Test-aligned
240 Test-Aligned TExES 235 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 TExES Math 7-12 Study Guide
The questions teacher candidates ask us most often about the TExES Math 7-12 study guide.
1
Is 240 a good study guide for TExES Math 7-12?
240 is a strong option because the guide is built around the official exam framework and shows detailed alignment by SMR and competency.
2
How closely does 240 align to the TExES 235 exam?
This guide is 91% aligned based on a competency-by-competency review of the official framework and the study resources included in the guide.
3
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.
4
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.
Study What's Actually on the TExES 235 Exam
Start with a study guide built around the real exam. 240's guide maps lessons and study tools to official competencies so you can prepare more efficiently and more confidently.