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 GACE Middle Grades Math (4–8) 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 GACE Middle Grades Math (4–8) (704) 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 GACE 704 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
3Domains
46Competencies reviewed
97%Test-aligned
43Covered
3Partially covered
0Gaps
- CoveredCompetency is comprehensively supported by the guide.
- Partially coveredCore content is covered, but some depth gaps remain.
- Coverage gap identifiedA content gap has been identified.
This study guide is based on the current official exam framework. We review and update alignment whenever the official framework changes so candidates are always studying current, accurate material.
Number Sense, Number Operations, Statistics, and Probability (4–8) (Domain 101)Partially covered
SMR 101.0001 · Understand numbers and operations.392 questions · 20 materials · 56 cards · 11 videosCovered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| a. Analyze the relationships between the subsets of the real numbers. | M.Characteristics of Rational Numbers | Covered | 8 | 1 | 8 | 0 | Covered by 1 topic (8 questions, 1 materials, 8 cards, 0 videos). |
| b. Analyze the role of place value in mathematical reasoning. | M.Place Value | Covered | 33 | 1 | 2 | 1 | Covered by 1 topic (33 questions, 1 materials, 2 cards, 1 videos). |
| c. Analyze the use of estimation in a variety of situations. | M.Mental Math and Estimation | Covered | 24 | 1 | 7 | 0 | Covered by 1 topic (24 questions, 1 materials, 7 cards, 0 videos). |
| d. Translate between different representations of numbers. | M.Order Real Numbers by Magnitude; M.Exponential and Scientific Notation; M.Square Roots and Radicals | Covered | 49 | 3 | 8 | 2 | Covered by 3 topics (49 questions, 3 materials, 8 cards, 2 videos). |
| e. Apply number-theory concepts (e.g., divisibility, prime factorization, greatest common factors) in problem-solving situations. | M.Prime and Composite Numbers; M.Factors; M.Prime Factorization; M.Justify and Prove Number Relationships; M.Divisibility Rules | Covered | 90 | 5 | 10 | 3 | Covered by 5 topics (90 questions, 5 materials, 10 cards, 3 videos). |
| f. Analyze relational and operational properties, including order of operations. | M.Operational Properties; M.Order of Operations | Covered | 69 | 2 | 4 | 2 | Covered by 2 topics (69 questions, 2 materials, 4 cards, 2 videos). |
| g. Apply a variety of conventional and alternative algorithms. | M.Operational Algorithm Relationships | Covered | 5 | 1 | 13 | 0 | Covered by 1 topic (5 questions, 1 materials, 13 cards, 0 videos). |
| h. Solve a variety of mathematical and real-world problems involving integers, fractions, and decimals. | M.Integers in Word Problems; M.Representations of Fractions in Word Problems | Covered | 23 | 2 | 4 | 1 | Covered by 2 topics (23 questions, 2 materials, 4 cards, 1 videos). |
| i. Solve a variety of mathematical and real-world problems involving rates, ratios, proportions, and percents. | M.Unit Rates; M.Proportions; M.Ratios and Percents; M.Proportional Reasoning - Word Problems | Covered | 91 | 4 | 4 | 2 | Covered by 4 topics (91 questions, 4 materials, 4 cards, 2 videos). |
SMR 101.0002 · Understand principles and techniques of statistics and probability.244 questions · 11 materials · 49 cards · 6 videosPartially covered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| a. Classify questions as statistical or nonstatistical and categorical or numerical. | M.Statistical Questions | Covered | 11 | 1 | 1 | 0 | Covered by 1 topic (11 questions, 1 materials, 1 cards, 0 videos). |
| b. Analyze the effects of bias and sampling techniques. | M.Sampling Methods | Covered | 12 | 1 | 5 | 0 | Covered by 1 topic (12 questions, 1 materials, 5 cards, 0 videos). |
| c. Use appropriate formats for organizing and displaying quantitative and qualitative data. | M.Graphs and Plots | Covered | 32 | 1 | 9 | 1 | Covered by 1 topic (32 questions, 1 materials, 9 cards, 1 videos). |
| d. Analyze univariate and bivariate data in a variety of representations. | M.Data Analysis - Frequency; M.Bivariate Data Analysis | Covered | 25 | 2 | 17 | 1 | Covered by 2 topics (25 questions, 2 materials, 17 cards, 1 videos). |
| e. Make inferences and predictions from data and sampling presented in a variety of contexts. | M.Data Analysis and Interpretation | Covered | 28 | 1 | 2 | 1 | Covered by 1 topic (28 questions, 1 materials, 2 cards, 1 videos). |
| f. Analyze the use of measures of central tendency and spread. | M.Measures of Center and Range | Covered | 56 | 1 | 4 | 1 | Covered by 1 topic (56 questions, 1 materials, 4 cards, 1 videos). |
| g. Determine probabilities of simple events. | M.Probability | Covered | 47 | 1 | 8 | 1 | Covered by 1 topic (47 questions, 1 materials, 8 cards, 1 videos). |
| h. Use the fundamental counting principle to calculate probabilities. | M.Fundamental Counting Principle | Covered | 10 | 1 | 1 | 1 | Covered by 1 topic (10 questions, 1 materials, 1 cards, 1 videos). |
| i. Use a variety of visual representations to calculate probabilities. | M.Diagrams | Covered | 16 | 1 | 2 | 0 | Covered by 1 topic (16 questions, 1 materials, 2 cards, 0 videos). |
| j. Demonstrate knowledge of methods for simulating probabilities. | M.Probability Simulations | Partially covered | 7 | 1 | 3 | 0 | Partial coverage by 1 topic (7 questions, 1 materials, 3 cards, 0 videos); limited supporting content. |
Algebra and Functions (4–8) (Domain 102)Partially covered
SMR 102.0001 · Understand patterns, relations, and functions.144 questions · 9 materials · 23 cards · 2 videosPartially covered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| a. Analyze a variety of patterns, including proportional patterns. | M.Simple Shape Patterns; M.Types of Sequences; M.Patterns - Developing an Expression; M.Patterns - Developing a Linear Formula | Covered | 63 | 4 | 9 | 2 | Covered by 4 topics (63 questions, 4 materials, 9 cards, 2 videos). |
| b. Analyze the properties of relations and functions in and across multiple representations (e.g., tables, graphs, equations, words). | M.Relation and Function Representations; M.Understanding Linear Functions and Their Properties | Covered | 54 | 2 | 7 | 0 | Covered by 2 topics (54 questions, 2 materials, 7 cards, 0 videos). |
| c. Analyze direct and inverse proportional relationships. | M.Directly and Inversely Proportional Relationships - Basic | Partially covered | 6 | 1 | 3 | 0 | Partial coverage by 1 topic (6 questions, 1 materials, 3 cards, 0 videos); limited supporting content. |
| d. Determine the effects of transformations on the graph of a function or relation | M.Parent Functions; M.Functional Transformations - Linear and Quadratic | Covered | 21 | 2 | 6 | 0 | Covered by 2 topics (21 questions, 2 materials, 6 cards, 0 videos). |
SMR 102.0002 · Understand algebraic techniques and applications.100 questions · 10 materials · 30 cards · 6 videosCovered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| a. Manipulate algebraic expressions, equations, and inequalities (e.g., simplify, transform, factor). | M.Equivalence of Expressions - To Simplify; M.Equivalence of Expressions - To Expand; M.Linear Expression Evaluation; M.Linear Expression Addition and Subtraction; M.Basic Polynomials; M.Operations with Polynomials; M.Properties of Inequality; M.Properties of Equality | Covered | 78 | 8 | 22 | 4 | Covered by 8 topics (78 questions, 8 materials, 22 cards, 4 videos). |
| b. Represent solutions to linear and nonlinear equations and inequalities. | M.Interpreting Inequalities | Covered | 12 | 1 | 4 | 1 | Covered by 1 topic (12 questions, 1 materials, 4 cards, 1 videos). |
| c. Connect appropriate algebraic notation to phrases and sentences. | M.Symbolic to Verbal | Covered | 10 | 1 | 5 | 1 | Covered by 1 topic (10 questions, 1 materials, 5 cards, 1 videos). |
SMR 102.0003 · Understand linear relations and applications.162 questions · 18 materials · 14 cards · 3 videosPartially covered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| a. Analyze the relationship between a linear equation or inequality and its representations. | M.Understanding Linear Equations and Their Properties | Covered | 25 | 1 | 2 | 0 | Covered by 1 topic (25 questions, 1 materials, 2 cards, 0 videos). |
| b. Solve systems of linear inequalities or equations with a variety of methods. | M.Solving One-Variable Equations; M.Solving Linear Inequalities; M.Solving Compound Linear Inequalities | Covered | 33 | 3 | 1 | 0 | Covered by 3 topics (33 questions, 3 materials, 1 cards, 0 videos). |
| c. Interpret the meaning of the slope and the y-intercept in various contexts. | M.Understanding Linear Equations and Their Properties; M.Interpreting Slopes and Intercepts of Linear Equations | Covered | 38 | 2 | 2 | 0 | Covered by 2 topics (38 questions, 2 materials, 2 cards, 0 videos). |
| d. Solve a variety of real-world problems by modeling them with linear equations, systems, and inequalities. | M.Solving Systems of Linear Equations; M.Solving Systems of Linear Equations - Scalar Note; M.Solving Systems of Linear Equations - Word Problems; M.Solving Systems of Linear Inequalities; M.Linear Inequality Word Problems; M.Linear Equation Word Problems; M.Solving Systems of Linear Inequalities - Word Problems | Covered | 56 | 6 | 5 | 2 | Covered by 7 topics (56 questions, 6 materials, 5 cards, 2 videos). |
| e. Analyze relationships between multiple representations of a nonlinear equation or inequality. | M.Quadratic Equations; M.Quadratic Equation - Solve via Graphing; M.Quadratic Equation - Solve via Factoring; M.Quadratic Equations - Forms; M.Solve Quadratic Inequalities - Algebraically; M.Solve Quadratic Inequalities - Graphically | Covered | 32 | 6 | 6 | 1 | Covered by 6 topics (32 questions, 6 materials, 6 cards, 1 videos). |
| f. Solve a variety of real-world problems by modeling them with nonlinear equations and inequalities. | M.Advanced Quadratic Equation - Real World Problems | Partially covered | 3 | 1 | 0 | 0 | Partial coverage by 1 topic (3 questions, 1 materials, 0 cards, 0 videos); limited supporting content. |
Measurement and Geometry (4–8) (Domain 103)Covered
SMR 103.0001 · Understand measurement principles, procedures, and applications.234 questions · 12 materials · 35 cards · 8 videosCovered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| a. Analyze the use of various units and unit conversions within the customary and metric systems. | M.Metric System; M.Converting Units - Proportional Reasoning; M.Converting Units - Dimensional Analysis; M.Measurement Tools | Covered | 86 | 4 | 14 | 4 | Covered by 4 topics (86 questions, 4 materials, 14 cards, 4 videos). |
| b. Calculate or estimate measures of lengths, areas, and volumes. | M.Area and Perimeter of Polygons; M.Volume in 3D; M.Surface Area in 3D | Covered | 99 | 3 | 7 | 2 | Covered by 3 topics (99 questions, 3 materials, 7 cards, 2 videos). |
| c. Apply the concepts of similarity, scale factors, and proportional reasoning to solve indirect measurement problems. | M.Attributes of Polygons - Symmetry; M.Proportional Reasoning - Scale Drawings; M.Proportional Reasoning - 2D Shapes; M.Proportional Reasoning - 3D Figures | Covered | 38 | 4 | 5 | 2 | Covered by 4 topics (38 questions, 4 materials, 5 cards, 2 videos). |
| d. Analyze precision, accuracy, and rounding in measurements and computed quantities. | M.Measurement Principles | Covered | 11 | 1 | 9 | 0 | Covered by 1 topic (11 questions, 1 materials, 9 cards, 0 videos). |
SMR 103.0002 · Understand Euclidean geometry in two and three dimensions.148 questions · 10 materials · 48 cards · 5 videosCovered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| a. Analyze properties and relationships of points, lines, segments, planes, edges, vertices, and angles. | 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). |
| b. Analyze the properties of triangles, quadrilaterals, and other polygons and circles, including by solving problems. | M.Angles in Triangles; M.Measurements in Circles | Covered | 30 | 2 | 3 | 2 | Covered by 2 topics (30 questions, 2 materials, 3 cards, 2 videos). |
| c. Apply principles of similarity and congruence. | M.Attributes of Polygons - Similar vs Congruent | Covered | 10 | 1 | 2 | 0 | Covered by 1 topic (10 questions, 1 materials, 2 cards, 0 videos). |
| d. Apply the Pythagorean theorem and its converse. | M.Pythagorean Theorem; M.Apply Triangle Properties; M.Measurements Inside Triangles | Covered | 43 | 3 | 21 | 1 | Covered by 3 topics (43 questions, 3 materials, 21 cards, 1 videos). |
| e. Use nets and cross sections to analyze three-dimensional figures. | M.Nets | Covered | 17 | 1 | 1 | 0 | Covered by 1 topic (17 questions, 1 materials, 1 cards, 0 videos). |
| f. Analyze geometric arguments using deductive reasoning. | M.Proofs | Covered | 8 | 1 | 3 | 0 | Covered by 1 topic (8 questions, 1 materials, 3 cards, 0 videos). |
SMR 103.0003 · Understand coordinate and transformational geometry.97 questions · 8 materials · 23 cards · 2 videosCovered
| Official competency | Matching 240 topics | Alignment | Qs | Mats | Cards | Vids | Notes |
|---|---|---|---|---|---|---|---|
| a. Analyze two- and three-dimensional figures using coordinate systems. | M.The Coordinate Plane; M.Coordinate Geometry; M.3D Coordinate Geometry | Covered | 35 | 3 | 11 | 1 | Covered by 3 topics (35 questions, 3 materials, 11 cards, 1 videos). |
| b. Connect algebra and geometry by applying concepts of distance, midpoint, and slope to classify figures and solve problems 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). |
| c. Analyze transformations of figures in the coordinate plane. | M.Rigid Transformations; M.Non-Rigid Transformations; M.Multiple Transformations | Covered | 40 | 3 | 10 | 0 | Covered by 3 topics (40 questions, 3 materials, 10 cards, 0 videos). |
| d. Analyze figures in terms of symmetry. | M.Congruence and Similarity with Transformations | Covered | 6 | 1 | 8 | 0 | Covered by 1 topic (6 questions, 1 materials, 8 cards, 0 videos). |
How 240 Creates The GACE Middle Grades Math (4–8) (704) 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 GACE Middle Grades Math (4–8).
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 GACE 704 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 GACE Middle Grades Math (4–8) Study Guide
The questions teacher candidates ask us most often about the GACE Middle Grades Math (4–8) study guide.
Is 240 a good study guide for GACE Middle Grades Math (4–8)?
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 GACE 704 exam?
This guide is 97% 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.