5164 · Syllabus & Exam Outline 2026
Praxis (5164): Middle School Mathematics
In short
The Praxis (5164) Middle School Mathematics exam has 66 selected-response and numeric-entry questions in 180 minutes, with passing scores that vary by state (commonly 157). It covers numbers and operations, algebra, functions, geometry and measurement, and statistics and probability. Free practice questions and a full study plan are below.
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- Questions
- 66 selected-response and numeric-entry questions
- Time limit
- 180 minutes
- Passing score
- Varies by state (commonly 157)
- Cost
- $130
- Format
- Selected-response (one answer choice) · Selected-response (one or more answer choices) · Selected-response (select an area) · Numeric-entry · Drag-and-drop · Table grid · Text completion
- Delivery
- Computer-delivered (at a test center or at home)
- Calculator
- An on-screen graphing calculator is provided.
- Prep time
- ~86 hours
Exam overview
The Praxis (5164) Middle School Mathematics exam evaluates the academic knowledge and competencies necessary for a beginning middle school math teacher. Developed alongside practicing educators and aligned with national mathematics standards, this comprehensive test spans critical subjects like algebra, geometry, probability, and foundational number theory. Unique to this exam, roughly 30% of the questions assess your ability to apply mathematical concepts to real-world teaching scenarios, evaluating how you identify student misconceptions, choose appropriate instructional models, and justify mathematical procedures. Preparing for the 66-question, 180-minute exam requires a strategic approach to a broad curriculum. The test is completely computer-delivered and features an on-screen graphing calculator. While a standard formula sheet is provided, candidates are expected to perform basic arithmetic operations smoothly and recall unlisted foundational unit conversions. To streamline your preparation, Only Ever maps every domain to focused, 15-minute study topics, helping you methodically tackle everything from complex algebraic inequalities to spatial geometry and statistical analysis.
Exam domains & weighting
Each domain's share of the exam — study deepest where the weight is highest. Open one for how to study it and its objectives.
How to study this domain
Focus heavily on ratio, proportion, and rate problem-solving, as these are foundational middle school concepts. Ensure you are comfortable shifting rapidly among fractions, decimals, and percents without relying entirely on a calculator. Be prepared to identify and apply fundamental properties like the distributive or commutative properties in mathematical justifications.
Key objectives
- Properties of Real Numbers
- Real Number Operations and Order of Operations
- Exponents, Radicals, and Scientific Notation
- Fractions, Decimals, and Percents
- Ratios and Rates
- Proportional Relationships and Percents
- Quantitative Reasoning and Dimensional Analysis
- Number Theory Concepts
Readiness self-check
Tick off everything you can confidently explain. Anything left unchecked is your study list — tap “Review” to jump straight into that domain.
Quick reference
On-Screen Provided Formulas (Area & Perimeter)
These formulas are explicitly provided on the testing interface reference sheet.
Rectangle Area
A = lw
Parallelogram Area
A = bh
Triangle Area
A = 1/2 bh
Trapezoid Area
A = 1/2(b_1 + b_2)h
Circle Area
A = πr²
Rectangle Perimeter
P = 2l + 2w
Circle Circumference
C = 2πr
On-Screen Provided Formulas (Volume & Surface Area)
3D geometric formulas available on the testing screen.
Right Rectangular Prism Volume
V = lwh
Right Prism Volume
V = Bh
B = area of base
Pyramid Volume
V = 1/3 Bh
Right Circular Cylinder Volume
V = πr²h
Right Circular Cone Volume
V = 1/3 πr²h
Sphere Volume
V = 4/3 πr³
Cube Surface Area
A = 6s²
Right Rectangular Prism Surface Area
A = 2lw + 2lh + 2wh
Right Circular Cylinder Surface Area
A = 2πrh + 2πr²
Sphere Surface Area
A = 4πr²
On-Screen Provided Formulas (Algebra & Geometry)
Quadratic Formula
x = (-b ± √(b² - 4ac)) / 2a
Arithmetic Sequence
a_n = a_1 + (n - 1)d
Pythagorean Theorem
a² + b² = c²
Sum of Interior Angles of Polygon
S = 180°(n - 2)
Provided Unit Conversions
The standard reference sheet provides the following conversions. Note: You must still recall fundamental conversions (like 1 yard = 3 feet) from memory.
Length (US to US)
1 mile = 5,280 feet
Length (US to Metric)
1 mile ≈ 1.61 kilometers
Length (US to Metric)
1 inch = 2.54 centimeters
Weight (US to US)
1 pound = 16 ounces
Weight (US to US)
1 ton = 2,000 pounds
Weight (US to Metric)
1 kilogram ≈ 2.2 pounds
Volume (US to US)
1 cup = 8 fluid ounces
Volume (US to US)
1 quart = 2 pints
Volume (US to Metric)
1 gallon ≈ 3.785 liters
Volume (US to US)
1 pint = 2 cups
Volume (US to US)
1 gallon = 4 quarts
Volume (Metric)
1 liter = 1,000 cubic centimeters
Frequently asked questions
Good to know
- Approximately 30% of the questions evaluate the 'Tasks of Teaching Mathematics', which test your ability to apply math knowledge to instructional decisions, analyze student misconceptions, and evaluate problem-solving strategies.
- The exam includes pretest items embedded seamlessly within the test; these questions do not count toward your final score.
- During numeric-entry questions, do not round intermediate calculator steps. An exact answer is generally required unless the specific question asks you to approximate or round.
- The test expects you to know unlisted fundamental conversions (e.g., 1 hour = 60 minutes, 1 minute = 60 seconds, 1 yard = 3 feet) and deduce secondary conversions dynamically (like finding how many fluid ounces are in a gallon given the provided table).
Reading isn’t remembering.
Most middle school math prep either feels like generic K–12 math review or ignores the instructional framing and scenario weighting that Praxis 5164 actually tests.
We translate the official ETS syllabus into a full learning map with topic-sized notes, explicit domain boundaries, and consistent coverage of tasks of teaching mathematics.