Welcome to the Achievable Praxis Math 5733 course!

Welcome to your course for the Praxis Core Academic Skills for Educators: Mathematics (5733) exam. The Praxis Math 5733 is more than a test requirement - it’s a chance to show the mathematical knowledge and problem-solving skills you’ll use as an educator.

This course is designed to help you strengthen your mathematical reasoning and build the skills and strategies you’ll use on test day. You’ll work through the same content areas the exam covers, with clear explanations, worked examples, and plenty of practice in the test’s format.

Each chapter focuses on a specific set of topics from the exam. Along the way, you’ll find definitions, step-by-step examples, problems to try on your own, and a summary of key points. Each section also ends with a 5-question quiz so you can check your understanding before moving on.

Eligibility

The Praxis Math 5733 is intended for aspiring educators seeking teacher certification or licensure. Many test-takers are college students or recent graduates in teacher preparation programs, but eligibility depends on your state’s requirements.

Check with your state’s department of education or your teacher preparation program to confirm the specific rules where you plan to teach.

Exam format

The Praxis Core Academic Skills for Educators: Mathematics test measures the math knowledge and reasoning used in teaching. Many questions emphasize problem-solving and applying concepts in realistic contexts.

The test is computer-delivered and includes approximately 56 questions to complete in 90 minutes. That works out to about 1.5 minutes per question, so pacing matters. An on-screen four-function calculator (with square root and memory functions) is available during the exam - personal calculators are not permitted. No formula sheet is provided, so you’ll want to be comfortable with key formulas going in. Some items may be unscored pretest questions that ETS is piloting; these are indistinguishable from scored items, so treat every question the same.

The computer-delivered interface also includes a few tools to help you manage the test: you can flag questions for review and return to them later, and scratch paper is provided so you can work through problems by hand.

You’ll encounter three types of questions:

• Multiple choice - Select the single correct answer from the listed options.
• Multiple response - Select one or more correct answers. The test does not indicate how many are correct.
• Numeric entry (short answer) - Type your answer directly as an integer or decimal. For fractions, the exam provides two separate boxes (one for the numerator and one for the denominator).

Content outline

The Praxis Math 5733 covers three major content areas. Each one tests a different set of skills and ways of thinking. The question counts and percentages below are approximate and based on current ETS published distributions.

Number and quantity (~20 questions, ~36%)

This section focuses on core number concepts, including integers, decimals, fractions, ratios, proportions, percentages, place value, and number properties. You’ll also work with measurement, unit conversions, rates, and proportional relationships. The exam assumes basic familiarity with both U.S. customary and metric measurement systems.

Data interpretation and representation, statistics, and probability (~18 questions, ~32%)

This section asks you to analyze and interpret data displays such as graphs, charts, and tables. You’ll calculate measures of central tendency (mean, median, mode), interpret relationships in data, make inferences from displays, and find probabilities of simple and compound events.

Algebra and geometry (~18 questions, ~32%)

This section covers algebra topics such as solving linear and quadratic equations, working with inequalities, understanding functions and their graphs, and simplifying algebraic expressions. Geometry topics include properties of 2D and 3D shapes, angle relationships, coordinate geometry, similarity, congruence, and calculations involving perimeter, area, and volume.

The Praxis Math 5733 uses a scaled scoring system ranging from 100 to 200, with most states requiring a minimum score between 142-150 for teacher certification. Check your state’s specific requirements, as passing scores vary by location.

Common pitfalls to watch for

As you work through this course, keep an eye out for a handful of traps that show up repeatedly on the Praxis Math 5733:

• Sign errors - Losing track of negatives when solving equations or simplifying expressions is one of the most frequent sources of wrong answers.

• “Less than” translation - Word problems that say “5 less than x” mean $x-5$, not $5-x$. The order matters. To sanity-check the rule with real numbers: “4 less than 7” is $7-4=3$, not $4-7=-3$. The number being reduced always comes first.

  Phrase	Correct	Common mistake
  “5 less than $x$”	$x-5$	$5-x$
  “4 less than 7”	$7-4=3$	$4-7=-3$

• Fraction operations - Adding or subtracting fractions requires a common denominator; a common mistake is operating on the numerators and denominators separately. Also remember that dividing by a fraction means multiplying by its reciprocal.

• Decimal and place value errors - When multiplying or dividing decimals, it’s easy to misplace the decimal point. Double-check by estimating: $0.3\times 0.4$ should be close to $0.12$, not $1.2$ or $0.012$.

Each of these will come up again with fuller explanations in the relevant chapters.

How to use this course

This course is organized to build skills step by step. Start with Chapter 1 and move through the sections in order, since later topics often rely on earlier ones. Each chapter includes:

• Clear explanations of key concepts and methods
• Worked examples showing solutions
• Practice problems with detailed explanations
• 5-question quizzes at the end of each section to check mastery
• Strategy tips for common question types
• A summary of key points at the end of each section

A few tips for working through the material:

• Work examples actively. When you reach a worked example, cover the explanation, try the problem yourself first, then uncover each step and compare your reasoning. This builds the problem-solving muscle you’ll need on test day far more effectively than passive reading.
• Focus on understanding, not just memorization. Know key formulas, but understand why methods work - that’s what helps you handle unfamiliar questions and spot mistakes.
• Use the process of elimination. On multiple-choice questions, cross out answers that are clearly wrong to improve your odds even when you’re not fully sure of the correct choice.
• Manage your time. With approximately 56 questions in 90 minutes, avoid getting stuck on one problem. Make your best choice, move on, and return later if time allows.
• Check your work when possible. Use estimation to see whether an answer is reasonable. For example, if calculating $18\%$ of $250$, the result should be less than $50$ (since $20\%$ of $250$ is $50$, and $18\%<20\%$). Quick checks like this can catch calculation errors.

Before diving in, take a few minutes to gauge where you stand. Use the questions below to identify which chapters deserve the most attention.

• Number and quantity: Are you comfortable converting between fractions, decimals, and percentages? Can you set up and solve a proportion or unit conversion from scratch?
• Statistics and data: Can you calculate a mean, median, and mode by hand? Do you feel confident reading bar graphs, line graphs, and two-way tables? Can you find the probability of a simple event or a compound event (like drawing two cards in a row)?
• Algebra: Can you solve a two-step linear equation and check your answer? Do you know how to graph a line from slope-intercept form? Are you comfortable solving basic inequalities and identifying a function from a graph or table?
• Geometry: Are you comfortable with the area and perimeter formulas for common shapes? Can you apply the Pythagorean theorem? Do you know how to find the volume of a basic 3D solid, such as a rectangular prism?

If you answered “not sure” or “no” to any of these, that chapter is a priority. If a topic feels familiar but rusty, still work through it - the exam tests these skills in applied, multi-step contexts that can trip up even confident students.

After you finish the content chapters, take the practice exams to gauge your readiness and find topics that need review. Use the answer explanations to identify what went wrong and how to approach similar problems.

Concluding chapter

The concluding chapter includes practical information about registering for the Praxis Math 5733, understanding your score report, and preparing for test day. You’ll also find resources for continued learning and professional development.