Praxis 5164
Praxis 5164 Middle School Math study guide
Every competency on the ETS outline for Middle School Mathematics, in order, with a worked lesson for each one. 90 practice questions come with it and all of them are free.
Start the 5164 lessons 5164 overviewWhere this material comes from
You are about to spend real study hours on this, so the honest answer matters more than a reassuring one. Every Middle School Math item in this app comes from one of two places, and the app tells you which for every single question.
| Part of the app | Where it comes from |
|---|---|
| Outline and competency titles | Transcribed word for word from the published ETS Study Companion. |
| Practice questions marked ETS | 0 transcribed from the Study Companion, carrying ETS’s own answer rationales. |
| Practice questions marked Authored | 90 written for this app against the official outline and the national standards that govern the subject. |
| How to tell them apart | The label is on the question itself. You are never guessing which kind you are looking at. |
The blueprint itself is ETS’s. It is published, free, and worth reading before you start: Praxis Middle School Mathematics (5164) Study Companion. Reading it is the fastest way to check this page against the real thing, and it costs nothing.
A score in this app is not a Praxis score and does not predict one. What it does tell you is which of the 50 competencies you are getting wrong, which a practice score on its own does not.
The full 5164 competency outline
ETS divides this exam into 5 content areas. The percentages are the share of the total score each one carries, which is not the same as the share of the questions.
| Area | Questions on the test | Share of the score |
|---|---|---|
| I. Numbers and Operations | 16 | 23% |
| II. Algebra | 15 | 23% |
| III. Functions | 11 | 17% |
| IV. Geometry and Measurement | 13 | 20% |
| V. Statistics and Probability | 11 | 17% |
INumbers and Operations16 questions · 23%
- Represents and solves word problems involving addition, subtraction, multiplication, and division of real numbers
- Uses the order of operations to simplify computations and solve problems
- Identifies and applies properties of operations on a number system (e.g., commutative, associative, distributive, identity)
- Compares and orders real numbers, including absolute values of real numbers
- Performs operations involving integer exponents
- Understands the relationships among fractions, decimals, and percents
- Uses the language of ratio and rate to describe relationships between two quantities
- Solves percent problems (e.g., expressing a percent as a ratio per 100, discounts, markups, taxes, tips, simple interest, percent error)
- Understands how to reason quantitatively and use units to solve problems
- Understands how to use basic concepts of number theory (e.g., divisibility, prime factorization, multiples) to solve problems
IIAlgebra15 questions · 23%
- Adds, subtracts, and multiplies linear and quadratic polynomials, including polynomials with rational coefficients
- Evaluates, manipulates, and compares algebraic expressions involving rational exponents (e.g., radicals, negative exponents)
- Uses variables to construct and solve equations and inequalities in real-world contexts
- Determines the nature of the solutions of a quadratic equation (e.g., interprets the graph, finds the discriminant, writes the equation in factored form)
- Rearranges formulas to solve for a specified variable (e.g., solve d = rt for t)
- Understands how to recognize and represent linear relationships algebraically
- Understands how to solve equations and inequalities
- Represents solutions to equations and inequalities (e.g., on a number line, in the xy-plane) and justifies each step in solving equations and inequalities
- Understands how to solve systems of equations and inequalities
- Graphs the solution set to a system of linear inequalities in the xy-plane and represents constraints in a modeling context
IIIFunctions11 questions · 17%
- Understands how to identify, define, and evaluate functions
- Knows how to determine and interpret the domain and the range of a function presented as a table of values, algebraically, or graphically
- Understands basic characteristics of linear functions (e.g., intercepts, slope)
- Understands the relationships among functions, tables, and graphs
- Knows how to analyze and represent functions (i.e., linear, quadratic, exponential) that model given information
- Understands differences between linear, quadratic, and exponential models, including how their equations are created and used to solve problems
- Is familiar with how to represent arithmetic sequences as functions
IVGeometry and Measurement13 questions · 20%
- Knows the properties of types of lines (e.g., parallel, perpendicular, intersecting) and angles
- Solves problems involving the Pythagorean theorem in two dimensions
- Understands the properties of triangles
- Knows the properties of quadrilaterals and other polygons
- Knows the concepts of transformations (i.e., translations, reflections, rotations, dilations)
- Given a figure, describes the transformations that map the figure onto itself, including reflection over a line of symmetry
- Understands the concepts of congruence and similarity
- Understands the properties of circles
- Knows how to interpret relationships between geometric objects in the xy-plane (e.g., distance, midpoint)
- Understands how to solve problems involving perimeter and area of polygons
- Knows how to solve problems involving solids
- Understands systems of measurement (i.e., metric, United States customary)
VStatistics and Probability11 questions · 17%
- Understands statistical processes and how to evaluate them
- Understands how to interpret, analyze, and represent data presented in a variety of displays
- Calculates relative frequencies for rows or columns in two-way tables and uses the calculations to describe possible associations between the two variables
- Uses the equation of a linear model to solve problems in the context of bivariate measurement data (e.g., interpreting the slope and intercept, interpolation)
- Solves for the mean and weighted average of given sets of data
- Determines and interprets measures of center (e.g., mean, median, mode) and spread (e.g., range, interquartile range) in a variety of problems
- Summarizes, describes, and compares numerical data sets in relation to their context
- Uses counting techniques (e.g., the counting principle, tree diagrams) to answer questions involving a finite sample space
- Solves probability problems involving simple events
- Knows how to use and evaluate probability models
- Interprets a uniform probability model and uses it to determine probabilities of events
The test is developed from the mathematics curriculum and state and national standards, including the Standards for the Preparation of Middle Level Mathematics Teachers (2020) by the National Council of Teachers of Mathematics (NCTM) and the Council for the Accreditation of Educator Preparation (CAEP).
How to actually study for this
The research on how people learn is consistent on one point: the method that works best is the one that feels least like studying. It is also the one anxious test-takers skip, which is why the practice here is built to be easy to start and impossible to fail.
- Do not just reread.Reading over material feels like studying and is the weakest use of your time. Recognition is not recall, and the exam asks you to recall.
- Answer questions from memory, then check.Retrieval practice, meaning self-testing, is one of the best-evidenced study methods there is. It beats rereading, restudying, and rereading your notes.
- Read the explanation either way.Right or wrong, the explanation is where the learning happens. Wrong answers especially: those are the ones you got lucky on.
- Come back tomorrow.Spacing beats cramming. The same hour split across five days is worth more than five hours on one night.
- Sit one timed run before test day.Full length, timed, no pausing. Pacing is a skill and it is learned by doing, not by thinking about doing.
Practice questions in this app are not the real exam, and your score on them is not your Praxis score. Use them to find the competencies you do not know yet. That is the whole job.
Praxis 5164 study guide questions
What is on the Praxis 5164 study guide?
All 50 competencies from the ETS content outline, grouped under the 5 official content areas, with a worked lesson for each one. Every competency has at least one of the 90 practice questions attached to it, so nothing on the outline is left untested.
Is this Praxis 5164 outline the official ETS one?
The competency titles below are transcribed from the published ETS Study Companion for this exam, word for word. Check it against ETS's own PDF; the link is above.
How long should I spend on Praxis 5164?
That depends on how much of the outline you already know, which is why the app reports accuracy per competency rather than one overall number. Work through the competencies you are weakest on first. The ones you can already answer are not where your remaining marks are.
Does the study guide cover the written-response section?
This exam is selected-response only, so every item here is auto-scorable and the accuracy figure covers all of it.
Other Praxis exams
Wrong code, or a second credential? Every exam here has the same shape: an outline you can read, a practice bank, and progress by competency.