Elementary Mathematics (Grades K–6). Number and operation, algebra, geometry and measurement for K–6 teachers. The test is
computer delivered and runs for 2 hours 30 minutes: 100
selected-response — choose one answer.
Consistent with the NCTM Standards and the Common Core State Standards for Mathematical Practice.
IMathematical Processes12 questions · 12%
Apply a problem-solving process: make sense of a problem, plan a solution, implement it, and reflect on the result
Use mathematical reasoning to make conjectures, justify claims with evidence, and evaluate the reasoning of others
Reason quantitatively from known quantities and relationships: choose operations by how a quantity changes, and use known mathematics to solve unfamiliar problems
Communicate mathematical thinking precisely: use mathematical vocabulary, explain reasoning step by step, and tailor a mathematical explanation to its audience and purpose
Recognize and use connections within mathematics and between mathematics and the world: connect number and operations to algebra, geometry, measurement, and data, and apply known mathematics in new contexts
Select, construct, and translate among mathematical representations — concrete, pictorial, verbal, symbolic, tabular, and graphical — and judge what each one shows and conceals
IINumber and Operations30 questions · 30%
Understand place value and positional notation: read, write, and decompose whole numbers, and use place value to compare and order them
Round whole numbers, locate them on a number line, and explain what the rounding process represents
Use number properties, factors, multiples, prime and composite factorization, exponent notation, and divisibility rules with whole numbers
Compute with whole numbers using standard algorithms and strategies, and explain why regrouping, place value, and the number properties make each step valid
Estimate using rounding, compatible numbers, and benchmarks, and judge the reasonableness of a computed result
Solve multi-step real-world problems with whole numbers, including money, elapsed time, units, and problems requiring more than one operation
Understand fractions as representations of parts of a whole and parts of a part: equivalence, simplest form, comparison, ordering, and location on a number line
Add and subtract fractions and mixed numbers using like denominators, unlike denominators, and least common multiples, and apply them in context
Connect decimals to fractions and place value: read, write, compare, and compute with decimals through the thousandths place
Understand ratio as a comparison of two quantities: equivalent ratios, rates, and unit rates, and how a ratio differs from a fraction
Understand and solve proportions using equivalent ratios, unit rates, and cross products, and apply proportional relationships including scale
Understand percent as a fraction with denominator 100: convert among percent, decimal, and fraction, find a percent of a quantity, and solve problems involving percent increase, decrease, discount, tax, and tip
IIIAlgebra30 questions · 30%
Recognize, describe, extend and justify patterns in numbers, shapes and figures, and identify the rule that generates them
Generalize from specific cases to a rule, and represent that rule with variables, constants and expressions
Evaluate and simplify expressions using order of operations and the properties of addition and multiplication
Define a function as an input-output relationship, identify its domain and range, and evaluate it from a table, diagram, graph, or description
Represent functions with tables, graphs, and verbal descriptions, and interpret what each representation shows
Identify constant, linear and nonlinear relationships and proportional relationships, and describe rate of change
Solve one-step equations using inverse operations, explain the process with the balance model, and check solutions by substitution
Solve multi-step equations involving integers, negative numbers and rational coefficients, and rearrange formulas to solve for a different variable
Interpret, graph and solve inequalities on the number line
IVGeometry and Measurement28 questions · 28%
Classify two-dimensional shapes by their attributes and describe the properties of polygons, triangles and quadrilaterals
Classify three-dimensional shapes and describe their faces, edges, and vertices, including prisms, pyramids, cylinders, cones, and spheres
Identify angle types and apply angle relationships, including triangle and quadrilateral angle sums and angles formed by parallel lines
Identify and apply translations, rotations, and reflections, and describe their effect on a figure’s position, orientation, and measurements
Define congruence and similarity, apply the triangle congruence conditions, and use dilations to establish similarity
Locate points and figures on a coordinate grid, describe transformations using coordinates, and carry out standard straightedge-and-compass constructions
Apply the measurement process, select an appropriate tool and unit, estimate before measuring, and report to the correct precision
Convert measurements within the customary and metric systems and between them, and select the most useful unit for a given quantity
Measure and compute time, elapsed time and time intervals, and apply time reasoning to schedules, countdowns and rates
Compute the area and perimeter of two-dimensional figures, including triangles, parallelograms, trapezoids, composite shapes, and the circumference of a circle
Compute the volume and surface area of three-dimensional figures using nets and unit cubes, and convert between units of volume and capacity
Apply the Pythagorean theorem to find the length of a missing side in a right triangle, and recognize its converse
About the outline above. These titles are
written against ETS's publicly documented content outline for the
5412; they are a faithful reconstruction, not ETS text. No ETS
sample questions are reproduced for this exam, and every item in the app is
labelled Authored. Verify the current test specification on ETS's own
page before you register.
What test day is actually like
If you have not sat a Elementary Mathematics test before, the part that
unnerves people is usually not the content. It is not knowing what you are
walking into. Here is the actual shape of it.
100Questions
2 hours 30 minutesTime limit
Computer DeliveredDelivery
Not permittedCalculator
Selected-response — choose one answerFormat
That works out to about 1 minute 30 seconds per question.It is the pacing, not the difficulty, that catches people out. Most
candidates lose marks by grinding one hard item and running out of time
on easy ones later. Answer the ones you know first, mark the rest, and
come back with whatever is left.
The content is split into 4 sections, weighted
like this:
Mathematical Processes12 questions, 12% of the test
Number and Operations30 questions, 30% of the test
Algebra30 questions, 30% of the test
Geometry and Measurement28 questions, 28% of the test
What Praxis Studio gives you for 5412
80 practice questions covering every competency on the outline, with explanations for right and wrong answers.
A worked curriculum for all 39 competencies: key terms, worked examples, and the traps the exam is known for.
A self-test that reports accuracy per competency, not one opaque number.
Progress you can actually see, broken down by content category so you know what to study next.
Offline and mobile. Install to your home screen; it works without a connection.
Open source under MIT, so the content and the scoring logic can be checked by anyone.
If you are bad at maths, read this first. Anxiety about maths is a
strong predictor of general test anxiety for teacher candidates, and it
pulls down performance on subjects you are otherwise fine in. Two things
help. First, the Progress tab breaks your accuracy down by competency, so
you can see exactly which Elementary Mathematics topics are costing you and which
are already fine. Second, nothing here is timed while you learn it, so the
first pass through is about the ideas, not the clock. Pacing comes later,
on purpose.
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.
One reassurance worth having. 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 5412 Elementary Mathematics: questions and answers
How many questions are on the Praxis Elementary Mathematics (5412) exam?
The official test is 100 questions in 2 hours 30 minutes. Selected-response — choose one answer. It is computer delivered, and a calculator is not permitted. Praxis Studio is built against that exact structure.
How many free practice questions does Praxis Studio have for 5412?
80 questions for this exam: 0 transcribed from ETS and 80 written against the official content outline, every one labelled in the app so you always know which is which. All 39 competencies on the outline have at least one question.
What content does the Praxis 5412 exam cover?
It is divided into 4 content categories: Mathematical Processes (12%), Number and Operations (30%), Algebra (30%), Geometry and Measurement (28%). The full competency outline is listed on this page and is broken down, taught and quizzed inside the app.
Is Praxis Studio really free? Is there a paywall?
Yes, and permanently. There is no account, no trial, no card and no premium tier. Progress is stored in your own browser. Signing in is optional and only adds cross-device sync.
Is this official ETS material?
No. Praxis Studio is an independent, open-source project and is not affiliated with or endorsed by ETS. This exam’s outline is a reconstruction from ETS’s public content description, so no ETS text or sample questions are reproduced. Buy the official Study Companion and the free practice test you receive with test registration straight from ETS if you want the authoritative version.
Can I use it offline or on my phone?
Yes. It installs to the home screen on iOS and Android and runs offline via a service worker. Progress lives in local storage, so there is nothing to sign into and nothing to lose if you clear the app.
Can I see how I am doing by competency?
Yes. The Progress tab breaks your accuracy down by competency and content category, so it is clear which part of the outline to study next rather than just your overall percentage.
Does it use AI, and do I need an API key?
Ms. Kaya is an optional in-app tutor that is scoped to whichever competency you are reading, so it answers against the real outline instead of generic study advice. It is entirely optional: every question, explanation and self-test works without it. Bring your own key if you want to use it.