Praxis 7813

Praxis 7813 Elementary Math CKT study guide

Every competency on the ETS outline for Elementary Education: Mathematics CKT, in order, with a worked lesson for each one. 63 practice questions come with it and all of them are free.

Start the 7813 lessons 7813 overview

4content areas

43competencies

63practice questions

0transcribed from ETS

Where 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 Elementary Math CKT item in this app comes from one of two places, and the app tells you which for every single question.

Provenance for Praxis 7813: what is ETS text, what was written for this app, and how to tell them apart.
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	63 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 Elementary Education: Content Knowledge for Teaching (7811) Study Companion. Reading it is the fastest way to check this page against the real thing, and it costs nothing.

What we are not claiming. TeachDayOne is not affiliated with ETS, and nothing here is ETS material. Praxis® and ETS® are registered trademarks of Educational Testing Service. The Study Companion above and the practice test included with your test registration both come from ETS, and both are worth your time. Use them alongside this, not instead of them.

A score in this app is not a Praxis score and does not predict one. What it does tell you is which of the 43 competencies you are getting wrong, which a practice score on its own does not.

The full 7813 competency outline

ETS divides this exam into 4 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.

Praxis 7813 content areas, with the number of questions on the real test and the percentage of the score each one carries.
Area	Questions on the test	Share of the score
I. Counting and Operations with Whole Numbers	16	30%
II. Place Value and Decimals	13	25%
III. Fractions, Operations with Fractions, and Ratios	13	25%
IV. Early Equations and Expressions, Measurement, and Geometry	10	20%

ICounting and Operations with Whole Numbers16 questions · 30%

Counts and skip counts whole numbers between 0 and 1,000
Connects counting to cardinality
Demonstrates understanding of one-to-one correspondence between numbers and objects being counted
Subitizes (recognizes small quantities by sight)
Identifies relationships between counting and the concept of larger and smaller numbers (i.e., that sets with higher counts are larger than sets with smaller counts)
Demonstrates understanding of representations of addition, subtraction, multiplication, and division (including objects such as manipulatives, drawings, and diagrams) and relates these representations of operations to expressions and equations
Solves mathematical and real-world problems involving the four operations, including solving problems by using properties of operations
6. Evaluating mathematical problems for how well they elicit a particular idea, support the use of a particular solution strategy or practice, fit a particular mathematical structure, address the same concept as another problem, or assess a particular student conception or error
13. Determining whether student work demonstrates the use of a particular mathematical idea or strategy
14. Determining whether a strategy is mathematically valid or generalizable
15. Interpreting a student’s mathematical error, including anticipating how it would replicate across similar problems, and choosing other work samples that demonstrate the same error

IIPlace Value and Decimals13 questions · 25%

Demonstrates a conceptual understanding of the value of the digits in a number
Compares multidigit and decimal numbers
Rounds multidigit and decimal numbers
Composes and decomposes multidigit numbers into groupings and understands why grouping and ungrouping are helpful in performing operations on multidigit and decimal numbers
Uses drawings and objects such as manipulatives to represent place value, relating these drawings and objects to numerical equations and written descriptions
2. Evaluating mathematical explanations for their validity, generalizability, explanatory power, and/or completeness
3. Determining the changes that would improve the validity, generalizability, completeness, and/or precision of a mathematical explanation
11. Selecting, creating, or evaluating representations or manipulatives for a mathematical purpose or to show a particular mathematical idea
16. Identifying tasks or situations in which student work or talk that seems mathematically valid might mask incorrect thinking

IIIFractions, Operations with Fractions, and Ratios13 questions · 25%

Demonstrates understanding of fractions as part-whole relationships, as multiples of unit fractions, as numbers, and as ratios, moving back and forth flexibly among these conceptualizations
Demonstrates understanding of characteristics of fractions that are less than one, equal to one, and greater than one
Demonstrates understanding of equipartitioning and that it is a building block for understanding fractions as part-whole relationships
Demonstrates understanding of fraction equivalence
Uses a variety of strategies for comparing fractions
Performs operations such as addition, subtraction, multiplication, and division with fractions as well as with fractions and whole numbers, understanding and using different strategies for these operations and building intuition about how the operations work (e.g., recognizing that multiplying a whole number by a fraction that is less than one makes the product smaller)
Demonstrates understanding of applications of operations on fractions (e.g., scaling)
1. Giving mathematically valid explanations for a process, conjecture, or relationship
4. Evaluating a student conjecture for its validity and/or generalizability on a given domain
8. Evaluating examples for how well they introduce a concept; illustrate an idea or relationship; illustrate the appropriateness of a strategy, procedure, or practice; or address particular student questions, misconceptions, or partial conceptions
12. Evaluating how representations or manipulatives have been used to show particular mathematical ideas, relationships between ideas, mathematical processes, or strategies in a text, talk, or written work

IVEarly Equations and Expressions, Measurement, and Geometry10 questions · 20%

Demonstrates understanding of what it means for algebraic terms, expressions, and equations to be considered equivalent, how the equal sign is used to represent relational equivalence, and that equations maintain their equivalence status under certain algebraic manipulations
Determines whether equations are true, identifies the missing values that would make them true, solves equations using the four operations, and solves relational statements by substitution
Follows the standard order of operations (including the use of parentheses and the distributive property of multiplication over addition)
Describes measurable attributes of objects; compares two objects with a common measurable attribute; chooses appropriate measurement tools and uses the tools to take measurements
Calculates and estimates perimeter, area, volume, and measurements of angles in mathematical and real-world problems; converts between measurement units
Demonstrates understanding of shapes and their attributes; classifies two-dimensional figures based on properties
Composes and decomposes shapes; draws shapes based on specific attributes such as number of angles and number of equal faces
Demonstrates understanding of lines, line segments, rays, and angles in two-dimensional figures
5. Evaluating mathematical definitions or other mathematical language for precision, validity, generalizability, usefulness in a particular context, and/or support for an instructional goal
7. Writing mathematical problems that fit a particular solution strategy or mathematical structure
9. Generating or identifying nonexamples or counterexamples to highlight a mathematical distinction or to demonstrate why a student conjecture is incorrect or partially incorrect
10. Choosing which mathematical topics are most closely related to a particular instructional goal

Content topics align with the NCTM Principles and Standards and the Common Core State Standards for Mathematical Practice, the standards frameworks the ETS outline was derived from.

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 Education: Mathematics CKT 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.

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 7813 study guide questions

What is on the Praxis 7813 study guide?

All 43 competencies from the ETS content outline, grouped under the 4 official content areas, with a worked lesson for each one. Every competency has at least one of the 63 practice questions attached to it, so nothing on the outline is left untested.

Is this Praxis 7813 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 7813?

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.

Practise 7813 free

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.

Compare all 8 exams