Common Core Math Standards & Grade Resources

What Common Core math is

The Common Core State Standards for Mathematics describe grade-level expectations for mathematical knowledge and understanding. They are standards rather than a complete curriculum: teaching materials, lesson sequences and classroom methods are chosen locally.

States can adopt, adapt or replace standards. Similar topic names do not establish that two state assessments have the same scope, difficulty or item formats. Check your state’s current standards and your school’s course or test outline. Our comparison guide provides additional context: Common Core vs. State math standards.

The 8 Standards for Mathematical Practice

The eight mathematical practices describe habits of reasoning and problem solving that students develop alongside grade-level content throughout K–12.

MP1, Make sense of problems and persevere in solving them

Read a problem, decide what it is asking, choose an entry point, and keep checking whether the approach is working.

MP2, Reason abstractly and quantitatively

Move between a real situation and the symbols that represent it, stripping context to compute and then putting the context back to interpret the answer.

MP3, Construct viable arguments and critique the reasoning of others

Justify a conclusion with definitions and prior results, and find the flaw in someone else’s argument.

MP4, Model with mathematics

Turn an everyday situation, a budget, a rate, a shape, into an equation, diagram or graph, then judge whether the model is good enough.

MP5, Use appropriate tools strategically

Choose sensibly among pencil and paper, a ruler, a calculator, a spreadsheet or estimation, and know the limits of each.

MP6, Attend to precision

Use exact language, correct units, and an accuracy appropriate to the problem.

MP7, Look for and make use of structure

See a pattern inside an expression or figure, that 7 × 8 is 7 × 5 plus 7 × 3, or that x² + 9x + 14 factors, and use it.

MP8, Look for and express regularity in repeated reasoning

Notice that a calculation repeats, and generalize it into a shortcut, rule or formula.

What each grade covers

Common Core groups content into domains. The domains change as students move up, which is why a grade 4 test looks nothing like a grade 8 test.

Kindergarten to grade 2

Counting and cardinality, addition and subtraction within 100, place value to 1,000, measurement and data, and basic shapes.

Grades 3 to 5

Multiplication and division fluency, fractions as numbers, decimals to the hundredths, area and perimeter, volume, and the coordinate plane.

Grades 6 and 7

Ratios and proportional relationships, all four operations with rational numbers, expressions and equations, area and surface area, and statistics and probability.

Grade 8

Linear functions, systems of equations, integer exponents, scientific notation, congruence and similarity, the Pythagorean theorem, and bivariate data.

High school

Number and quantity, algebra, functions, modeling, geometry, and statistics and probability, usually taught as Algebra 1, Geometry and Algebra 2.

Common Core math practice tests by grade

• Grade 3 Common Core math practice test · top 10 grade 3 questions
• Grade 4 Common Core math practice test · top 10 grade 4 questions
• Grade 5 Common Core math practice test · top 10 grade 5 questions
• Grade 6 Common Core math practice test · full-length grade 6 test
• Grade 7 Common Core practice tests · full-length grade 7 test
• Grade 8 Common Core math practice test · full-length grade 8 test
• Common Core Algebra 1 and Common Core Algebra 2

Common Core math worksheets by grade

• Grade 3 worksheets
• Grade 4 worksheets
• Grade 5 worksheets
• Grade 6 worksheets
• Grade 7 worksheets
• Grade 8 worksheets
• Algebra 1 worksheets

Full step-by-step courses are available for grade 6, grade 7 and Common Core Algebra 1.

Common questions about Common Core math

Is Common Core a curriculum?

No. It is a list of end-of-grade expectations. Textbooks, lesson order and teaching methods are chosen by states and districts, which is why two Common Core classrooms can look very different.

Which states still use Common Core?

Adoption and revisions are state decisions. Use your state education department’s current mathematics standards and your school’s course guidance to confirm which expectations apply; a renamed set of standards is not automatically identical to Common Core.

Why does Common Core math use several methods for one calculation?

Practices MP7 and MP8 ask students to see structure and generalize it. Area models and number lines exist to make place value and regrouping visible before the standard algorithm is taught, not to replace it.

Which tests are aligned to Common Core?

Smarter Balanced content specifications connect its assessments to Common Core. Other state assessments have their own specifications. Match practice to the current grade, subject and assessment outline instead of assuming that a Common Core label establishes alignment.

What does a Common Core math question look like?

A task may ask a student to calculate, model a situation, interpret a representation or explain a method. Common Core describes knowledge and mathematical practices; it does not prescribe one question format or a fixed number of explanation items for every test.

How should a student prepare?

Take a timed practice test for the grade, note which domain each missed question came from, then work the worksheets for that one domain before retesting.

Standards references

• Common Core mathematics standards
• Standards for Mathematical Practice
• Smarter Balanced test-development guidance

These primary references explain standards and assessment design. Effortless Math resources are independent study materials.