United States · Kindergarten to grade 8 · Live online tutoring

Common Core math tutor online, grades K to 8

Most requests for a Common Core math tutor begin the same way: a worksheet comes home with number bonds, ten frames or a ratio table, the child is stuck, and the adult at the table was taught something else. A tutor who knows the standards can see what that worksheet is aiming at, teach the idea behind it, and connect it to the methods the family already trusts. This page sets out what the standards ask for in each grade from kindergarten to grade 8, what the eight practices look like on real homework, and how our live lessons fit around the curriculum your school chose.

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In short

A Common Core math tutor helps a child meet the Common Core State Standards for Mathematics, the grade-by-grade goals published at thecorestandards.org and used by most US states, including the eight Standards for Mathematical Practice. Modern Age Coders teaches grades K to 8 live online, in a group of 15 to 20 or one to one, through our Elementary Math course and Middle School Math course, alongside the curriculum your school uses. The first class is free.

Where to start

Three courses that teach to the Common Core goals

Pick by grade. Every course follows the standards for the grade and works with whatever books or apps the school sends home.

Elementary Maths for Grades 1-5 course thumbnail

CC / 01

Elementary math, grades 1 to 5

Place value, operations, fractions and measurement, with the models schools use.

Open the syllabus →
Middle School Mathematics Mastery course thumbnail

CC / 02

Middle school math, grades 6 to 8

Ratios, expressions, equations and the first functions.

Open the syllabus →
Mental Maths for Kids course thumbnail

CC / 03

Mental math and number sense

Making ten, splitting numbers and estimating, the habits behind fluency.

Open the syllabus →

Grade by grade

What does Common Core math cover in each grade?

Each grade from kindergarten to grade 8 opens with a short introduction naming two to four critical areas, the topics where instructional time should go first. Knowing your child's critical areas tells you which homework matters most this year.

Critical areas named in the Common Core grade introductions, kindergarten to grade 8 (thecorestandards.org, read 31 October 2026; wording shortened by us except where quoted)
GradeNumber of critical areasWhat the standards put first
KTwoRepresenting and comparing whole numbers; describing shapes and space. "More learning time in Kindergarten should be devoted to number than to other topics."
1FourAddition and subtraction with "strategies for addition and subtraction within 20"; place value in tens and ones; measuring length; composing shapes
2Four"extending understanding of base-ten notation"; fluency with addition and subtraction; standard units of measure; shapes
3FourMultiplication and division within 100; fractions, "especially unit fractions (fractions with numerator 1)"; arrays and area; two-dimensional shapes
4ThreeMulti-digit multiplication and division; "fraction equivalence" and adding fractions with like denominators; classifying figures by their properties
5ThreeAdding and subtracting fractions fluently; dividing by 2-digit divisors and decimals to hundredths; "developing understanding of volume"
6Four"connecting ratio and rate to whole number multiplication and division"; negative numbers and rational numbers; expressions and equations; statistical thinking
7FourProportional relationships; operations with rational numbers and linear equations; scale drawings, area, surface area and volume; "drawing inferences about populations based on samples"
8ThreeLinear equations and systems; "grasping the concept of a function"; distance, angle, similarity, congruence and the Pythagorean Theorem

Domains: the folders inside each grade

Inside each grade the standards are grouped into domains. Kindergarten to grade 5 use Operations and Algebraic Thinking, Number and Operations in Base Ten, Measurement and Data, and Geometry, with Counting and Cardinality only in kindergarten and Number and Operations, Fractions from grade 3 to grade 5.

Grades 6 and 7 switch to Ratios and Proportional Relationships, The Number System, Expressions and Equations, Geometry, and Statistics and Probability. Grade 8 drops ratios and adds Functions. A homework code such as 4.NF.B.3 reads as grade 4, Number and Operations, Fractions, cluster B, standard 3.

Limits written into the standards

Some standards carry footnotes that narrow them. The grade 4 fractions domain says "Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100." Grade 3 is limited to halves, thirds, fourths, sixths and eighths.

So a fourth grader adding sevenths is working beyond the grade, and a teacher who sticks to twelfths and hundredths is following the text exactly. When we plan lessons we check these limits first, so practice matches what the class will be assessed on.

Sources: the grade introductions and domain pages at thecorestandards.org/Math, read 31 October 2026. Modern Age Coders is an independent school and is not connected with the Common Core State Standards Initiative, the NGA Center, CCSSO, any state or any school district.

The eight practices

What are the Common Core math practice standards, and how do they show up in homework?

There are eight Standards for Mathematical Practice, and they apply in every grade. They are why a worksheet says "explain how you know" or "solve it another way". Here is how each one tends to appear on paper, and what a tutor does with it.

The eight Standards for Mathematical Practice (names from thecorestandards.org, read 31 October 2026); the homework and tutoring columns are ours
PracticeHow it often appears on homeworkWhat our teacher asks the child
MP1 Make sense of problems and persevere in solving themA word problem with no hint about the operation"What is the question asking for, before any numbers?"
MP2 Reason abstractly and quantitativelyWrite an equation for a story, then say what the answer means"Your answer is 12. Twelve what?"
MP3 Construct viable arguments and critique the reasoning of others"A classmate says 3/8 is bigger than 3/4. Agree or disagree?""Convince me, using a drawing."
MP4 Model with mathematicsTape diagrams, bar models, tables from a situation"Draw what is happening, then write the math."
MP5 Use appropriate tools strategicallyChoose a number line, a ruler or a table"Which tool makes this quicker?"
MP6 Attend to precisionLabel units; use the equal sign correctly"Is 3 + 4 = 7 + 2 = 9 true? Fix it."
MP7 Look for and make use of structureSplit 7 x 8 into easier facts"Which fact you already know is hiding inside this one?"
MP8 Look for and express regularity in repeated reasoningComplete a pattern, then describe the rule"What stays the same each time?"

Checking by a second route

The MP1 text says mathematically proficient students "check their answers to problems using a different method", and that they keep asking whether the answer makes sense. That single habit explains most "show another way" questions.

In our lessons it becomes a routine: solve once, check once by a different route, and only then move on. A child who learns that early catches a large share of their own mistakes without anyone telling them.

The equal sign and the hidden fact

MP6 asks students to state what their symbols mean, "including using the equal sign consistently and appropriately". Children who write running chains such as 3 + 4 = 7 + 2 = 9 are recording steps, but the line is false, and the standards want them to notice.

MP7 gives its own example: students "will see 7 x 8 equals the well remembered 7 x 5 + 7 x 3", which is the distributive property years before it gets a name. We teach facts that way, so a forgotten fact can be rebuilt from two known ones.

Common Core math examples

Common Core math examples, worked step by step

These are our own examples, written in the style the standards describe, one or two per grade band. Each pairs the model a worksheet might use with the equation that records it, because seeing the two side by side is usually what unlocks the homework.

Worked examples by grade (ours; the standard each one practices is from thecorestandards.org)
Grade and standardProblemModel or strategyRecorded as
1, making ten (1.OA.C.6)9 + 7Move 1 from the 7 to fill the 9 to a ten9 + 7 = 9 + 1 + 6 = 10 + 6 = 16
1, decomposing to ten (1.OA.C.6)15 - 7Take 5 to reach ten, then 2 more15 - 7 = 15 - 5 - 2 = 10 - 2 = 8
2, add within 1000 (2.NBT.B.7)368 + 457Add hundreds, tens and ones separately700 + 110 + 15 = 825
4, decompose a fraction (4.NF.B.3)5/6 two waysFraction strip cut into sixths5/6 = 1/6 + 4/6 = 2/6 + 3/6
4, mixed numbers (4.NF.B.3)2 3/4 as a fractionTwo wholes of four fourths, plus three4/4 + 4/4 + 3/4 = 11/4
4, fraction times whole (4.NF.B.4)4 x 2/3Four groups of two thirds4 x 2/3 = 8 x 1/3 = 8/3, between 2 and 3
5, unlike denominators (5.NF.A.1)2/3 + 1/4Rename both in twelfths8/12 + 3/12 = 11/12
6, ratio table (6.RP.A.3)A recipe uses 3 cups of flour for 2 cups of milk. Milk for 15 cups of flour?Ratio table 3:2, 6:4, 9:6, 12:8, 15:1010 cups of milk
6, equivalent expressions (6.EE.A.3)Rewrite 4(3 + y)Area model: a 4 by (3 + y) rectangle4(3 + y) = 12 + 4y; check y = 5: 32 and 32
8, linear equation (8.EE.C.7)3(x - 2) = x + 8Balance: expand, then collect x on one side3x - 6 = x + 8, 2x = 14, x = 7; check 15 = 15

Why the models come first

In the grade 2 example, 368 + 457 is solved by adding 300 and 400, then 60 and 50, then 8 and 7. Standard 2.NBT.B.7 asks children to add within 1000 using place-value strategies and to "relate the strategy to a written method". The written method comes next, and the regrouping in it is the 110 and the 15 above, compressed.

Place value is the foundation the whole sequence rests on. Standard 2.NBT.A.1 says "706 equals 7 hundreds, 0 tens, and 6 ones". A child who can say that sentence for any three-digit number rarely struggles with carrying.

Why fractions trip children up

The grade 4 example 4 x 2/3 is often answered as 8/12, because the child multiplies both parts. Reading it as four groups of two thirds, or eight thirds, makes the right answer obvious and lets the child estimate: eight thirds is a little under three.

Our teachers ask for that estimate before any calculation. It is MP2 in practice, and it turns a fraction rule that is easy to forget into a picture that is hard to forget.

The grade 8 example shows where the elementary models lead. Expanding 3(x - 2) uses the same distributive idea as the area model for 4(3 + y), which in turn is the 7 x 8 = 7 x 5 + 7 x 3 idea from grade 3. When a tutor can show a child that thread, algebra feels like an old friend in new clothes rather than a new subject.

With your curriculum

How do we tutor alongside a Common Core curriculum?

The standards are goals, not lesson plans, so every district picks its own materials. Our job is to teach the goal behind each page your child brings home, in the representation the school uses, and to keep the homework the child's own work.

Standards and curriculum are different things

The Common Core FAQ puts it in one line: "the Common Core is what students need to know and be able to do, and curriculum is how students will learn it." It adds that the standards "do not mandate the use of any particular curriculum."

That is why two children in different districts can meet the same standard with very different worksheets. We ask families which program their school uses, look at a recent page together, and teach in that program's language.

What a lesson looks like

A typical hour opens with five minutes of facts or mental math, moves to the week's critical-area topic with a model and its equation, and closes with a short mixed set the child does alone while the teacher watches the reasoning.

If there is homework, the child reads the question aloud and explains the first step. The teacher asks questions and draws, but the pencil stays with the child. We never complete graded work for a student.

  1. Share one recent worksheet or a photo of it. It tells us the program, the unit and the representation in use.
  2. Book the free first class. The teacher finds where the child's understanding breaks, usually one or two grades back in the same domain.
  3. Agree a short plan. Most plans pair the current unit with one older gap, for example place value under a multi-digit unit.
  4. Choose a format. A group of 15 to 20 children at the same grade, or 1-on-1 lessons paced to your school's calendar.
  5. Review each month. We look at recent class work with you and adjust the next month's focus.

Quoted from the Common Core FAQ, read 31 October 2026. The lesson outline and plan steps are our own practice.

At home

Can parents help with Common Core math homework?

Yes, and the initiative itself expects that it may feel unfamiliar. Its FAQ says parents "may find the methods and approaches different or have difficulty helping their children with homework", and suggests starting with a conversation with the teacher.

Four questions that work at the kitchen table

Ask "what is the problem about?" before "what is the answer?". Ask "can you draw it?" when a child is stuck. Ask "how could you check it a different way?" once there is an answer. And ask "what do you already know that looks like this?" when a fact or step has been forgotten.

None of these needs you to know the method on the page. Each one matches a practice standard, so you are helping with exactly what the homework is aiming at.

Which states use the standards

The initiative reports that forty-one states, the District of Columbia, four territories and the Department of Defense Education Activity have adopted the standards, and that states may change or add to them. Some states publish their own standards under another name.

Our teachers work from whichever set your state uses. The big ideas, place value, fractions, ratio and early algebra, appear in every version we have taught to.

A short Common Core practice set across the grades (ours; answers in brackets)
GradeProblemTry it withAnswer
KWhich number makes 10 with 6? (K.OA.A.4)Ten frame or fingers(4)
18 + 5 by making ten8 + 2 + 3(13)
2546 - 230Hundreds, tens and ones separately(316)
36 x 7 from 6 x 5 and 6 x 2Split array(30 + 12 = 42)
43 x 3/4Three groups of three fourths(9/4, between 2 and 3)
51/2 + 2/5Rename in tenths(5/10 + 4/10 = 9/10)
6A ratio of 5 red to 3 blue beads. Red beads if there are 12 blue?Ratio table(20)
7Is y = 2.5x proportional? (7.RP.A.2)Table: does it pass through (0, 0)?(Yes, constant 2.5)
85(x + 1) = 2x + 17Expand, then balance(x = 4; check 25 = 25)

Where your child is

Four stages we see in Common Core math

Our description of how children move from models to fluent, flexible methods. Most children are in different stages for different domains.

Stages of understanding we use when planning lessons (ours)
StageWhat we see in the workWhat we do next
1. CountingCounts every object; fingers for every factTen frames, making ten, fact families
2. ModelsDraws the strip, the array or the table, slowlyConnect each picture to its equation
3. RecordsWrites the equation; the model is optionalMixed practice; check by a second route
4. FlexiblePicks the quickest route and explains itHarder word problems and the next grade's ideas

For parents

A child in stage 2 is not behind. The standards spend a year on models before asking for a fast written method, and that year is where understanding is built.

The warning sign is a child who jumps to stage 3 without stage 2 and cannot say why a step works. That is where we usually start.

For students

Drawing a quick picture is not babyish. Strong mathematicians sketch all the time.

When you know a fact, ask how you could rebuild it if you forgot. That question is your safety net.

The catalogue

Nine courses from first numbers to algebra

Each one is taught live and lines up with the grade goals in the standards.

I

First years

Kindergarten to grade 2

CC / E / 01

Early math foundations

Counting, comparing and shapes, with objects.

Open the syllabus
II

Upper elementary

Grades 3 to 5

CC / U / 01

Elementary math

Operations, fractions and measurement.

Open the syllabus
III

Middle school

Grades 6 to 8

CC / M / 01

Middle school math

Ratio, rational numbers and equations.

Open the syllabus

CC / M / 03

Math competitions

For children who want harder problems.

Open the syllabus

How lessons run

Live Common Core math lessons around the school week

Weekdays or weekends, flexible: choose your batch, or for a very personalised plan choose 1-on-1 at your convenience, weekend mornings or weekdays.

School nights

Short lessons that follow this week's unit.

Weekends

Longer sessions to close older gaps.

1-on-1

Timed around your district's calendar.

Model, then equation

Each picture is matched to the math it records.

Your school's program

We teach in the representation your child sees in class.

Eight practices

Explaining and checking are part of every lesson.

Own work only

We teach the idea; the child writes the homework.

Gaps found early

A free first class locates the missing step.

Batch or private

A class of 15 to 20, or a teacher to yourself.

Student work

What our students make

Older students often turn a math idea into a small program. Browse them on student labs.

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Fees

Fees

Common Core tutoring is charged by the month with no long contract, so a family can add lessons for a hard fractions unit and stop once the unit is done.

Free first class

USD 0

no card required

  • A free first class
  • Bring a recent worksheet
  • No card required
Book it

Group batch

USD 100

a month, billed in US dollars

  • 15 to 20 children
  • The same teacher each week
  • Pick a batch time
  • Billed monthly
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One to one

USD 150

a month, billed in US dollars

  • One child, one teacher
  • Follows your school's units
  • Times you choose
Enquire

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Questions from parents

Common Core math tutoring: common questions

What does a Common Core math tutor do?

A Common Core math tutor teaches the goals in the Common Core State Standards for your child's grade, in the methods the school uses, and builds the eight practices such as explaining and checking. Our teachers also find older gaps, often in place value or fractions, that make the current unit hard.

Is there a Common Core math tutor near me?

Our lessons are live online, so distance does not matter. Your child joins by video from home and works with the same teacher each week, in a group or one to one.

What are the Common Core math practice standards?

They are eight Standards for Mathematical Practice that apply in every grade, from making sense of problems and persevering (MP1) to looking for regularity in repeated reasoning (MP8). They describe habits of mind rather than topics.

Which grades do you tutor in Common Core math?

Kindergarten to grade 8 on this page. For high school, our algebra, geometry, Algebra 2 and precalculus tutoring continue from where grade 8 ends.

Will the tutor do my child's homework?

No. The teacher explains the idea with a fresh example, asks questions and checks the reasoning, but the child writes their own homework. Graded work stays the student's own.

My child's school uses its own Common Core curriculum. Is that a problem?

No. The standards do not prescribe a curriculum, so districts choose their own. Send us a recent worksheet and the teacher will work in the same representations your child sees in class.

Why does Common Core homework use drawings and models?

Many standards ask children to use models such as ten frames, arrays, fraction strips or ratio tables before moving to a faster written method. The model shows why the method works, which makes later topics easier.

How quickly will my child catch up?

It depends on the gap and on practice between lessons, so we do not promise a timescale or a grade. After the free first class the teacher explains what is missing and suggests a plan, and we review progress with you each month.

When are your Common Core math classes?

Weekdays or weekends, flexible: choose your batch, or for a very personalised plan choose 1-on-1 at your convenience, weekend mornings or weekdays.

Are you connected with the Common Core initiative or my school district?

No. Modern Age Coders is an independent online school. We quote the published standards and link to them, and we are not affiliated with the initiative, any state or any district.

Elsewhere on this site

Related math pages

More help for US families, by grade and by topic.

Common Core vs traditional math

Where the standard algorithms appear, compared with older methods.

Second grade math tutoring

Base-ten understanding and fluent addition.

Fourth grade math tutoring

Multi-digit work and fraction equivalence.

Sixth grade math tutoring

Ratios, rates and first expressions.

Eighth grade math tutoring

Linear equations and functions.

Homeschool math curriculum

Planning a math year at home.

Online math tutoring for kids

Our live math lessons for younger US children.

Algebra tutoring

The next step after grade 8.

Related pages in this guide

Part of the guide: US state math tests by state

Standards behind the tests

State tests, grades 3 to 8

High school end-of-course and graduation tests

More guides: US gifted and selective school tests · US math placement and college readiness tests · Homeschool and school math curricula guide · US math and coding competitions guide

Start here

Book a free first class

Tell us the grade and send a photo of a worksheet that caused trouble. The teacher will work through a fresh problem of the same kind with your child and show you where the difficulty starts.

Read about how we teach, or see every course we offer.

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