What math should my child know in each grade, from 1st to 6th?

By the end of grades 1 and 2 a child reads and writes numbers to 1,000 and knows every sum of two one-digit numbers from memory. By the end of grades 3 and 4 they know every product of two one-digit numbers, divide within 100, and compare fractions. By the end of grades 5 and 6 they compute with decimals and fractions and handle ratios, percent and negative numbers.

Is my child behind if they still count on their fingers?

Counting on fingers matters only for facts that should already be in memory. Fingers for a new or awkward sum are fine at any age. Fingers for sums of two one-digit numbers after the end of grade 2, or for the times tables after the end of grade 3, mean the facts are not yet in memory. A few weeks of short daily practice on that one set usually fixes it.

Do these grades match my country?

Math skills arrive in almost the same order everywhere, but the ages shift. Some systems introduce written division or negative numbers a year earlier or later, and grade names differ. Read the skills in sequence, find the lowest one your child has not mastered, and ignore the number on the row.

How far behind is a real problem?

One weak topic inside the current grade is normal, and it usually closes in a few weeks of short practice. A child working a full year below grade level across several topics, for a term or more, needs the school involved rather than more homework at the kitchen table.

How much daily practice is enough to close a gap?

Ten focused minutes on five days a week closes most single-topic gaps. Short, frequent sessions move facts into long-term memory better than one long session, and they keep a child who already finds math stressful willing to sit down at all.

Should I have my child assessed?

Ask the school for an assessment if the difficulty lasts several months despite regular practice, if your child forgets facts they clearly knew, or if they avoid math with real distress. Assessment is done by the school or an educational psychologist. Practice apps and worksheets support learning; they do not diagnose or treat anything.

What Math Kids Should Know by Grade

How do I use this checklist?

The point of a grade-by-grade checklist is to find the lowest skill your child has not yet mastered. Math is cumulative: a child who is shaky on place value will look weak at long division two years later, and drilling division will not help. The quickest way out of a gap is to go back to the missing skill and rebuild it.

Hold the grade numbers loosely. The progression here follows the order of the US Common Core State Standards for Mathematics, which most national curricula resemble in sequence even when the ages do not match. England's statutory national curriculum for mathematics asks for the tables up to 12 × 12 in Year 4, at ages 8 to 9; the US standards ask only for one-digit products at that age. Check your school's curriculum and shift the rows if your system starts earlier or later.

Grade	Core skills	Quick check (mastered if the child…)
1	Count to 120, read and write two-digit numbers, tens and ones, add and subtract within 20	Says what is 10 more than 47 without counting up
2	Hundreds, tens and ones to 1,000; add and subtract within 100; time to five minutes; money	Knows every sum of two one-digit numbers from memory
3	Multiply and divide within 100; unit fractions; rounding to 10 and 100; area	Answers 7 × 8 in about three seconds, without counting
4	Multi-digit multiplication and division; equivalent fractions; decimals to hundredths; factors	Works out 36 × 24 on paper and explains the steps
5	Decimals to thousandths; add, subtract and multiply fractions; volume	Adds two fractions that have different denominators
6	Divide fractions; ratios and percent; negative numbers; letters in expressions	Finds 15% of 60 and places −3 correctly on a number line

Grades 1 and 2: numbers to 1,000 and facts to 20

By the end of grade 2 a child reads, writes and compares numbers to 1,000, sees them as hundreds, tens and ones, adds and subtracts within 100, and knows every sum of two one-digit numbers from memory. Grade 1 lays the floor for that: counting to 120 from any number, two-digit place value, and adding and subtracting within 20.

A first grader compares two-digit numbers with the greater-than and less-than signs and adds using strategies such as making ten; fluency is expected within 10, and within 20 your child may still visibly think. A second grader pushes the same idea one place further: 853 is 8 hundreds, 5 tens and 3 ones. Second graders also skip-count, tell time to five minutes and add coins; pocket money and the kitchen clock rehearse both.

The memory milestone of grade 2 is addition: US standard 2.OA.B.2 asks children to "know from memory all sums of two one-digit numbers" by the end of the year. Quick check: ask 6 + 7, 8 + 5 and 9 + 4 out of order, in the car or while the pasta boils. Answers should arrive in a second or two, without fingers.

A place-value check takes 20 seconds. Write 407 on the back of an envelope and ask how many tens it has, then what happens to 340 when you add 10, and then 100. A child who has to recount is not ready for written subtraction. Practice the digits with the place value game and the comparison signs with comparing numbers, and find the wider set in math games for 2nd graders.

Play free in your browserPlace ValueGrade 1–2

Grades 3 and 4: times tables, division and the first fractions

Grade 3 is the year multiplication becomes a memorized fact, and grade 4 is the year those facts get used on bigger numbers. By the end of grade 3 a child knows every product of two one-digit numbers and divides within 100. By the end of grade 4 they multiply and divide multi-digit numbers and generate equivalent fractions.

US standard 3.OA.C.7 asks children to "know from memory all products of two one-digit numbers" by the end of grade 3. Along the way a third grader reads 5 × 7 as five groups of seven, solves word problems with equal groups and arrays, and adds and subtracts within 1,000. Fractions arrive as numbers: a whole cut into equal parts, marked on a number line. A pizza cut into eighths teaches that faster than a page of shading.

Grade 4 scales all of it up. Place value runs to 1,000,000, rounding works to any place, and written addition and subtraction move to the standard method. Children multiply a four-digit number by a one-digit number and two two-digit numbers together, then divide a four-digit number by a one-digit divisor and interpret the remainder. Standard 4.NF.A.1 adds fraction equivalence: children explain why a fraction keeps its value when its parts get smaller and more numerous together, compare unlike denominators against a benchmark such as one half, and write tenths and hundredths as decimals.

If your child is fluent with the tables but loses written multiplication, the gap is usually rounding and estimation. Practice with rounding numbers, then check the whole grade with a mixed 3rd grade worksheet and the rest of the set in math games for 3rd graders.

Free printable worksheetMixed Operations — 3rd GradersWorksheet · PDF

Grades 5 and 6: decimals, fraction operations and ratios

Grade 5 finishes arithmetic and grade 6 turns it into proportion and early algebra. By the end of grade 5 a child computes with decimals to hundredths, divides by two-digit divisors, and adds, subtracts and multiplies fractions. By the end of grade 6 they divide a fraction by a fraction, use ratios and percent, and work with negative numbers.

US standard 5.NBT.B.7 names the grade-5 workload: "add, subtract, multiply, and divide decimals to hundredths". Children also round decimals to thousandths, multiply multi-digit numbers with the standard algorithm, rewrite unlike denominators to add and subtract them, divide a whole number by a unit fraction, and find the volume of a box by layers.

Children in grade 6 divide a fraction by a fraction and divide multi-digit numbers and decimals with the standard written methods. Standard 6.RP.A.3 brings ratios, unit rates and percent, defined there as "a rate per 100". Negative numbers come with the number line, absolute value and the coordinate plane, and letters start standing for numbers in expressions with exponents.

How do I know if my child is a year behind?

A child who is a year behind shows it during the work, not in the mark at the end of it. Six signals turn up at home long before a report card says anything.

Counting on fingers for facts that should be in memory: sums of one-digit numbers after grade 2, times tables after grade 3.
Cannot say what the 4 in 4,205 is worth, or what 10 more than a number is without recounting.
Says 0.7 is smaller than 0.25 because it has fewer digits, or that one fifth is bigger than one third.
Re-reads a two-step word problem three times and still writes one operation.
Speed is the problem rather than accuracy: a page the class finishes in 10 minutes takes 40, with correct answers.
Refuses to start, or calls themselves stupid, before the first question.

One signal on a tired Thursday means nothing. Several of them, across different topics, for two months or more, is the pattern to act on. If the difficulty holds despite regular practice, and especially if your child loses number facts they clearly knew last week, read the signs of dyscalculia in children and ask the school about an assessment. Only a school, an educational psychologist or a specialist can assess a learning difficulty; a parent cannot, and neither can an app.

What do I do about a gap?

A gap closes fastest when you rebuild the skill where it starts, ten minutes a day, instead of drilling whatever the class is doing this week.

Find the floor. Go back one grade at a time through the grade-by-grade table until you reach a skill your child does quickly and correctly.
Practice at the floor, at the skill your child missed. Ten minutes a day, five days a week, beats one long weekend session: "space learning over time" is the first recommendation of the US Department of Education's What Works Clearinghouse.
Separate facts from method. If the tables are missing, drill the tables. Do not drill long division that only fails because of them.
Keep the list small. Five new facts a week, reviewed daily, is a realistic pace.
Retest after two weeks: 20 questions, the same set, timed. Compare the time as well as the score.
Tell the teacher which skill you are rebuilding. They can tell you whether the class is about to need it.

Progress looks like the same page done faster, not a harder page done slowly.

Where can we practice each skill?

Twenty-two of MathIt's game types play free in the browser with no sign-up, so you can test a skill in a minute: place value, comparing numbers and rounding for grades 1 to 4, then fractions, percentages and order of operations higher up. The free app for iOS and Android carries about 90 game types with adaptive difficulty that raises or lowers the numbers as your child answers, plus 2 to 5 player battles. For a calm test with no timer, the printable worksheets cover grades 1 to 6 and every one has an answer key.