Math at Home · By the MathIt team · Published · 8 min read
What math should a 2nd or 3rd grader know?
By the end of 2nd grade most children read and write numbers to 1,000, know every sum of two one-digit numbers from memory, and add and subtract within 100. By the end of 3rd grade they know every product of two one-digit numbers from memory, divide within 100, round to the nearest 10 and 100, and compare simple fractions.
Read it to find the lowest skill your child has not mastered, not to score them. Maths 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 year a country introduces written division, decimals or negative numbers can move by a year either way, and grade names differ everywhere. The progression below follows the broad order of the US Common Core State Standards for Mathematics, which most national curricula resemble in sequence even when the ages do not match. Check your school's curriculum for the exact wording, and shift the rows if your system starts earlier or later.
| Grade | Core skills | Can do it if… |
|---|---|---|
| 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 |
The work of these two years is the number system, not calculation speed. A first grader counts to 120 starting from any number, sees the two digits of a number as tens and ones, compares two-digit numbers with the greater-than and less-than signs, and adds and subtracts within 20 using strategies such as making ten.
Fluency is expected within 10; 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. They count within 1,000, skip-count by fives, tens and hundreds, compare three-digit numbers, and add and subtract within 100 fluently, with written work up to 1,000. Two smaller markers belong here too: telling time to the nearest five minutes, and adding coins. Pocket money and the kitchen clock rehearse both. Odd and even numbers and small rectangular arrays start the multiplication idea without naming it.
The memory milestone: by the end of grade 2 your child should know every sum of two one-digit numbers from memory. 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. Practise the digits with the place value game and the greater-than and less-than signs with comparing numbers, and find the wider set in math games for 2nd graders.
Play free in your browser Place Value Grade 1–2Grade 3 is the year multiplication turns into a fact rather than a procedure. By the end of it your child knows every product of two one-digit numbers from memory, and divides within 100 with the same facts.
Along the way they read 5 × 7 as five groups of seven, solve word problems with equal groups and arrays, round whole numbers to the nearest 10 and 100, add and subtract within 1,000, and tell time to the minute. Fractions arrive as numbers: a whole cut into equal parts, marked on a number line, with equivalences such as one half and two quarters, and comparisons between fractions that share a numerator or a denominator. 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 addition and subtraction move to the standard written method. Children multiply a four-digit number by a one-digit number, and two two-digit numbers together. They divide a four-digit number by a one-digit divisor and interpret the remainder. In fractions they generate equivalents, compare unlike denominators against a benchmark such as one half, add and subtract with the same denominator, multiply a fraction by a whole number, and write tenths and hundredths as decimals. Factor pairs up to 100 and the words prime and composite appear here.
If your child is fluent with the tables but loses written multiplication, the gap is usually rounding and estimation, not the tables. Practise 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 worksheet Mixed Operations — 3rd Graders Worksheet · PDFGrade 5 finishes arithmetic. Grade 6 turns it into algebra and proportion.
In grade 5, children read, compare and round decimals to thousandths, multiply multi-digit numbers with the standard algorithm, divide by two-digit divisors, and add, subtract, multiply and divide decimals to hundredths. In fractions they add and subtract unlike denominators by rewriting them, multiply fractions, and divide a whole number by a unit fraction and a unit fraction by a whole number. They also write and read expressions such as 2 × (8 + 7) without calculating them, and find the volume of a box by layers.
In grade 6, children divide a fraction by a fraction, divide multi-digit numbers and decimals with the standard written methods, and find the greatest common factor of two numbers up to 100. Ratios, unit rates and percent as a rate per 100 arrive here. Negative numbers come with the number line, absolute value and all four quadrants of the coordinate plane, and letters start standing for numbers in expressions with whole-number exponents.
Watch what happens during the work, not the mark at the end of it. These are the things you see at home before a report card says anything.
One of these 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 good teaching — 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.
Go back to where it starts and rebuild it there, ten minutes a day.
Progress looks like the same page done faster, not a harder page done slowly.
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 at the kitchen table: 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, which raises or lowers the numbers as your child answers, and 2 to 5 player battles for the evenings when practice must feel like a game. For paper work, and for a calm test with no timer, the printable worksheets cover grades 1 to 6 and every one has an answer key.
Practise it in the MathIt app
About 90 math games with adaptive difficulty, daily practice and 2–5 player battles — free on iOS and Android.
It depends on the fact. 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.
The skills come in this order almost 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.
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 — not more homework at the kitchen table.
Ten focused minutes on five days a week. Short and frequent moves facts into long-term memory better than one long session, and it keeps a child who already finds maths stressful willing to sit down at all.
Ask the school if the difficulty lasts several months despite regular practice, if your child forgets facts they clearly knew, or if they avoid maths 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.
Practise it in the MathIt app
About 90 math games with adaptive difficulty, daily practice and 2–5 player battles — free on iOS and Android.
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