PlusyMath by grade: what to expect from 1st through 6th
Schools expect addition and subtraction facts from memory by the end of 2nd grade, the times tables by the end of 3rd grade (Year 4 in England), and the written column methods between 4th and 6th grade. Here is each year in the standards' own words, with what it looks like in homework.
You may recognise this: a worksheet comes home, your child is counting on fingers for 8 + 5 or drawing boxes to multiply, and you cannot tell whether that is behind, ahead or exactly where the class is meant to be. Nobody handed you the list. This guide is the list, for arithmetic with whole numbers, taken from two published sets of standards and nothing else.
What should my child know in math, and by when?
By the end of 2nd grade a child is expected to know single-digit sums from memory, and by the end of 3rd grade the multiplication facts. The written methods follow: column addition and subtraction by the end of 4th grade, long multiplication by 5th, and long division by 6th. England's curriculum asks for most written methods about a year earlier.
The US column below quotes the Common Core State Standards, published in 2010. The England column quotes the national curriculum for mathematics, published by the Department for Education in 2013 and statutory from 2014. By age, a US grade lines up with the UK year one number higher, so 3rd grade and Year 4 are the same children: 8 and 9 year olds.
| Grade (US) / year (UK) | Common Core: by the end of the grade | England: by the end of the year |
|---|---|---|
| 1st grade / Year 2 | Working toward the 2nd grade goal: sums of two one-digit numbers from memory | Addition and subtraction facts to 20, fluently. The 2, 5 and 10 times tables |
| 2nd grade / Year 3 | Add and subtract within 20 fluently. Know all sums of two one-digit numbers from memory (2.OA.2) | The 3, 4 and 8 times tables. Column addition and subtraction with up to 3 digits |
| 3rd grade / Year 4 | Multiply and divide within 100 fluently. Know all products of two one-digit numbers from memory (3.OA.7) | All tables up to 12 × 12. Column addition and subtraction with up to 4 digits. Written multiplication by a one-digit number |
| 4th grade / Year 5 | Add and subtract multi-digit numbers fluently with the standard algorithm (4.NBT.4) | Long multiplication. Short division by a one-digit number |
| 5th grade / Year 6 | Multiply multi-digit numbers fluently with the standard algorithm (5.NBT.5) | Long division by a two-digit number |
| 6th grade / Year 7 | Divide multi-digit numbers fluently with the standard algorithm (6.NS.2) | Past the primary curriculum, which ends at Year 6 |
States and schools vary. Each US state sets its own standards, and a school chooses its own order and pace inside the year. England's curriculum applies to England, not the whole UK. Treat this page as a map, and your child's teacher as the one who knows the route the class is taking.
How should I read a list like this?
Read each line as the end of the school year, not the start. A standard that says 3rd graders know the multiplication facts from memory describes June, so a child who cannot do it in October is not behind. "From memory" means the answer arrives without working it out, and "fluently" means a method done accurately and without strain.
That matters for one common worry. The Common Core names the standard algorithm for addition and subtraction at 4th grade, as the year fluency is expected. The text does not say the column method may not be taught sooner, and a school may introduce it earlier. If your child is drawing place value pictures in 2nd grade, the columns are still coming. The methods you may not recognise are covered in new math methods explained.
What is expected in 1st grade (Year 2)?
In 1st grade (US) and Year 2 (UK), children are building the addition and subtraction facts that the next year expects from memory. England's national curriculum expects Year 2 pupils to "recall and use addition and subtraction facts to 20 fluently", and to know the 2, 5 and 10 times tables.
The year before, in Year 1, the same curriculum asks pupils to "represent and use number bonds and related subtraction facts within 20". A number bond is a pair that makes a total: 6 and 4 make 10, so 10 take away 4 is 6.
In homework it looks like short sums such as 8 + 5, missing-number questions such as 7 + _ = 10, and pictures of ten-frames or number lines. Counting on fingers is normal here. If it worries you, read is counting on fingers a problem?
One way to practice: make ten. For 8 + 5, ask "how many does 8 need to make 10?" Two. Then "what is left of the 5?" Three. So 10 and 3 more: 13. Five sums a day done this way, said out loud, is plenty.
What is expected in 2nd grade (Year 3)?
By the end of 2nd grade, Common Core standard 2.OA.2 expects children to "fluently add and subtract within 20 using mental strategies" and to "know from memory all sums of two one-digit numbers". In England, Year 3 adds the 3, 4 and 8 times tables and column addition and subtraction with up to three digits.
This is the year counting is meant to give way to knowing. England's curriculum words the Year 3 written method as "add and subtract numbers with up to 3 digits, using formal written methods of columnar addition and subtraction".
In homework it looks like a mixed page of facts, sums with a two-digit number, and in England the first column sums with carrying (also called regrouping or exchanging):
347 + 285 ----- 632
One way to practice: cover and recall. Write five facts your child finds hard on five scraps of paper, answers on the back. Ask each one cold, turn it over to check, and put the missed ones back in the pile. Tomorrow, swap in one new fact. The slips to watch for once columns start are in carrying and borrowing mistakes.
What is expected in 3rd grade (Year 4)?
Third grade (US) and Year 4 (UK) are the times tables year in both countries. Common Core standard 3.OA.7 says that by the end of 3rd grade children should "know from memory all products of two one-digit numbers". England's curriculum expects Year 4 pupils to recall the facts for the tables "up to 12 × 12".
In England, Year 4 also brings the Multiplication Tables Check in June: 25 questions on screen with 6 seconds for each. The Standards and Testing Agency, which runs it, says there is no expected standard threshold, so it cannot be passed or failed. It leans on the 6, 7, 8, 9 and 12 tables, which the agency calls the most difficult. More in the Year 4 multiplication tables check.
Year 4 pupils in England are also expected to add and subtract numbers with up to four digits in columns, and to "multiply two-digit and three-digit numbers by a one-digit number using formal written layout".
In homework it looks like 7 × 8, then 56 ÷ 7, then a gap to fill such as 7 × _ = 56.
One way to practice: fact families. Take one fact and say all four members: 7 × 8 = 56, 8 × 7 = 56, 56 ÷ 7 = 8, 56 ÷ 8 = 7. One family learned is four answers. If the tables keep slipping away, see why times tables don't stick.
What is expected in 4th grade (Year 5)?
By the end of 4th grade, Common Core standard 4.NBT.4 expects children to "fluently add and subtract multi-digit whole numbers using the standard algorithm", the column method with carrying and borrowing. England's curriculum expects Year 5 pupils to use long multiplication and to divide by a one-digit number with short division.
Multiplication and division in 4th grade are a different story in the US. The standards have children multiply and divide "using strategies based on place value and the properties of operations", shown with "equations, rectangular arrays, and/or area models". This is where the box drawings come from. For 23 × 6, a child splits 23 into 20 and 3, works out 20 × 6 = 120 and 3 × 6 = 18, and adds them: 138.
In homework it looks like subtraction across zeros, the question that undoes many children:
4000 - 1267 ------ 2733
One way to practice: estimate before the first digit is written. 4,000 take away about 1,300 is about 2,700, so an answer of 3,267 or 273 is wrong before anyone checks a column. Ask for the estimate out loud, every time, until it is a habit.
What is expected in 5th grade (Year 6)?
By the end of 5th grade, Common Core standard 5.NBT.5 expects children to "fluently multiply multi-digit whole numbers using the standard algorithm", which is long multiplication. England's curriculum expects Year 6 pupils to divide numbers of up to four digits by a two-digit number using long division.
Division with a two-digit divisor does appear in US 5th grade, but the standards still describe it as done with place value strategies, not yet the standard algorithm. So a 5th grader may bring home 1,248 ÷ 24 solved in chunks, taking away 24s in easy groups, and that is the method the grade asks for.
In homework it looks like this:
46
x 23
----
138
920
----
1058One way to practice: have your child name each row before adding. "This row is 46 times 3. This row is 46 times 20, which is why it ends in a zero." A child who can say that will not forget the zero, which is an easy slip to make in long multiplication.
What is expected in 6th grade (Year 7)?
By the end of 6th grade, Common Core standard 6.NS.2 expects children to "fluently divide multi-digit numbers using the standard algorithm", which is long division. A companion standard, 6.NS.3, extends the standard methods to decimals. In England the same method is expected a year younger, in Year 6, the last year of the primary curriculum.
Long division is the last of the four written methods to arrive because it uses the other three. Every step is a multiplication fact, then a subtraction, often with borrowing. A child who is slow on the tables will find long division slow for that reason, and the fix is the tables, not more division.
In homework it looks like 1,248 ÷ 24 set out under a bracket, with the answer 52 on top. Every digit of that example is worked through in long division step by step.
One way to practice: multiply back. When the answer is 52, your child works out 52 × 24. If it comes to 1,248, the division is right, and they have found that out without asking you.
What should I do if my child is behind the list?
If your child is behind this list, find the earliest line they are not sure of and start there, not at this week's homework. Arithmetic stacks: the tables rest on addition facts, and long division rests on the tables. Our suggestion is a few short sessions a week on the earlier skill before extra time on the current one.
Find the earliest gap
Go down the table from the top. Ask five questions from each line, with no clock and no comment. The first line where your child has to work answers out slowly is your starting point.
Tell the teacher what you found
One line is enough: "She is quick on the 2, 5 and 10 tables and works out the rest." The teacher knows the class's route and may already be on it.
Practice that one thing, briefly
A handful of facts or two written questions a day, spread across the week. There is no researched number of minutes for home practice; this is our suggestion. See how much math practice a day.
Check again in a month
Ask the same five questions. If little has changed after steady practice, that is worth a conversation with the teacher about what else might be going on.
A gap is information, not a verdict. For the wider picture, read why is my child struggling with math?
Where does Plusy fit?
Plusy is a math practice app for children 6 to 12. Four of its five roads follow the same ladder as this page: addition, subtraction, times tables and division, from first facts to long division. The fifth road is fractions, up to mixed numbers, which this page does not cover. Decimals are not in Plusy. Every road, world and game is free.
When a new child starts, Plusy asks their age and plays a short first round, then opens each road at a world that fits. The times tables come in the order schools usually teach them, starting with 2, 10 and 5, and the bigger questions are worked in columns, the way they are written on paper. See the five roads and their worlds and column questions.
For a grade in particular, a grown-up can type a description such as "5th grade" or "Year 6" into AI list and get a practice list for it, or photograph the school's own sheet with Scan a worksheet. See make a list and scan a worksheet. Start free.
Questions
What math should a 3rd grader know?
By the end of 3rd grade, Common Core standard 3.OA.7 expects a child to multiply and divide within 100 fluently and to know from memory all products of two one-digit numbers. Addition and subtraction facts should already be secure from 2nd grade. States and schools vary, so check your own state's list.
When should kids know their multiplication tables?
By the end of 3rd grade in the Common Core, for products of two one-digit numbers, and by the end of Year 4 in England, for tables up to 12 × 12. Those are the same age: 8 and 9 year olds. Both describe the end of the school year.
What grade is long division taught?
The Common Core expects fluent long division with the standard algorithm by the end of 6th grade (6.NS.2). Division by two-digit numbers appears in 5th grade using place value strategies. England's national curriculum expects long division in Year 6, and short division by a one-digit number in Year 5.
What should my child know in math by the end of 2nd grade?
Common Core standard 2.OA.2 expects a child to add and subtract within 20 fluently using mental strategies, and to know from memory all sums of two one-digit numbers. That means 6 + 7 is known, not counted.
Is my child behind if they still use drawings and boxes in 4th grade?
Not by the standards. In 4th grade the Common Core asks for multiplication and division using place value strategies, shown with equations, arrays or area models. The standard algorithm for multiplication is expected by the end of 5th grade.
Do all US states follow the Common Core?
No. Each state sets its own standards. Some use the Common Core, some use an adapted version, and some use their own. The order of skills is broadly similar, but the grade for a given skill can differ, so your state's or school's own list is the one that counts.