Addition and subtraction: maths lessons by year

Lessons to watch

How to add small numbers by counting on

Start at the first number and count on, one jump at a time.

How to add bigger numbers in columns

Line the numbers up by place, then add the ones, then the tens, then the hundreds.

How to add with regrouping

When a column makes ten or more, write the ones and carry the ten to the next column.

How to take away small numbers by counting back

Start at the first number and count back, one jump at a time.

How to subtract bigger numbers in columns

Line the numbers up by place, then take away the ones, then the tens.

How to subtract with regrouping

When the top digit is too small, change one ten into ten ones, then take away.

How to make ten to add

Use ten as a stepping stone: fill up to ten first, then add the rest.

Sheets only, lesson coming

Number bonds: The pairs that make a number, such as 3 and 7 making 10.
Finding the missing number in adding: Finding the number that is missing from an addition.
Finding the missing number in taking away: Finding the number that is missing from a subtraction.

What's taught, year by year

The steps in addition and subtraction, in the order children usually meet them. Years are named as in Australia; the ages are a guide.

Before school ages 3–5

Add one more or take one away (to 5). Change a small group by adding one or taking one away and say the new amount.

Foundation ages 5–6

Add by putting two groups together (within 10). Join two groups of objects and count them all to find the total.
Take away and count what is left (within 10). Remove some objects from a group and count how many remain.
Part-part-whole: split a number up to 10. Break a number up to 10 into two parts in different ways.
Number bonds to 5. Know all the pairs of numbers that make 5.
Make 10: find the partner number. Find the number that goes with a given number to make 10, using a ten frame.
Addition and subtraction stories (within 10). Act out and solve simple join and take-away stories with objects or drawings.

Year 1 ages 6–7

Write addition and subtraction sentences. Record a picture or story using +, - and = in a number sentence.
Count on to add (within 20). Start from the bigger number and count on to find a total.
Count back to subtract (within 20). Count back from a number to take some away.
Find the difference: how many more?. Compare two numbers and count up to find how many more or fewer.
Turn-around facts (addition in any order). See that 3 + 5 and 5 + 3 give the same total, but subtraction cannot be swapped.
Number bonds to 10 and related subtraction. Know pairs that make 10 and use them to subtract from 10.
Number bonds to 20. Use bonds to 10 to know pairs that make 20 and the related facts.
Doubles and near doubles. Use double facts like 6 + 6 to work out 6 + 7.
Add by bridging through 10. Split the second number to make 10 first, e.g. 8 + 5 = 8 + 2 + 3.
Subtract by bridging back through 10. Take away in two steps through 10, e.g. 13 - 5 = 13 - 3 - 2.
Fact families for addition and subtraction. Write the four related facts that use the same three numbers.
Find the missing number. Work out the unknown in sentences like 7 + ? = 12 or ? - 4 = 9.
Add three single-digit numbers. Add three small numbers, looking for pairs that make 10 or doubles first.
Word problems: join, separate and compare (within 20). Choose to add or subtract to solve one-step problems within 20.
Add and subtract multiples of 10. Use known facts to add and subtract tens, e.g. 40 + 30 or 70 - 20.
Add ones or tens to a two-digit number. Add a one-digit number or a multiple of ten to a two-digit number.

Year 2 ages 7–8

Recall addition and subtraction facts to 20. Know all sums and differences within 20 quickly from memory.
Add two two-digit numbers (no regrouping). Add two two-digit numbers where the ones total less than 10.
Add two two-digit numbers (with regrouping). Add two-digit numbers where the ones make a new ten.
Subtract two-digit numbers (no regrouping). Subtract a two-digit number where no ten needs breaking.
Subtract two-digit numbers (with regrouping). Subtract when a ten must be exchanged for ten ones.
Split strategy: partition to add and subtract. Add or subtract the tens and ones separately, then combine.
Jump strategy on an empty number line. Add or subtract in jumps of tens and ones along a blank number line.
Add several two-digit numbers. Add three or four two-digit numbers using place value.
Check with the inverse operation. Check a subtraction by adding back, and an addition by subtracting.
Two-step addition and subtraction problems. Solve word problems that need two steps of adding or subtracting.
Column addition of three-digit numbers (no regrouping). Line up hundreds, tens and ones and add each column.

Year 3 ages 8–9

Column addition with regrouping (three digits). Use the column method, carrying a ten or a hundred into the next column.
Column subtraction with exchanging (three digits). Use the column method, exchanging a ten or hundred when needed.
Subtract across zeros. Subtract from numbers like 503 by exchanging through the zero.
Add and subtract ones, tens or hundreds mentally. Add or subtract ones, tens or hundreds to a three-digit number in your head.
Compensation: add 9 or 19 by adjusting. Add 10 or 20 and then take 1 away (and similar) to calculate quickly.

Year 4 ages 9–10

Column add and subtract four-digit numbers. Use column methods with numbers up to four digits.
Multi-step word problems: choose the method. Decide which operations and methods to use in two- and three-step problems.

Year 5 ages 10–11

Add and subtract numbers with more than four digits. Use column methods with five- and six-digit numbers.
Mental addition and subtraction with large numbers. Use place value to add and subtract large round numbers mentally, e.g. 12 500 + 3 000.