Multiplication and division: maths lessons by year

Lessons to watch

Make groups of the same size, then count them by skip counting.

Add the same number again and again: 3 lots of 4 is 4 + 4 + 4.

Doubling: Adding a number to itself, and knowing doubles by heart.
Halving: Splitting a number into two equal halves.
Multiplication facts: How multiplication facts belong together, and how one gives you others.
Times tables: Knowing the times tables by heart, up to 12 × 12.
Sharing equally: Dividing by sharing things out fairly, one at a time.
Dividing into groups: Dividing by making groups of the same size and counting them.
Division facts: Using times tables to divide, such as 4 × 5 = 20 so 20 ÷ 5 = 4.
Short division: Dividing bigger numbers by a one-digit number, written step by step.
Long division: Dividing by a two-digit number, written step by step.

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

Share equally (fair shares). Share objects one at a time so each group gets the same amount.

Make equal groups. Put objects into groups of the same size and say how many groups and how many in each.
Double numbers to 20. Double small numbers using objects, fingers or known facts.
Count equal groups by skip counting. Find the total of equal groups by counting in 2s, 5s or 10s.

Multiplication as repeated addition. Write equal groups as a repeated addition and as a multiplication.
Arrays: rows and columns. Use rows and columns of objects to show and solve multiplication.
Write multiplication sentences with x and =. Record equal groups and arrays as multiplication number sentences.
Multiplication in any order. See from arrays that 3 x 4 = 4 x 3, while division cannot be swapped.
Halve even numbers to 20. Split an even number into two equal halves.
The 2 times table. Learn and recall the 2 times table and link it to doubling.
The 10 times table. Learn and recall the 10 times table and link it to place value.
The 5 times table. Learn and recall the 5 times table and link it to the 10s.
Division as grouping. Find how many groups of a given size fit into a number.
Division facts for 2, 5 and 10. Use the 2, 5 and 10 tables to answer division facts.
Multiplication and division word problems. Solve simple equal-group and sharing problems in everyday contexts.

The 3 times table. Learn and recall the 3 times table.
The 4 times table. Learn the 4 times table by doubling the 2s.
The 8 times table. Learn the 8 times table by doubling the 4s.
The 6 times table. Learn the 6 times table by doubling the 3s.
The 9 times table. Learn the 9 times table and its patterns.
The 7 times table. Learn the 7 times table using facts already known from other tables.
Multiply by 0 and 1. Know that a number times 1 stays the same and a number times 0 is 0.
Fact families for multiplication and division. Write the four related facts from one multiplication fact.
Find the missing number in x and ÷ sentences. Work out the unknown in sentences like 6 x ? = 42 or ? ÷ 3 = 5.
Multiply a multiple of 10 by a one-digit number. Use a known fact to work out products like 4 x 30.
Multiply a two-digit number by a one-digit number. Partition into tens and ones and multiply each part, e.g. 23 x 4.
Two-step problems with all four operations. Solve problems that need two steps using any of +, -, x and ÷.

Recall all times-table facts. Recall mixed multiplication and division facts up to 10 x 10.
The 11 and 12 times tables. Learn and recall the 11 and 12 times tables.
Multiply three numbers. Multiply three numbers by choosing a helpful pair first.
Multiply and divide by 10, 100 and 1000. Shift digits left or right to multiply or divide whole numbers by 10, 100 or 1000.
Partition to multiply mentally. Split a number into tens and ones to multiply in your head, e.g. 14 x 6.
Grid (area) method for multiplication. Use a grid or area model to multiply two- and three-digit numbers by one digit.
Short multiplication: three digits by one digit. Use the column method to multiply a three-digit number by a one-digit number.
Short division with no remainder. Use the short (bus stop) method to divide two- and three-digit numbers by one digit.
Division with remainders. Divide when the amount does not share equally and record what is left over.
Times as many: comparison problems. Solve problems that say one amount is a number of times another.
Correspondence problems. Solve 'how many combinations' problems, e.g. 3 shirts and 4 hats.

Short division of four-digit numbers with remainders. Divide numbers up to four digits by one digit using short division.
Interpret remainders in word problems. Decide whether to round up, round down or ignore a remainder in context.
Write remainders as fractions or decimals. Express the remainder of a division as a fraction or decimal.
Long multiplication by a two-digit number. Multiply numbers up to four digits by a two-digit number using the column method.
Multiply and divide mentally with known facts. Use facts and place value for calculations like 7 x 800 or 4200 ÷ 6.
Divide by a two-digit number using chunking. Divide up to four-digit numbers by two-digit numbers by taking away groups.

Long division by a two-digit number. Use formal long division with a two-digit divisor and interpret remainders.