How to teach multiplication

Begin with equal groups and arrays so the meaning is clear, then connect multiplication to repeated addition. Drill one times table at a time to automatic recall before mixing tables, then move to two-digit by one-digit multiplication and finally long multiplication.

Multiplication is usually introduced in Grade 2 with equal groups and arrays, and develops through Grade 5. The times tables are learned across Grades 2 to 4, and formal long multiplication of larger numbers typically comes in Grades 4 and 5, once table facts are fluent.

Start with arrays and equal groups of real objects so children see that 3 times 4 means three groups of four. Link it to repeated addition, then use skip counting to build each table. Concrete and visual first, memorised facts second, keeps the meaning attached to the numbers.

Addition combines any amounts, while multiplication is repeated addition of equal groups only. So 3 times 4 means 4 plus 4 plus 4, which is three equal groups of four. Because the groups must be equal, an array of rows and columns is the clearest picture of multiplication.

Often the times-table facts have been memorised by rote without understanding equal groups, so they break down under pressure. Place-value slips cause errors in two-digit multiplication, and adjacent facts like the 6s, 7s and 8s get confused. Rebuild meaning with arrays, then drill one table at a time.

An array is a rectangle of objects set out in equal rows and columns, such as 3 rows of 4 counters. It shows multiplication visually: counting the rows and columns gives the two factors, and the total is the product. Arrays also show that 3 times 4 equals 4 times 3.

Division is the natural next step, because it is the inverse of multiplication and shares the same fact families. Fluent times tables also underpin fractions, factors, area and long multiplication, so secure multiplication facts make almost all later maths quicker and less error-prone.