Multiplication Strategies

What it means: Multiplication is putting together equal groups. When you add the same number many times, you are multiplying. We show this with numbers and pictures so the idea becomes clear.

For example, 4 + 4 + 4 is three groups of 4. We can write this as 3 × 4 = 12. The first number tells how many groups there are and the second tells how many in each group. Using repeated addition helps when you are learning tables. It also helps you check answers: if 3 × 4 = 12, you can add 4 + 4 + 4 to see 12.

Children should practise making simple sums into multiplication sentences. They should also learn that multiplication gives the same result no matter the order of factors (this is the commutative idea). Picture drawings of circles or boxes each holding the same number of objects are useful tools to move from adding to multiplying.

What is an array? An array is a neat picture made of rows and columns. It shows equal groups in a rectangle and helps make multiplication visible. When children draw arrays they can count faster because the objects are arranged in order. An array gives a clear link between a multiplication sentence and a shape made of objects.

To create an array, decide how many rows and how many columns you need. For 3 × 4 draw three rows with four items in each row. Count across each row or down each column to find the total. A 3 by 4 array has 12 items. Arrays also show the same fact in two ways: the 3 by 4 rectangle turned on its side becomes a 4 by 3 rectangle. This is a visual proof of the commutative property: rows × columns = columns × rows.

Use blocks, coins or small stickers to build arrays. Ask children to write the multiplication sentence that matches each array. Arrays are also helpful when breaking a larger multiplication into smaller parts: two smaller arrays placed side by side can be added to give one larger product. Practise drawing arrays for different tables and encouraging learners to count by rows or by columns to find products quickly.

Number line method: A number line helps children see multiplication as jumps along a line. Place numbers in order from 0 and make equal jumps. Each jump adds the same number. For 4 × 3, start at 0 and make four jumps of three. The point you land on is the product. Drawing jumps shows how groups of the same size move you forward step by step.

Number lines are useful for small products and for showing what happens when numbers grow. They also allow children to use left-to-right thinking, which many find natural. Number line drawings can be used to show doubling or combining jumps: two jumps of 6 equal one jump of 12, for example. This visual link supports mental strategies.

Skip counting: Skip counting is the spoken form of the number line. When you count by twos you say 2, 4, 6, 8. Counting by fives gives 5, 10, 15. Skip counting turns multiplication facts into patterns and rhythms, which are easier to remember. Ask children to use fingers, claps or stepping stones to practise skip counting. Combine skip counting with arrays or objects so the counting has a real reference. Over time skip counting and number-line jumps help children answer multiplication questions mentally and check answers quickly.

Grouping: Grouping means putting items into equal piles or sets. It is a concrete way to understand multiplication because learners can touch and move objects. Give children counters or small toys and ask them to make, for example, four groups with three items in each group. Counting all groups gives the product and shows how repeated addition works in real life.

Grouping is useful for classroom tasks like making teams, packing boxes or sorting sweets. Show how a picture of groups can be written as a multiplication sentence. For instance, five groups of four pencils is 5 × 4. Encourage children to write the number of groups first and the size of each group second to match the picture to the sentence.

Equal shares and checking: Grouping also links to fair sharing. If you have 12 stickers and you share them equally into 3 groups, each group will have 4. This shows that 3 × 4 = 12 and connects multiplication with division. Teach students to check multiplication by making groups again or by adding each group to see if the total matches. Practising grouping with different objects helps children pick correct multiplication sentences and understand why multiplication is useful for everyday problems.

Commutative idea: One helpful rule in multiplication is that factors can be swapped. If you know 3 × 7 = 21 then you also know 7 × 3 = 21. Teach children to look for the easier order to multiply. For example, if a child finds 2 × 9 easier than 9 × 2 they can swap the order and get the same answer. Showing this with arrays or objects makes the idea clear: turn the rectangle and the number of rows becomes columns.

Known facts: Children build speed by remembering small multiplication facts such as the twos, fives and tens. These known facts become tools to find new answers. For instance, if a child knows 3 × 4 = 12 and 3 × 2 = 6 they can add these to get 3 × 6 = 18. This is a simple use of splitting a number into parts and using addition of known products.

Teach learners to break a harder multiplication into smaller known facts. Use examples like 6 × 7 = (6 × 5) + (6 × 2). Practise swapping factors, breaking numbers, and combining results. These mental strategies reduce the need to rely only on rote memory and make solving problems faster and more flexible.

Doubling: Doubling means multiplying by two. It is a fast mental tool because children can often picture doubling objects or use fingers. For example, double 7 gives 14. Doubling helps when a factor is 2, 4 or 8 because these can be made by repeated doubling. For instance, to do 4 × 6 a child can double 6 to get 12 and double 12 to get 24.

Halving: Halving is the reverse of doubling and is useful when one factor is even. If a factor is large but even, halving that factor and doubling the other factor keeps the product the same and might make the multiplication easier. For example, 6 × 9 can be changed to 3 × 18 by halving 6 to 3 and doubling 9 to 18. If a child knows 3 × 18 = 54, the original product is found quickly.

Teach children simple rules: doubling an even number is quick; halving only works cleanly when the number is even. Use objects to double groups and split groups in half to show halving. Give practice problems that invite students to decide when to double or halve. This strategy builds number sense and supports solving facts beyond immediate recall.

Place value trick: Multiplying by 10 or 100 uses the idea of place value. Each time you multiply by 10 every digit moves one place to the left: ones become tens, tens become hundreds. For whole numbers this is the same as placing a zero at the end. For example 7 × 10 = 70 and 12 × 10 = 120. Multiplying by 100 moves digits two places left, which is like adding two zeros: 12 × 100 = 1200.

Children should practise this with charts showing ones, tens and hundreds. Use physical counters grouped into tens to show how a group of 12 items becomes 12 tens when multiplied by 10. Link the rule to real situations such as selling packets of 10 pens or 100 stickers. Explain that multiplying by 10 or 100 is different from multiplying by other numbers because it only shifts place value; digits do not change except their position.

Combine place value with other methods: to find 12 × 6 a child might use 12 × (5 + 1) = 12 × 5 + 12 × 1, or compute 6 × 12 as (6 × 10) + (6 × 2). Practise such splits so learners see several ways to use place value in multiplication. This makes calculations faster and gives a good checking tool for answers found by other strategies.

Word problems: Short story problems make multiplication useful and help children practise choosing a method. Teach a five-step habit: read the problem, find how many equal groups there are, decide how many in each group, write the multiplication sentence, and calculate the answer. Encourage drawing groups, arrays or number lines to set up the problem so the sentence is clear.

Use familiar contexts: trays of cupcakes, school benches, boxes of pencils or rows of plants. Ask students to underline the numbers that show groups and group size. Show how to write the multiplication sentence that matches the drawing. After finding an answer teach checking methods: add the groups again, use division to reverse the multiplication (for example check 4 × 5 = 20 by seeing 20 ÷ 5 = 4), or estimate by rounding numbers to see if the product is reasonable.

Checking helps avoid mistakes made by careless counting or wrong setup. Give practice with different question types: pure multiplication, mixed arrays, and problems that need splitting numbers into parts. Praise neat work and clear labelling of units (pens, apples, chairs). Over time students will learn to pick a strategy that makes the problem easiest to solve and to check their answers confidently.