ACARA v9 CONTENT DESCRIPTION “develop efficient strategies and use appropriate digital and other tools to recall multiplication facts and related division facts, and to multiply and divide using arrays, partitioning and the commutative and distributive properties”
Multiplication is repeated equal groups, and the clearest picture of it is an array: equal rows of objects. Three rows of four dots is 3 times 4, and counting them gives twelve. The array turns a fact into a shape, where the answer is the rows multiplied by the columns. Year 4 work is to recall these facts quickly, but quick recall rests on understanding what a fact means. Seeing 6 times 7 as six rows of seven, rather than a mystery to memorise, is what makes the facts stick and what every strategy in this unit builds on.
Multiplication is an array
A multiplication fact is equal rows of objects, counted as rows times columns.
3 rows of 4 dots. How many dots in all?
Order does not change it
The first powerful idea is that multiplication can be done in any order: 3 times 5 equals 5 times 3. Turning an array a quarter turn shows why — three rows of five and five rows of three are the same dots counted two ways, both fifteen. This is the commutative property, and it nearly halves how many facts must be learned, because every fact comes as a matching pair. Knowing 8 times 4 means knowing 4 times 8 for free. Recognising that order does not matter is the first strategy that turns a long list of facts into a much shorter one.
Order does not matter
Turning an array shows that a times b equals b times a.
3 rows of 5 makes 15. Turn the array a quarter turn and count again.
Splitting a hard fact
A fact that is hard to recall can be split into two easy ones. To find 7 times 6, split the six into five and one: 7 times 5 is 35, plus one more 7 is 42. Splitting an array with a line shows the two easy parts that add to the whole. This is the distributive property, and it turns any tricky fact into facts a child already knows — usually the fives and the small facts. Rather than memorising every fact in isolation, splitting lets a child rebuild a forgotten fact from sure ones, which is faster and far more reliable.
Split a hard fact
A hard fact can be split into two easy ones and added.
A tricky fact: 7 x 6. Split it into easier parts.
Factors as rectangles
The factors of a number are the whole numbers that divide it exactly, and they come in pairs that each make a rectangle. Twelve can be one by twelve, two by six or three by four, so its factors are 1, 2, 3, 4, 6 and 12. Seeing factor pairs as rectangles connects multiplication to division: if three by four makes twelve, then twelve shared into three rows gives four. Knowing the factor pairs of the numbers up to a hundred is part of fluent multiplication, and it is the same array idea read backwards — from the product to the sides that make it.
Factor pairs
The factor pairs of a number are the rectangles that make it.
12 can be made as 1 x 12. Every factor pair is a rectangle of 12 squares; the factors of 12 are the side lengths that work.
Leaning on a round fact
Facts near a round number are easy if you start from the round fact and adjust. To find 9 times 6, use 10 times 6, which is 60, then take away one 6 to get 54. To find 19 times 3, use 20 times 3 and subtract a 3. The tens are the easiest facts of all, so leaning on a nearby ten and stepping back is a fast strategy for the nines and other near-multiples. This is the same splitting idea in another form: build the fact you want from a fact you find easy, then make a small adjustment.
Use a near multiple
A fact near a round number is found from the round fact, then adjusted.
9 is close to 10. Use the round fact, then adjust.
Facts worth knowing by heart
With arrays to picture a fact, order to halve the list, splitting and near-multiples to rebuild the hard ones, and factor pairs to link to division, the multiplication facts become a small, connected set rather than a hundred things to memorise. A strip of the times table shows each fact growing by the base number, the repeated adding underneath made quick. The goal of Year 4 is genuine fluency: recalling the facts fast, but always with a strategy to fall back on when memory slips. These facts and strategies are the engine for all the multiplying, dividing and fraction work that follows.
A times-table strip
A row of the times table grows by the base number each step.
Each fact has a product. Reveal them and watch each one grow by the base.
Quick self-check
1. What is 6 x 7?
2. Because order does not change a product, 4 x 8 is equal to...
3. A good way to work out 7 x 6 is to split it into...