AC9M4A02 · YEAR 4 · ALGEBRA

Multiplication and Division Facts

ACARA v9 CONTENT DESCRIPTION recall and demonstrate proficiency with multiplication facts up to 10 x 10 and related division facts; extend and apply facts to develop efficient mental strategies for computation with larger numbers without a calculator
Builds on: Finding Unknowns in Number Sentences (AC9M4A01). This unit builds fluent recall of the multiplication facts to 10 x 10 and their related division facts, then extends them into mental strategies for larger calculations.

A fact is an array

A multiplication fact can be pictured as an array: rows and columns of dots, where the total is the rows times the columns. Seven rows of eight is 7 x 8 = 56. Seeing facts as arrays gives them meaning rather than leaving them as things to chant, and it shows why each fact is a definite amount. Year 4 works towards fluent recall of all the facts up to 10 x 10, and the array picture is the foundation: every fact is the size of some rectangle of dots, which is why multiplication and area are so closely linked.

A fact as an array
A multiplication fact is an array: rows times columns gives the total.
7 rows of 8: what is 7 x 8?

Order does not matter

Multiplication is commutative: a x b always equals b x a. Turning an array on its side shows it at once — six rows of four has the same dots as four rows of six, both 24. This halves the work of learning the facts, because every fact comes as a pair: knowing 6 x 4 means knowing 4 x 6 too. Recognising that order does not change a product is one of the most useful properties in all of multiplication, and it lets a child recall a fact from whichever way round it is asked.

Order does not matter
Multiplication is commutative: a x b equals b x a, so each fact comes as a pair.
6 x 4 and 4 x 6 both equal 24: turning the array on its side does not change the total. Knowing one fact gives you its partner for free.

Division in the family

Every multiplication fact brings division facts with it, forming a fact family. From 7 x 8 = 56 come 56 divided by 8 is 7, and 56 divided by 7 is 8: dividing the product by one factor gives the other. Division is multiplication undone, so the facts are two sides of the same relationship. Knowing this means the division facts do not have to be learned separately — they fall out of the multiplication facts already known. Recalling the related division facts is exactly what the curriculum asks alongside the multiplication facts themselves.

Related division facts
Each multiplication fact has matching division facts: the product divided by a factor.
From 7 x 8 = 56, which division fact follows?

The pattern in a table

Each times table has a steady pattern: it goes up by the same step every row. The 9 times table climbs by 9 each time, the 5s by 5, and so on to 10 x 10. Seeing the step turns a list to be memorised into a pattern to be understood, making the facts easier to recall and to rebuild if forgotten. The regular step is also the link to the number patterns met elsewhere. Knowing each table's step is a reliable way towards the fluent recall of all the facts to 10 x 10 that Year 4 aims for.

A times table's pattern
Each times table grows by a fixed step, which helps you recall the facts up to 10 x 10.
The 9 times table goes up by 9 each time, all the way to 9 x 10 = 90. Spotting the step is the key to recalling the facts.

Reaching bigger numbers

The facts are not the end in themselves; they are tools for bigger calculations. Known facts extend mentally: 6 x 12 is 6 x 10 plus 6 x 2, which is 60 + 12 = 72; 7 x 9 is 7 x 10 minus 7. Splitting a number, doubling, or using a near fact lets a child compute with larger numbers without a calculator. This is the real goal of fluent facts — not recall for its own sake, but a foundation for efficient mental strategies. Extending and applying the facts this way is written into the descriptor itself.

Extending to bigger numbers
Known facts extend to larger calculations using mental strategies, no calculator needed.
Use the strategy 6 x 10 + 6 x 2 to work out 6 x 12.

The facts toolkit

Pulling the unit together, fluency means knowing the multiplication facts to 10 x 10, their related division facts, and how to extend them. A table makes the pairing clear: 7 x 8 = 56 sits beside 56 divided by 8 is 7. With facts seen as arrays, known both ways round through commutativity, paired with their division partners, organised by each table's step, and extended by mental strategies, a child has a complete toolkit for calculation. These facts underpin almost all later arithmetic, which is why fluent, confident recall matters so much in Year 4.

Facts and their partners
The multiplication facts to 10 x 10 and their division partners form the toolkit for computation.
Each multiplication fact has a division partner. Reveal each.
Quick self-check
1. What is 7 x 8?
2. If 6 x 4 = 24, then 4 x 6 equals...
3. Which division fact belongs to 7 x 8 = 56?
4. The 9 times table goes up in steps of...
5. A good mental way to work out 6 x 12 is...
Teaching pack: free to printReady-to-teach plans, student sheets, cut-outs and answers for this unit. Print or save as PDF.