Multiplication Tables to 12 × 12
Multiplication Tables to 12 × 12
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Multiplication Tables to 12 × 12
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Learning goal
I can recall and use multiplication tables up to 12 × 12 with increasing speed and accuracy.
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One word or fact you link with multiplication tables
Use this to surface prior knowledge such as groups, doubling, 5s, 10s, arrays or quick facts. Invite a few students to explain their word.
What multiplication means
Multiplication shows equal groups
It can also mean repeated addition
3 × 4 means 3 groups of 4
So 3 × 4 = 4 + 4 + 4 = 12
Stress that multiplication is not just a fact to memorise; it has meaning. Link the first number to the number of groups and the second number to the size of each group.
Equal groups in number sentences
A multiplication sentence matches a group model.
2 × 5 = 2 groups of 5
4 × 3 = 4 groups of 3
6 × 2 = 6 groups of 2
The total is found by adding the equal groups
You may want to draw quick group sketches or arrays while reading each example aloud. Keep the wording consistent: 'groups of'.
Repeated addition patterns
Repeated addition helps us build each table.
5 × 3 = 3 + 3 + 3 + 3 + 3
4 × 6 = 6 + 6 + 6 + 6
Each step adds the same amount again
This creates a pattern in the answers
Point out that repeated addition is useful for understanding, but recall should become quicker over time. This prepares students for seeing patterns in tables.
Arrays show multiplication clearly
Rows and columns make equal groups easy to see
3 rows of 4 shows 3 × 4
The same array can also show 4 × 3
Arrays help us notice useful patterns
Use the array to bridge into commutativity on the next slides. Students often grasp table facts more securely when they can visualise rows and columns.
What does 3 × 4 mean?
3 groups of 4
4 groups of 3
3 add 4
4 less than 3
Tests the meaning of multiplication from the equal-groups slides. '4 groups of 3' is a useful distractor because it gives the same product but not the meaning of the original sentence.
Complete the ideas about multiplication
Multiplication shows equal groups. It can also mean repeated addition. In an array, rows and columns help us see the pattern clearly.
Echoes the wording from slides 2 to 5 and checks the key vocabulary in context.
Using multiplication tables
Multiplication tables list facts in a pattern.
The 2, 5 and 10 tables are often used most
Secure recall means knowing facts without counting each time
Fast recall helps with mental maths and written methods
The full set goes up to 12 × 12
This slide opens the main table-focus part of the lesson. Emphasise that some facts are used very often, but all facts to 12 × 12 matter.
Commonly used facts
Some facts appear again and again.
2s double a number
5s end in 0 or 5
10s add a zero to a whole number
Knowing these well helps with harder facts
Keep language simple: students do not need place value detail beyond 'add a zero' at this level, unless you choose to expand orally with whole-number examples.
The 10 times table
The 10 times table has a simple pattern.
1 × 10 = 10
4 × 10 = 40
9 × 10 = 90
Each product is ten groups of the number
Link back to equal groups: 4 × 10 is 4 groups of 10 or 10 added four times, depending on how you phrase it. Keep one interpretation stable if students are unsure.
The 5 times table
The 5 times table also has a clear pattern.
Products end in 0 or 5
5, 10, 15, 20, 25...
It is half of the 10 times table
Example: 6 × 5 = 30 and 6 × 10 = 60
A useful oral link is 'multiply by 10, then halve' for ×5. Keep this concrete with one or two examples only.
Commutativity
In multiplication, order does not change the product
3 × 7 = 7 × 3
This means one fact can help with another
Arrays show why this works
Use the term commutativity, but explain it in plain language. This is one of the most powerful strategies for reducing the number of facts students feel they must memorise.
Turn known facts around
Commutativity helps us use facts we already know.
If you know 4 × 8 = 32
then you also know 8 × 4 = 32
If one fact is secure, its partner fact is secure too
This is a good place to remind students that multiplication has fewer separate facts than it first appears because of turned-around pairs.
Which fact shows commutativity?
6 × 5 = 30
7 × 3 = 21
4 × 8 = 8 × 4
9 × 10 = 90
Checks the idea that turned-around factors keep the same product, not just that a multiplication fact is correct.
Complete the table patterns
The 10 times table has a simple pattern and its products are ten groups of a number. The 5 times table ends in 0 or 5 and is half of the 10 times table. Because of commutativity, 4 × 8 and 8 × 4 have the same product.
Brings together the patterns in 5s and 10s with the turned-around fact strategy.
Square numbers
Square numbers come from a number multiplied by itself.
1 × 1 = 1
4 × 4 = 16
7 × 7 = 49
12 × 12 = 144
You can mention that these sit on the diagonal of a multiplication grid. Many students find square numbers easier to remember as anchor facts.
Patterns across the tables
The 2 times table counts in 2s
The 5 times table counts in 5s
The 10 times table counts in 10s
Patterns help us predict the next product
Keep the focus on number patterns that directly support recall, not on extending into unrelated sequences.
Known facts help with new facts
A less familiar fact can be worked out from a familiar one.
Know 6 × 5 = 30
Then 6 × 6 = 30 + 6 = 36
Know 7 × 10 = 70
Then 7 × 5 is half of that: 35
This is the key strategy slide. Make clear that known facts act as stepping stones to less secure facts.
Build from nearby facts
We can adjust from a fact we know well.
8 × 4 = 32, so 8 × 3 = 32 - 8 = 24
9 × 5 = 45, so 9 × 6 = 45 + 9 = 54
This saves time when recall is not instant
Encourage efficient thinking, not counting in ones. Students should see multiplication facts as connected rather than separate.
If 7 × 10 = 70, what is 7 × 5?
75
35
14
65
Uses the strategy slide: ×5 is half of ×10 for the same first factor.
Use known facts to help
A square number comes from a number multiplied by itself. A less familiar fact can come from a known fact. For example, if 8 × 4 = 32, then 8 × 3 = 24 by subtracting 8.
Checks two ideas from this block: square numbers and adjusting from a nearby secure fact.
Division is the inverse
Division is linked to multiplication.
If 4 × 6 = 24
then 24 ÷ 6 = 4
and 24 ÷ 4 = 6
These facts belong to the same fact family
Use the phrase 'inverse' and immediately connect it to undoing multiplication. Keep examples within secure table facts.
Fact families
A fact family uses the same three numbers
Example: 3, 8, 24
3 × 8 = 24
24 ÷ 8 = 3
You can also mention 8 × 3 = 24 and 24 ÷ 3 = 8 aloud, even though the slide keeps the set compact.
Use multiplication to divide
Knowing multiplication facts makes division quicker.
To solve 36 ÷ 6, think: 6 × ? = 36
Since 6 × 6 = 36, the answer is 6
To solve 42 ÷ 7, think: 7 × ? = 42
This is an important mental strategy: division questions can often be solved by recalling a multiplication fact rather than using repeated subtraction.
Accuracy and speed together
Good table knowledge means:
answers are correct
recall is quick
patterns and strategies are used
multiplication and division facts are linked
Keep the message balanced: speed matters, but only with accuracy. Students should feel that strategy supports speed, not that speed replaces understanding.
Which division fact matches 4 × 6 = 24?
24 ÷ 6 = 4
24 ÷ 4 = 24
6 ÷ 24 = 4
24 ÷ 6 = 6
Checks inverse understanding and fact-family links. The distractors reflect common reversal errors.
Complete the fact family idea
Division is the inverse of multiplication. A fact family uses the same three numbers. To solve 36 ÷ 6, we can think of the multiplication fact 6 × 6 = 36.
Reinforces the language and the mental strategy for using multiplication to divide.
What helped you most in this lesson?
Students may mention equal groups, repeated addition, arrays, 5s and 10s patterns, commutativity, square numbers, using known facts, or inverse facts with division.
What is one fact or strategy you will remember?
Students may mention a specific table, remembering turned-around facts, using division, or working out less familiar facts from known ones.
Glossary
multiplication - finding the total of equal groups
equal groups - groups with the same number in each group
repeated addition - adding the same number again and again
array - a set of rows and columns used to show multiplication
commutativity - when numbers can change order and keep the same product
square number - the result of a number multiplied by itself
inverse - an operation that undoes another operation
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Glossary
division - sharing into equal groups or finding how many groups there are
product - the answer to a multiplication calculation
factor - a number multiplied by another number
fact family - related multiplication and division facts using the same numbers
times table - a set of multiplication facts for one number
pattern - a repeated rule or order in numbers
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