Multiplication by Partitioning
Multiplication by Partitioning
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Multiplication by Partitioning
Central question: how can partitioning make larger multiplication facts easier to work out accurately? Learning objective: I can multiply using partitioning with 2-, 3- and 4-digit numbers.
Our learning goal
I can multiply using partitioning with 2-, 3- and 4-digit numbers.
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What words come to mind when you hear partitioning in multiplication?
Use this to surface prior knowledge such as split, parts, tens, hundreds, easier, add, multiply and place value.
What is partitioning?
Partitioning means splitting a number into parts.
For multiplication, we split a large number into tens, hundreds and thousands so each part is easier to multiply.
Example: 34 = 30 + 4
Keep the focus on place value. Students should see that partitioning uses what they already know about tens and ones, then extends to hundreds and thousands.
Why partitioning helps
turns one hard calculation into smaller ones
uses known multiplication facts
helps organise place value clearly
makes written working easier to check
works with 2-, 3- and 4-digit numbers
Link to Year 4 fluency: children often know 3 × 4 or 6 × 7, but partitioning helps them apply these facts inside larger calculations.
Start with a 2-digit number
23 × 4
23 = 20 + 3
20 × 4 = 80
3 × 4 = 12
80 + 12 = 92
Model each line slowly. Emphasise that the number is split first, each part is multiplied, then the partial products are added.
The steps to follow
Partition the number.
Multiply each part.
Add the answers together.
This method works the same way each time.
Encourage students to say the routine aloud: partition, multiply, add. This consistent language supports later slides.
Another 2-digit example
46 × 3
46 = 40 + 6
40 × 3 = 120
6 × 3 = 18
120 + 18 = 138
Point out that 40 × 3 uses 4 tens × 3 = 12 tens = 120. This helps avoid children writing 12 instead of 120.
What is the correct order for partitioning multiplication?
Multiply, add, partition
Partition, multiply, add
Add, partition, multiply
Partition, add, multiply
Checks the routine from slides 4 to 6: partition first, multiply each part, then add the partial products.
Complete the 2-digit method
To work out 46 × 3 by partitioning, split 46 into 40 + 6. Then multiply each part to get 120 and 18. Finally, add the partial products to make 138.
All blanks come directly from the worked 2-digit example and the routine taught in this subtopic.
Moving to 3-digit numbers
A 3-digit number can be split into hundreds, tens and ones.
Example:
324 = 300 + 20 + 4
Then multiply each part before adding them together.
This slide marks the transition from 2-digit to 3-digit numbers. Keep the method unchanged so the new challenge is only the extra place value part.
A 3-digit example
324 × 2
300 × 2 = 600
20 × 2 = 40
4 × 2 = 8
600 + 40 + 8 = 648
Ask pupils to notice that each part keeps its value: 300 stays in the hundreds, 20 stays in the tens, and 4 stays in the ones until the final addition.
Keeping place value clear
When multiplying a partitioned number:
hundreds stay as hundreds
tens stay as tens
ones stay as ones
This helps stop place value mistakes.
Common misconception: students may multiply digits without place value, for example treating 30 × 4 as 12 instead of 120. Reinforce the value of each part.
Another 3-digit example
213 × 4
200 × 4 = 800
10 × 4 = 40
3 × 4 = 12
800 + 40 + 12 = 852
Draw attention to the zero in the tens place when partitioning 213. It can be written as 200 + 10 + 3, which keeps the structure tidy.
In 324 × 2, what is 20 × 2?
4
40
24
400
Targets the place value point that tens stay as tens. A common error is treating 20 × 2 as 4.
Complete the 3-digit example
A 3-digit number can be split into hundreds, tens and ones. In 213 × 4, the partial products are 800, 40 and 12. When you add them, the answer is 852.
Reinforces both structure and accuracy from slides 7 to 10.
How would you explain 213 × 4 using partitioning?
Look for these elements in pupil answers: partition 213 into 200, 10 and 3; multiply each part by 4; keep place value clear; add 800, 40 and 12 to make 852.
Now try 4-digit numbers
A 4-digit number can be split into:
thousands
hundreds
tens
ones
Example: 2,431 = 2,000 + 400 + 30 + 1
Keep confidence high by stressing that the method has not changed; only one more place value part has been added.
A 4-digit example
1,234 × 2
1,000 × 2 = 2,000
200 × 2 = 400
30 × 2 = 60
4 × 2 = 8
2,000 + 400 + 60 + 8 = 2,468
Read the number carefully with students so they hear the place values: one thousand, two hundred, thirty-four.
Lining up the parts
Good layout helps you check your work.
Write each partial product clearly, then add them carefully:
2,000 + 400 + 60 + 8
This slide is about presentation supporting accuracy. Encourage one line per partial product for children who need structure.
Another 4-digit example
3,021 × 3
3,000 × 3 = 9,000
20 × 3 = 60
1 × 3 = 3
9,000 + 60 + 3 = 9,063
Useful example because it includes a zero hundreds digit. You can mention that the missing hundreds part does not change the method.
One method, bigger numbers
The same pattern works every time:
partition → multiply each part → add the parts
The number may be bigger, but the method stays the same.
This slide resolves the lesson arc by showing that partitioning is a scalable method, not a separate trick for each size of number.
Which partition is correct for 2,431?
2,000 + 400 + 30 + 1
2,000 + 40 + 30 + 1
200 + 400 + 30 + 1
2,000 + 431
Checks secure understanding of thousands, hundreds, tens and ones before multiplying.
Complete the 4-digit method
In 1,234 × 2, the number is split into 1,000, 200, 30 and 4. The partial products are 2,000, 400, 60 and 8. When they are added, the total is 2,468.
Echoes the exact method from the 4-digit worked example and keeps the focus on place value.
Which part of partitioning helps you most?
Splitting the number
Multiplying each part
Adding the parts
Lining up neatly
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What is one thing you will remember about partitioning?
Encourage pupils to mention one clear takeaway, such as splitting into place value parts, multiplying each part, or checking by adding partial products.
Which part of today’s lesson felt hardest for you?
Use responses to identify misconceptions or steps pupils still find difficult, especially place value errors with tens, hundreds or thousands.
Glossary
partitioning - splitting a number into smaller place value parts
place value - the value of a digit because of its position in a number
digit - one numeral from 0 to 9 used to make numbers
multiply - to find the total in equal groups
product - the answer to a multiplication calculation
partial product - the answer from multiplying one part of a partitioned number
ones, tens, hundreds, thousands - place value columns in whole numbers
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