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Expanded Column Method

What is the expanded column method?

The expanded column method of addition is an intermediate step between adding numbers by partitioning and using the formal column method of addition.

There is also an expanded column method of multipication which is an intermediate step between multiplying numbers by partitioning and the formal column method of multiplication.

How does the expanded column method work? (addition)  

The expanded column method is so called because each part of the addition is 'expanded' and recorded. This is in contrast to the 'compact' column method that children will eventually be taught to use. The expanded column addition method is effective because it ensures that when children move on to the compact method, they actually understand what they are doing in each step rather than simply learning a process by rote.

Let's look at 36 + 23 as an example.

Step 1: Add the ones  
expanded column method ones
Step 2: Add the tens  
expanded column method tens
Step 3: Find the total  
expanded column method total

Here is an example of the expanded column method used to add two three-digit numbers:

expanded column method HTO

Ideas for using the expanded column method (addition)  

It is likely that children will first be introduced to the expanded column method in Year 3. They will have a lot of experience at adding two-digit numbers by partitionin them into tens and ones from KS1. Children will be familiar with using place value equipment (such as base 10, straws or place value counters) to help them add two-digit numbers.

Therefore, when starting to use the expanded column method, children should have access to these resources to support their calculations.

Base 10

How does the expanded column method work? (multiplication)  

The expanded column method is so called because each part of the multiplication is 'expanded' and recorded. This is in contrast to the 'compact' column method for multiplication that children will eventually be taught to use. Again, the benefit of the expanded column multiplication method is that it helps children understand what is happening at each stage when they move on to the compact method.

Let's look at 16 x 3 as an example.

Step One: Multiply the ones
expanded column method multiplication
Step Two: Multiply the tens
expanded column method multiplication
Step Three: Find the total
expanded column method multiplication

When are children taught the expanded column method?

Children are required by the National Curriculum to be taught the column method of additon in Year 3. Therefore, it is likely that children will be introduced to the expanded colum method for addition in lower KS2 to support them understanding the compact method.

The National Curriculum requires children to be taught the formal column method for multipliciationm in Year 4 (1-digit x 2-digit) and states that children should move towards a formal method in Year 3. Therefore, they will be introduced to the expanded column method within lower KS2.

LESSON PACK Methods of Addition - The Expanded Method


LESSON PACK What's the Total? Decomposition and Expanded Methods


LESSON PACK Mental and Written Addition - Formal Column Methods