When I first heard of the split strategy and my child’s inadequacy of being able to perform it, my first reaction was, “ Split what?? ” It can seem like a convoluted means of being able to add numbers, but there’s a method to the mathematical madness.
The split strategy is a mathematical technique to help your child add larger numbers: two-digit numbers and up. It is a technique that helps your child to learn the place value of numbers, and their relationship to each other.
Prerequisites
Before getting started, your child needs to be confident in being able to add single digit numbers, and adding numbers beyond 10.
If your child doesn’t know how to add numbers, then this could end up being a frustrating exercise. See our previous articles on adding simple numbers first.
Getting started
Start with a simple mathematical problem and write the problem horizontally as shown:
22 + 37
How does your child tackle this problem?
If your child is confused, then this is an opportunity to teach them about place values. If your child wants to align the numbers vertically, then stop your child and ask them to try and answer the problem as it is written.
Teaching Place Value
To teach a child place value, they need to understand the reason why numbers are written as they are.
If you begin counting 1 to 10, we can see that the representation of numbers for single digits is easily written as an individual number: 1, 2, 3, 4, 5, 6, 7, 8, 9.
Write these number from 1 to 9 in a horizontal fashion like so, all in alignment and all one under the other (leave some space to the left of the column), like so:
1
2
3
4
5
6
7
8
9
But what happens when we get to the next number – how do we represent the number ten ?
Why can’t we write the number ten like so?
1
Obviously, because we already have this number represented as the number one!
To represent the number ten, we have two options:
- We can create our own unique squiggle for what it represents (like what the Romans did by representing ten with the squiggle we identify as “X”); or
- We could use an existing number, but position it differently.
Thankfully, with math today we don’t have a unique squiggle for each unique number. We reuse the same digits, but position them differently.
If one is represented like this:
1
Then ten is represented like this:
10
Notice how the number ten uses the familiar number one, but puts it in a different position, and to show the differing position a zero is placed where the other single digits were when we were counting to ten.
This position to the left of where the single digits were written is known as the tens digit. As we don’t need any single digits to represent the number ten we put a zero where the single digit number sat. This is why the number ten is written as it is:
10
1 to represent 1 ten, and 0 to represent no single digits.
Understanding Tens Place Value
With a basic understanding of how ten is written, let’s see how we write numbers that are greater than ten, such as eleven.
Eleven is a number 1 unit after 10 – it is one single digit, and one tens digit.
How would we write a number like this?
Using our positions, we would write it as follows (I’m using a table to help align the numbers here, and you’d be looking to align the numbers similarly too):
| Tens | Units |
|---|---|
| 1 | 1 |
What would be the next number after 11?
Well, the next number after 11, is one digit, one unit, more than 11. This means we add one to the number in the units column. So, if 11 has 1 in the units column what would happen if we added 1 to that number? 1 + 1 = 2
Let’s write that number down:
| Tens | Units |
|---|---|
| 1 | 2 |
Keep repeating the process, until you get to 19. Then ask the question: what would be the next number after 19?
We know that 9 + 1 = 10, so we need to add another ten to the number of tens we already have. How many tens do we currently have? 19 has 1 tens, therefore, 1 + 1 = 2, and our next number would be written like this:
| Tens | Units |
|---|---|
| 2 | 0 |
It’s important to emphasise this jump, where when adding two units together, it increases the figure represented in the tens column. Without this understanding, the split strategy will be a struggle to do.
When the jump from units to tens is grasped, challenge your child by asking a question like this, what would 10 + 10 be?
As these numbers are already represented purely as tens our answer would be two lots of tens, or represented as the number 20 in the table directly above.
It’s important to retain the zeroes with numbers represented as tens, to help with the next step. Therefore, even though we might say 1 tens, or 2 tens, we still want to show that 1 tens looks like 10, and 2 tens looks like 20 (etc).
Keep testing the jump from 9 to 10, and when you’re satisfied of your child’s understanding, move on to the last step where a basic usage of the split strategy is applied.
Adding Numbers Horizontally
While we’ve shown how to get to a number that contains a tens place value number, like 10 and 20 (etc), it’s important to check a child can interpret a number and break up the place value. For example, can your child break up this number into its place values:
| Tens | Units |
|---|---|
| 2 | 5 |
By breaking a number up your child should easily be able to perform the split strategy with any form of addition.
For example, taking our original question at the beginning of this article we asked what was 22 + 37?
If we look at the place values for each number we could break up these numbers into their place values like so:
(20 + 2) + (30 + 7)
22 + 37
Furthermore, we can cluster the tens values together, and the units values together, like so:
(20 + 30) + (2 + 7)
22 + 37
By combining the tens values together to form the tens place value number, and the units values together to form the units place value number, we have our answer:
| Tens | Units |
|---|---|
| 5 | 9 |
With continued practice you can improve the speed of operation as your child scans each number in the question, can determine their place value, and then writes the answer accordingly.
But what do you do when the units values produce a tens value, for example, 25 + 37?
Once again, break the question up slowly into each miniscule step, like so:
(20 + 5) + (30 + 7)
25 + 37
Then cluster the tens values and the units values together:
(20 + 30) + (5 + 7)
25 + 37
Add the tens numbers and the units numbers up:
50 + 12
25 + 37
Break apart the value of 12 into its tens and units value:
50 + (10 + 2)
25 + 37
Once again, combine the tens place values:
(50 + 10) + 2
25 + 37
This will now get you to the final step:
60 + 2
25 + 37
The answer being 62.
Wow! That’s a lot of work which could so easily be done another way.
I know.
It can feel like that with learning the split strategy, but this strategy leads into other forms which can help with the other operations such as subtraction, multiplication and division.
Split Strategy Addition Worksheets
Here are some basic worksheets to get you started on performing the split strategy, there are two pages to each worksheet the first side checks the child’s understanding by adding a unit number to a number greater than ten. Then the second page checks the child’s understanding by adding numbers greater than ten.
Summary
The split strategy may seem verbose in trying to teach a simple concept, however, the underlying principles behind the strategy are to equip children to understand place values easier.
The split strategy for addition is the quickest way to begin to understand the method, provided the way in which the method is taught goes slowly and increments in difficulty when the child begins to comprehend the meaning of place value and how numbers are written.