The Algorithm isn’t the Starting Point
I teach 2-digit addition strategies before I teach the standard algorithm.
The standard algorithm works for teaching 2-digit addition, but I don’t start there.
When I taught the algorithm first, students would learn the procedure for lining up numbers and then how to carry without really understanding what is happening.
They would get the right answer, but not know why.
I’d ask them how they got their answers and I’d be met with shoulder shrugs and the words, “I don’t know.”
I knew there had to be a different way to start so students could understand the numbers before just following a procedure.
That’s why I teach different strategies before for 2-digit addition.
Table of Contents
What I Mean by Addition Strategies
I teach students how to solve problems using base ten blocks, break apart or partial sums, and an open number line.
These strategies help students visualize the numbers and actually see what happens during addition.
I start with smaller numbers and numbers that do not require regrouping. Once students are comfortable with those, I move on to numbers that are larger and/or require regrouping.
If you want to learn more about these strategies, you can find them here:
Want a quick reference for teaching these strategies?
How 2-Digit Addition Strategies Build Place Value Understanding
2-digit addition isn’t just about manipulating numbers.
Students need to understand:
- tens and ones
- composing a new ten
- decomposing a ten
- why regrouping happens
- what the digits actually represent
For example, with 38 + 27, students can see that they have 15 ones and need to compose 1 ten and 5 ones.
That understanding makes the eventual standard algorithm make more sense.
The strategy isn’t just another way to get the answer. It’s helping students understand why the algorithm works.
Strategies Give Students Different Ways to Think About Numbers
Flexibility is a huge part of teaching these strategies. What makes sense to one student might be confusing to another, so I want students to have more than one way to approach an addition problem.
For example:
47 + 25 =
A student might think:
- 47 + 20 + 5
- 40 + 20 + 7 + 5
- 47 + 3 + 22
- Start at 47 and jump 20, then 5 on a number line
They’re all different ways of working with the same numbers.
Some students might understand the problem best when they can physically build it with base ten blocks. Others might prefer breaking numbers apart or using an open number line.
I don’t expect every student to use every strategy forever. The goal is to give students different tools and help them understand when and why these tools work.
That flexibility is part of building number sense. I want students to look at a problem and think about the numbers instead of feeling like there’s only one way to solve it.
Students Can Explain Their Thinking
This is another major benefit of teaching strategies before the algorithm.
With the standard algorithm, a student can sometimes say:
“I put the 7 under the 6, added, and carried the 1.”
But that doesn’t necessarily tell you whether they understand the math.
With strategies you can ask:
- What did you do first?
- Why did you break apart that number?
- Where did the extra ten come from?
- Why did you make that jump?
- How do you know your answer makes sense?
Their answers give you much more information about what they understand, and if they don’t understand something, they give you somewhere to start with reteaching.
Strategies Make Regrouping Less Mysterious
Instead of introducing regrouping as:
“If you have more than 9 ones, carry the 1.”
Students can first experience:
14 ones = 1 ten + 4 ones
Then later, when they see the standard algorithm, the notation has meaning.
When students understand that 14 ones can be regrouped as 1 ten and 4 ones, the “1” that appears in the standard algorithm isn’t just a random number they have to remember to write.
I want students to understand that we’re not magically “carrying a 1”. We’re composing a new ten.
But Isn’t the Standard Algorithm Easier?
I often heard from parents who were frustrated with the strategies and just wanted us to teach the algorithm because it works.
And they’re right. The standard algorithm does work.
But “works” and “helps students understand” aren’t necessarily the same thing.
So When Do I Teach the Standard Algorithm?
I’m not saying to never teach the standard algorithm. I do think it has its place in the learning process.
I am saying not to start with the algorithm.
Use the strategies to build up number sense and the conceptual understanding first.
Once you are confident your students understand the math behind the strategies, the algorithm becomes another tool they can use to solve problems efficiently.
As adults, we can look at problems and decide whether a particular strategy or the standard algorithm will be more efficient. That’s what I want my students to be able to do eventually.
The progression I’m aiming for is:
Understand -> compare -> choose -> become efficient
Rather than:
Memorize a procedure -> hope they understand
How I Introduce the Strategies
My general progression is:
- Start with addition without regrouping.
- Use concrete models first, especially base ten blocks.
- Move toward drawings and representations.
- Introduce addition with regrouping.
- Compare the different strategies.
- Talk about which strategies students find helpful or efficient and why.
- Introduce the standard algorithm once students have a strong understanding of the underlying place value.
The Goal Isn’t to Make Addition Harder
I’ve had parents say to me, why are you teaching them three ways to do something they could just line up and add?
My response is… I’m not teaching multiple strategies because I want students to do more work. I’m teaching them because I want them to understand the math behind the work.
I want students to be able to look at 2-digit addition and think about the numbers, not just remember a set of steps.
Go Deeper Into the Strategies
Want to see each strategy in action?
If you’re looking for the worksheets, diagnostics, reteaching, and extra practice I use with these strategies, you can also check out my 2-Digit Addition Toolkit.
Want to Read More About 2-Digit Addition?
Pin this to Pinterest for later
