Basic Addition Facts, Part 6: The Numerical Reasoning Strategy of Compensation

Unlocking Basic Fact Addition Fluency with the Compensation Strategy

Supporting kids in learning math can be easier when they have multiple strategies. 

Welcome to the final post in our series, Understanding Addition of Simple Numbers! So far, we’ve explored how to support children in understanding the meaning of addition and building skills in counting on. Today, we’re focusing on our final essential numerical reasoning strategy: compensation. This strategy is designed to help kids build confidence and fluency in addition while developing a deeper understanding of numbers.

If you’re a parent, teacher, or caregiver looking to help kids master addition in a fun, effective way, this post is for you. We’re sharing the compensation strategy for addition—a powerful tool for building math fluency. We’ll explain how it works, compare it to the "make a ten" Strategy, and share practical ways to support your child at home.

---

What Is the Compensation Strategy for Addition?

The compensation strategy is an approach where you adjust one number in an addition problem to create a "friendlier" number, making calculations easier. Afterward, you compensate by reversing the adjustment. This approach helps kids develop number sense and boosts their ability to solve problems mentally.

How to Teach the “Compensation” Strategy Using Ten Frames

We recommend using a double (or two) ten frames which is simply two ten frames next to each other as your child first works with this strategy. When you start noticing that your child can engage in the thinking more automatically, you can shift away from the visual ten frames.

Double Ten Frame

If you’re not familiar with the ten frame, check out our blog post or video where we introduce and explore it in more detail. We also have free printable versions of both a single and double ten frame on our printables page for you. 

 If your child has never used a ten frame before, it would be best to first introduce your child to a single ten frame and allow them to get familiar with it before using the double ten frame. 

---

A Step-by-Step Example of the Compensation Strategy

Let’s try solving 9 + 6 using compensation:

1. Set It Up: Use two ten frames (or draw them). Place 9 counters on one ten frame and 6 on the other.

2. Think About It: Is one of these numbers close to another “friendly” number that we could create by “giving it a little extra?”   

 Notice that 9 is close to 10, which is easier to work with.

3. Adjust: Add 1 to the 9 to make it 10. The problem becomes 10 + 6 = 16.

   
   

   

   
   

4. Compensate: Since you added 1 extra when turning the nine into a ten, subtract 1 from the total. 16 - 1 = 15.

   
   

---

Compensation vs. the “Make a Ten” Strategy

At first, the compensation strategy might seem similar to the make a ten strategy, but there’s a key difference:

• Make a Ten Strategy: Move counters from one number to the other to create a ten.

• Compensation Strategy: Add extra to one number to create a “friendly” number and adjust at the end.

• 
  

Example: 8 + 7

Solving Using “Make a Ten”: 

Take 2 from the 7 to make the 8 a 10, leaving 5 from the 7. 10 + 5 = 15.

Solving Using Compensation: 

Add 2 to the 8 to make it 10, keeping the 7 unchanged. 10 + 7 = 17. 

Subtract the extra 2: 17 - 2 = 15.

---

Building Confidence with Compensation: Why Ten Frames Are a Great Starting Point

As children practice using compensation to solve addition problems, ten frames serve as a helpful bridge between concrete examples and mental strategies. 

Over time, the need for ten frames diminishes. As kids gain confidence and develop a deeper understanding of how compensation works, they begin to picture the groups in their minds and solve problems without physical aids. Ten frames aren’t just tools for solving problems—they’re stepping stones to more advanced mental math skills.

---

Flexibility in Problem-Solving

Just like with the other strategies we’ve shared, you may notice that lots of different strategies could be used to solve these problems. This isn’t a coincidence—it’s because math is built on patterns and relationships that can be explored in many ways. When kids see that problems can be solved using different approaches, they build a deeper understanding of how numbers work.

Each child may naturally gravitate toward a particular method, and certain numbers might lend themselves to specific strategies. This is also why exposing children to multiple approaches is so valuable—it allows them to choose the strategy that feels most intuitive for the situation.

---

Getting Started at Home

Here’s how you can help your child learn and practice the compensation strategy at home:

1. Download our free printable ten frames

2. Work through solving problems like 9 + 6 and 8 + 7 together

3. Ask guiding questions to encourage critical thinking:

Before Solving:

• What do you notice about the numbers?

• Do you see any number that’s close to a friendly number like 10? Or if you’re working with bigger numbers: 20, or 50?

• Is there a way to make one of the numbers simpler to work with?

  
  

While Solving:

• What did you change, and why?

• What number did you take from or add to the other number?

• Does your new equation (or problem) seem easier to solve? Why?

  
  

After Solving:

• How did using this strategy help you?

• Could you solve this problem another way?

• What would happen if you changed a different number instead?

• Do you think this strategy would work for bigger numbers? Why or why not?

  
  

Encourage your child to explain their thinking—it’s a great way to strengthen their understanding and problem-solving skills.

---

Keep Learning with Us!

The Compensation strategy is just one of many ways to help kids build a strong foundation in addition. Be sure to explore the other posts and videos in our Understanding Addition of Simple Numbers series for more tips and strategies!

Don’t forget to like, share, and subscribe to support our mission of building confident, happy math learners. Together, we can make math a joyful experience for the next generation!

Make Sure to Stay Connected!

We have lots more resources so that you can support your child in becoming excited, confident, capable doers of mathematics. Follow us on Instagram and YouTube to stay up to date! @MathHappinessProject

Looking For More Information on This Topic? Check Out Our YouTube Video!