Basic Addition Facts, Part 3: The Numerical Reasoning Strategy of Doubles

What’s Next? Mastering Numerical Reasoning Strategies!

In our first two posts on addition, we discussed how to help kids understand the meaning of addition and build skills in counting on. After your child has demonstrated a strong understanding of what it means to add and is able to count on consistently, it is time to take it to the next level with some new strategies—what we call numerical reasoning strategies. These strategies not only help with mastering addition facts, they also build number sense, a critical skill for more complex math later on.

We’re particularly excited about sharing numerical reasoning strategies because they are often missed in traditional math instruction. BUT they are essential for developing math confidence and fluency and allow students to lean into some of their intuitive math thinking.

Introducing Doubles: A Powerful Addition Strategy

Let’s dive into one of our favorite strategies, doubles! You’ve probably noticed that kids often learn their doubles—like 2 + 2 and 3 + 3—before they master other facts. Doubles are not only easy to remember but also powerful tools for solving other addition problems. Students can look for and use doubles that are familiar to them to help them with unknown addition facts. Here’s how it might look:

Using Doubles to Solve Addition Problems

Example: Adding 3 + 4 with Doubles

Our first problem is 3 +4. Think about those two numbers. Is there a double (a number that can repeat within both numbers) in there that you could use?

You might have noticed that 4 has a 3 inside of it:

We know 4 can be seen as 3 + 1, so we can use a known fact of 3 + 3 = 6. Once you know that, you just need to add the extra 1 from the 4, which gives you 7. So, 3 + 4 = 7. 

Example: Adding 6 + 7 with Doubles

What about 6 and 7? Again, we can use doubles to help. We know there’s a 6 inside 7.

So we start with 6 + 6 = 12. Then add the extra 1 from the 7, which gives you 13. 

Another approach is to think of 7 + 7 = 14. Since we essentially gave an extra 1 to 6 to make it a 7 we then need to subtract that extra 1 to get 13.

The beauty of this strategy is that you can go both directions. The key is helping your child find what makes sense for them and encourage flexible thinking.

Encouraging Flexible Thinking with Doubles

If this seems a little abstract for your child at first, don’t worry! You can always encourage them to draw the numbers to visualize the hidden doubles inside. Visualizing the relationships between numbers can make this strategy more concrete and easier to understand.

Questions for "Use Doubles" (Building Addition Fluency)

Asking questions is a great way to support your child in thinking more deeply and making long lasting connections. Below we have some questions you can ask your child when engaged in this work.

Questions to Explore the Concept of Doubles

Discovering Doubles:

• “What does it mean when we say something is a double? Can you show me an example?”

• “What doubles do you already know by heart? Can you say them out loud?”

Recognizing Doubles in Problems:

• “Can you spot a double in this problem? For example, in 3 + 4, is there a double you can use to help solve it?”

• “What’s a double close to 6 + 7 that might help us figure it out?”

Questions to Practice Using Doubles

Applying the Strategy:

• “If we know 3 + 3 = 6, how can we use that to solve 3 + 4?”

• “When you see 6 + 7, what’s the first double you think of? How can you use it to solve the problem?”

Thinking Both Ways:

• “Do you think it’s easier to start with 6 + 6 or 7 + 7 when solving 6 + 7? Why?”

• “If we used 7 + 7 to solve 6 + 7, what do we need to do next?”

Building Math Confidence Through Numerical Reasoning

Remember, doubles are just one of several numerical reasoning strategies to help build math confidence and success. By focusing on strategies like these, we’re helping kids develop flexible thinking and a positive relationship with math.

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