Learning Addition and Subtraction Facts Through Mental Math and Number Sense
🧠 Learning Addition and Subtraction Facts Through Number Sense — Not Memorization
While many of us remember learning addition and subtraction facts using flashcards, repetition, and timed drills, this traditional approach doesn’t work for every learner. For many students, it becomes a stressful memorization task—more like cramming for a spelling test than learning meaningful math.
As a math interventionist, I’ve worked with countless students who struggle to memorize math facts. These students often end up relying on counting on their fingers, which slows them down and can lead to frustration or a sense that they “just aren’t good at math.”
But there’s a better way. One that builds number sense, encourages confidence, and actually leads to stronger fact fluency in the long run.
💡 What Is Math Fact Fluency?
True fluency in math is not just about memorizing. It’s about being able to solve problems in a way that is:
✅ Accurate – Getting the correct answer consistently
⚡ Efficient – Using a method that is quick and logical
🔁 Flexible – Being able to try different strategies when needed
We want our students to understand how numbers work, not just remember answers. That’s where number sense comes in.
🧱 Step 1: Build a Strong Foundation
We begin with two foundational fact sets: doubles and combinations that make ten. These are facts we do aim to commit to memory, because they become the building blocks for many other strategies.
Doubles Facts (1+1, 2+2, 3+3…)
These are often the easiest to memorize and the most useful for deriving other facts.
Fun ways to learn doubles:
🎲 Games with dice or dominoes
🎵 Songs or chants that highlight patterns
🔢 Counters or connecting cubes to make pairs and groups
Example:
I know 4 + 4 = 8, so I can use that to solve 4 + 5.
Combinations of 10 (Make Ten Facts)
These are the pairs of numbers that add up to 10:
1+9, 2+8, 3+7, 4+6, 5+5, etc.
This set is crucial for both addition and subtraction, especially as numbers get larger.
Visual strategies to build this skill:
🟦 Ten frame flashcards – students can see how two parts make a whole
🧩 Matching games to pair up numbers that equal ten
🧠 Mental math practice with hands-on tools
Example:
I know 3 + 7 = 10 → then I can solve 30 + 70 = 100 or 300 + 700 = 1000
🔁 Step 2: Use Derived Fact Strategies
Once students are confident with doubles and make-ten facts, we can teach new facts using what they already know. This is where number sense truly shines!
Doubles Plus One
This is when students solve a near-double by adding one more.
Example:
I know 6 + 6 = 12, so 6 + 7 = 13
How to model this:
🧱 Use connecting cubes to build a double, then add one more cube to see the total.
Add 9 Strategy: Think 10, Then Subtract 1
Instead of memorizing all the +9 facts, students can think flexibly by turning the 9 into a 10, then adjusting.
Example:
9 + 5 → Think 10 + 5 = 15 → then subtract 1 → 14
This approach promotes mental math skills and builds place value awareness.
✏️ Extending Strategies Into Second Grade
As students move into second grade, these early strategies lay the groundwork for more complex thinking with larger numbers.
Place Value Patterns with Combinations of 10
If students know their basic make-ten facts, they can apply them to tens and hundreds with confidence.
Example:
I know 3 + 7 = 10, so:
🔹 30 + 70 = 100
🔹 300 + 700 = 1,000
🔹 33 + 7 = 40
These patterns help students solve multi-digit addition and subtraction more efficiently—without always relying on algorithms or regrouping.
❤️ Why This Approach Works
When students learn how numbers relate to each other, they:
Are more confident problem solvers
Develop stronger mental math
Rely less on finger counting or rote memory
Are better prepared for more advanced math in later grades
This approach builds not only fact fluency but also a deep sense of number relationships that supports lifelong math learning.