Break Apart Ones To Make A Ten

Mastering the break apart ones to make a ten strategy is a important milestone in early mathematics education. Instead of relying solely on counting fingers or memorizing isolated facts, students learn to manipulate numbers flexibly, developing a deep, intuitive sense of how numbers relate to one another. Often introduced in first and second grade, this mental math technique—sometimes called "bridging through ten" or the "make a ten strategy"—transforms how young learners approach addition. This foundational skill builds the number sense necessary for complex multi-digit arithmetic, algebra, and real-world problem solving later in life Simple, but easy to overlook. That's the whole idea..

Why Making a Ten Changes Everything

The base-ten number system is the bedrock of modern mathematics. Because our system revolves around groups of ten, the number ten acts as a critical anchor or benchmark. When children learn to break apart ones to make a ten, they are essentially learning to restructure a problem into a friendlier format.

Consider the problem $8 + 5$. A novice counter might start at eight and count up five times: nine, ten, eleven, twelve, thirteen. So this works, but it is slow, prone to error, and doesn't scale well to larger numbers like $48 + 35$. A student fluent in the make-a-ten strategy sees the $5$ differently. They recognize that $8$ needs $2$ to become $10$. They instantly decompose (break apart) the $5$ into $2$ and $3$.

This shift—from counting to structural thinking—is the essence of computational fluency. It teaches students that numbers are not fixed symbols but flexible quantities that can be taken apart and reassembled without changing their total value.

The Prerequisite Skills: Building the Foundation

Before a student can successfully break apart ones to make a ten, three specific conceptual understandings must be solidly in place. Rushing this strategy without these foundations leads to rote memorization of a procedure rather than genuine understanding It's one of those things that adds up..

1. Fluency with Combinations of Ten

Students must automatically know the "friends of ten" pairs: $1+9, 2+8, 3+7, 4+6, 5+5$. If a student has to count on fingers to find what goes with $8$ to make $10$, the cognitive load of the larger strategy becomes overwhelming. Games like "Ten Frame Flash" or "Make Ten Go Fish" are excellent for solidifying these bonds.

2. Understanding Teen Numbers as "Ten and Some More"

The strategy results in a "ten plus a number" equation (e.g., $10 + 3$). Students must understand that $13$ is $10$ and $3$. Using double ten-frames or base-ten blocks helps visualize that the "1" in $13$ represents a group of ten, not just a digit in the tens place.

3. Part-Part-Whole Relationships (Decomposition)

This is the engine of the strategy. Students need practice breaking numbers apart in multiple ways. For the addend $5$, they need to see it as $2+3$, but also $1+4$ and $5+0$. Number bonds and part-part-whole mats are the standard tools for developing this flexibility.

Step-by-Step: How to Teach the Strategy

Effective instruction moves through the Concrete-Representational-Abstract (CRA) sequence. Do not skip the concrete phase; the physical manipulation of objects creates the mental imagery required for abstract execution Took long enough..

Phase 1: Concrete (Hands-On Manipulatives)

Tools: Double ten-frames and two-color counters (red/yellow).

1. Build the Addends: Place $8$ red counters on the first ten-frame (filling the top row and three on the bottom). Place $5$ yellow counters on the second ten-frame.
2. Identify the Need: Ask, "How many more red counters do we need to fill the first ten-frame?" (Answer: $2$).
3. The "Break Apart" Action: Physically move $2$ yellow counters from the second ten-frame to the first ten-frame to complete the ten.
4. Analyze the Result: The first frame is now full ($10$). The second frame has $3$ yellow counters left.
5. Connect to Notation: Write $8 + 5 = 10 + 3 = 13$. Explicitly show the decomposition: $5 = 2 + 3$.

Phase 2: Representational (Visual Models)

Tools: Number bonds, drawn ten-frames, or number lines Still holds up..

• Number Bonds: Draw the whole ($5$) with two parts ($2$ and $3$). Connect the $2$ to the $8$ to show the new ten.
• Number Lines: Show a jump of $2$ from $8$ to land on the "friendly" number $10$, then a jump of $3$ to reach $13$. This visualizes the "bridging" concept.

Phase 3: Abstract (Mental Math & Symbols)

Once the visual model is internalized, students practice the internal dialogue:

"I have $8$ and $5$. $8$ needs $2$ to make $10$. I take $2$ from the $5$, leaving $3$. $10$ plus $3$ is $13$."

Encourage students to write the number bond decomposition ($5 = 2 + 3$) next to the equation as a scaffold until the process becomes automatic.

Extending the Strategy: Beyond Basic Facts

The true power of learning to break apart ones to make a ten reveals itself when applied to multi-digit numbers. The logic remains identical; only the magnitude changes Nothing fancy..

Addition with Two-Digit Numbers

Problem: $37 + 16$

1. Focus on the Ones: Look at the ones digits ($7$ and $6$).
2. Make a Ten: $7$ needs $3$ to make $10$. Break the $6$ into $3 + 3$.
3. Regroup: $37 + 3 = 40$. (This is the "new ten" created in the tens column).
4. Add the Rest: $40 + 3 = 43$.

This mirrors the standard algorithm's "carrying" or "regrouping" step but grounds it in place value understanding rather than a memorized "carry the one" rule Not complicated — just consistent. That alone is useful..

Subtraction (The "Take from Ten" Strategy)

The strategy reverses beautifully for subtraction. For $13 - 5$:

1. Break $13$ into $10 + 3$.
2. Subtract $5$ from the $10$ (easy: $10 - 5 = 5$).
3. Add the remaining $3$: $5 + 3 = 8$. This is significantly more efficient than counting backward five times.

Common Pitfalls and How to Address Them

Even with good instruction, students develop misconceptions. Watch for these common errors: