Introduction
When students encounter the subtraction problem 14 - 6, they are often taught to move beyond simple counting backward and instead put to use a powerful mental math strategy known as "making a ten" or using a "tens fact." The instruction to "show the tens fact you used" asks the learner to make their thinking visible by demonstrating how they decomposed numbers to use the base-10 number system. In the specific case of 14 - 6, the tens fact used is 10 - 4 = 6 (or the related addition fact 4 + 6 = 10). This approach transforms a potentially tricky subtraction across a decade boundary into a manageable two-step process anchored by the number 10. Understanding this concept is a cornerstone of early numeracy, building the flexible number sense required for advanced arithmetic, algebra, and everyday mental calculation.
Detailed Explanation
The concept of a "tens fact" refers to the pairs of numbers that combine to make 10 (e.Plus, g. Because of that, , 1+9, 2+8, 3+7, 4+6, 5+5). These are often called "number bonds to ten" or "friends of ten.Day to day, " In subtraction, specifically when subtracting a single-digit number from a teen number (like 14 - 6), the total (14) is larger than 10, but the subtrahend (6) is too large to simply subtract from the ones digit (4) without regrouping or bridging. The "tens fact strategy" (often labeled "Take from Ten" or "Break Apart to Make Ten") utilizes the structural knowledge that a teen number is composed of a ten and some ones (14 = 10 + 4).
Instead of counting back six times (13, 12, 11, 10, 9, 8), the student recognizes that 14 consists of a bundle of ten and four loose ones. The strategy involves ignoring the four ones temporarily, subtracting the 6 from the ten (using the tens fact 10 - 6 = 4), and then adding the remaining four ones back to the result. This shifts the cognitive load from a slow, error-prone counting procedure to a rapid retrieval of a memorized fact (10 - 6 = 4) followed by a simple addition (4 + 4 = 8). When a worksheet asks a child to "show the tens fact you used," the teacher is looking for evidence of this decomposition: the explicit writing of 10 - 6 = 4 (or 6 + 4 = 10) as the engine driving the solution Turns out it matters..
Step-by-Step Concept Breakdown
To fully grasp how to "show the tens fact" for 14 - 6, it helps to break the process down into distinct, logical phases. This mirrors the Concrete-Representational-Abstract (CRA) instructional sequence used in modern mathematics education.
Phase 1: Decompose the Minuend (The Total)
The first step is recognizing the place value structure of the number 14. The student must explicitly break 14 into its constituent parts: 10 and 4 And that's really what it comes down to..
- Action: Write 14 = 10 + 4 (or draw a number bond with 14 on top, 10 and 4 on the bottom).
- Reasoning: This isolates the "friendly number" (10) which serves as the anchor for the calculation.
Phase 2: Identify and Apply the Tens Fact
Now the student looks at the subtrahend (6). Since 6 cannot be easily taken from the 4 ones, the subtraction must happen from the 10 Worth keeping that in mind..
- The Tens Fact: The student retrieves the fact 10 - 6 = 4. (Alternatively, they think: "6 plus what makes 10? 4." So, 6 + 4 = 10).
- Action: Write the number sentence 10 - 6 = 4. This is the specific answer to the prompt "show the tens fact you used."
Phase 3: Combine the Remainders
After taking 6 away from the 10, there are 4 left from that ten. But we must not forget the original 4 ones that were set aside in Phase 1 Simple, but easy to overlook..
- Action: Add the result from the tens fact (4) to the leftover ones (4).
- Number Sentence: 4 + 4 = 8.
Phase 4: State the Final Answer
- Conclusion: 14 - 6 = 8.
Real Examples
To solidify this understanding, let’s look at how this appears in different classroom contexts and real-world scenarios.
Example 1: The Standard Worksheet Format (Number Bonds)
A typical 1st or 2nd-grade workbook page might present the problem horizontally with scaffolding boxes:
14 - 6 = __ 14 = 10 + __ (Student writes 4) 10 - 6 = __ (Student writes 4 — This is the Tens Fact) __ + __ = __ (Student writes 4 + 4 = 8) 14 - 6 = 8
Here, the blank next to "10 - 6 =" is the exact location where the student "shows the tens fact."
Example 2: The "Arrow Way" or Mental Math Notation
In curricula like Eureka Math or EngageNY, students often use arrow notation to track the mental jumps:
14 - 6 14 → 10 (subtract 4) → 4 (subtract 2 more? No, that's different). Correction for "Take from Ten": 14 = 10 + 4 10 - 6 = 4 (Tens Fact Shown Here) 4 + 4 = 8
Example 3: Real-World Context — Money
Imagine a child has $14 (one $10 bill and four $1 bills). They want to buy a toy costing $6 And that's really what it comes down to..
- They cannot pay with just the four $1 bills.
- They must hand over the $10 bill.
- The cashier gives back $4 change (because 10 - 6 = 4 — the tens fact).
- The child now has the $4 change plus their original four $1 bills.
- Total money left: $4 + $4 = $8. This physical enactment mirrors the abstract strategy perfectly.
Scientific or Theoretical Perspective
The pedagogical justification for demanding students "show the tens fact" is rooted deeply in cognitive science and mathematics education research.
Base-10 Structure and Place Value
Our number system is base-10. Fluency requires automaticity with the composition and decomposition of 10. Research by Karen Fuson and the National Research Council (Adding It Up, 2001) emphasizes that "making a ten" is a critical benchmark for procedural fluency. It moves students away from unitary counting strategies (counting by ones), which are cognitively taxing, limited in scalability, and prone to off-by-one errors, toward composite unit strategies (working with chunks of ten).
Cognitive Load Theory
From a Cognitive Load Theory perspective (Sweller, 1988), counting back 6 steps (14, 13, 12, 11, 10, 9, 8) occupies significant working memory. The student must maintain the starting number, the current count, the
target, and the direction of subtraction simultaneously. This demands sequential attention and increases the risk of errors. In contrast, the "take from ten" strategy reduces cognitive load by breaking the problem into two simpler, independent subproblems: 10 – 6 and 4 + 4, both of which are likely already memorized or easily computed. By leveraging the brain’s capacity to handle smaller chunks of information, students conserve mental resources for more complex problems later in mathematics.
Curriculum Alignment and Long-Term Benefits
The emphasis on "showing the tens fact" aligns with standards like the Common Core State Standards for Mathematical Practice (CCSS.MP.7), which prioritize structure recognition and reasoning. Here's a good example: understanding that 14 – 6 can be rephrased as 10 – 6 + 4 lays groundwork for algebraic thinking, where rewriting expressions (e.g., x – 6 = (x – 10) + 4) becomes second nature. This fluency also supports multi-digit subtraction (e.g., 145 – 67), where decomposing numbers into tens and ones is essential. By mastering this strategy early, students build a flexible toolkit for tackling advanced operations, reducing reliance on rote memorization.
Conclusion
The directive to "show the tens fact" is far more than a procedural hurdle—it is a pedagogical scaffold designed to cultivate mathematical agility. By anchoring subtraction in the base-10 system, it transforms abstract numbers into tangible relationships, making arithmetic both intuitive and scalable. Whether through structured worksheets, mental math notation, or real-world analogies like money, this approach empowers students to see patterns, minimize errors, and develop a deeper conceptual understanding. As cognitive science underscores, the goal is not just to compute answers but to build neural pathways that enable lifelong mathematical confidence. In essence, teaching students to "take from ten" is not about shortcuts—it’s about strategic thinking that prepares them to manage the complexities of mathematics with clarity and precision.
