Understanding how to show the tens fact you used and write the difference is a important milestone in early mathematics education. This specific phrasing often appears in elementary curricula—particularly in first and second grade—as a way to assess a student’s grasp of the "Make a Ten" subtraction strategy. In practice, it moves children beyond counting backward on their fingers and toward flexible, mental math thinking. Mastering this concept builds the number sense required for complex arithmetic, algebra, and real-world problem solving later in life.
What Does "Show the Tens Fact You Used" Actually Mean?
When a worksheet or teacher asks a student to "show the tens fact you used," they are asking for the intermediate step where the student decomposes a number to land on a friendly "ten." The number ten is the anchor of our base-10 number system. This leads to it is easy to subtract from ten because the facts are memorized early (10 - 1 = 9, 10 - 2 = 8, etc. ) And that's really what it comes down to..
The instruction usually accompanies a subtraction problem where the subtrahend (the number being subtracted) is larger than the ones digit of the minuend (the starting number), forcing the student to "break" a ten.
Example Problem: 15 – 8 = ?
A student using a counting strategy might count back eight times: 14, 13, 12, 11, 10, 9, 8, 7. * 4. *I need to get to 10 first.*From 15, I subtract 5 to land on 10.Now, * 2. * (This is the Tens Fact: 15 – 5 = 10) 3. In real terms, a student using the Tens Fact Strategy thinks:
- *I have subtracted 5, but I need to subtract 8 total. Worth adding: *
- So *10 – 3 = 7. That said, i still need to subtract 3 more. That's why this is slow and prone to error. *The difference is 7.
When the prompt says "Show the tens fact you used," the correct response is writing out that bridge step: 15 – 5 = 10 (or 5 + 5 = 10, depending on the curriculum's specific notation). When it says "Write the difference," the student writes the final answer: 7 The details matter here. No workaround needed..
Why This Strategy Matters: The Cognitive Shift
This isn't just a trick to get the right answer; it represents a fundamental shift from counting to calculating.
1. Developing Number Sense
Number sense is the intuition for how numbers relate to one another. By forcing the decomposition of the subtrahend (breaking 8 into 5 and 3), the student internalizes that numbers are composite. They see 8 not just as "eight," but as "5 and 3" or "2 and 6." This part-whole understanding is the bedrock of algebraic thinking Not complicated — just consistent..
2. Reducing Cognitive Load
Counting backward requires holding the starting number in working memory while tracking the count. For 15 – 8, that is eight distinct steps. The "Make a Ten" strategy reduces this to two simple, known facts: a "ten fact" (15-5=10) and a "ten minus" fact (10-3=7). It frees up working memory for more complex problem solving Simple as that..
3. Building Fluency for Multi-Digit Math
Consider the problem 72 – 28. A student who understands "tens facts" doesn't just "borrow" mechanically. They might think: Take 2 from 72 to get 70. Take 20 from 70 to get 50. Take the remaining 6 from 50 to get 44. Or they might use the standard algorithm but understand why they are crossing out the 7 and making it a 6 (decomposing a ten). Without the foundational "show the tens fact" work in 1st grade, the standard algorithm in 3rd grade is just meaningless symbol manipulation.
Step-by-Step Guide: How to Teach and Execute the Strategy
If you are a parent helping with homework or a teacher introducing the concept, here is the scaffolded progression And that's really what it comes down to..
Phase 1: Mastery of "Friends of Ten" (Prerequisite)
Before a student can use a tens fact, they must know the tens facts automatically.
- Goal: Instant recall of pairs that make 10 (1+9, 2+8, 3+7, 4+6, 5+5).
- Activity: Use ten frames, rekenreks, or fingers. "Show me 6. How many more to make 10?"
Phase 2: Subtracting From Ten (The Second Half)
The strategy relies on the second step: 10 – x.
- Goal: Instant recall of 10 – 1 through 10 – 9.
- Why: In the example 15 – 8, once you hit 10, you must instantly know 10 – 3 = 7 without counting.
Phase 3: The "Break Apart" Move (Decomposing the Subtrahend)
This is the hardest cognitive leap. The student must look at the subtrahend (the 8 in 15–8) and decide how to break it to reach the ten.
- The Question: "Look at 15. Look at the ones place (5). What do I subtract from 15 to get to 10?"
- The Answer: 5.
- The Decomposition: "So I will use 5 of the 8. I break 8 into 5 and 3."
Phase 4: Notation – "Show the Tens Fact"
Curriculums vary on notation. Common formats include:
Format A: Number Bonds / Decomposition
15 – 8 = ? 8 = 5 + 3 (Showing the break) 15 – 5 = 10 <-- THE TENS FACT 10 – 3 = 7 Difference = 7
Format B: Sequential Equations (Common in EngageNY/Eureka Math)
15 – 8 = ? 15 – 5 = 10 <-- THE TENS FACT 10 – 3 = 7 15 – 8 = 7
Format C: Arrow Way / Number Line Jumps
15 --(minus 5)--> 10 --(minus 3)--> 7 Label the first jump "Tens Fact."
The Critical Instruction: Whatever the format, the "Tens Fact" is always the step that lands exactly on a multiple of ten (10, 20, 30, etc.).
Worked Examples: From Simple to Complex
Example 1: Basic Teen Minus Single Digit (13 – 6)
- Problem: 13 – 6
- Think: I have 13. I need to get to 10.
