Show The Tens Fact You Used. Write The Difference

Understanding tensfacts is a foundational skill that helps learners build fluency in addition, subtraction, and place‑value concepts. By recognizing how numbers combine to make ten, students can quickly decompose and recompose values, which speeds up mental math and lays the groundwork for more complex operations. This article shows exactly how to show the tens fact you used and then write the difference between the original problem and the tens‑based solution, providing clear steps, examples, and tips for mastery.

What Are Tens Facts?

A tens fact is any pair of single‑digit numbers that add up to ten. The classic list includes:

• 0 + 10
• 1 + 9
• 2 + 8 - 3 + 7
• 4 + 6
• 5 + 5
• 6 + 4
• 7 + 3 - 8 + 2
• 9 + 1
• 10 + 0

These facts are sometimes called number bonds to ten because they illustrate how two parts bond together to form the whole of ten. In a base‑ten system, ten acts as a natural benchmark; knowing these bonds lets students “bridge” to the next ten when adding or subtracting larger numbers.

Why Tens Facts Matter

1. Mental‑math efficiency – Instead of counting on fingers, a student can instantly recall that 6 + 4 = 10 and then add any remaining amount.
2. Place‑value understanding – Recognizing that ten ones make one ten reinforces the concept of regrouping.
3. Foundation for algorithms – The standard addition algorithm relies on carrying tens; fluency with tens facts makes this process intuitive.
4. Problem‑solving flexibility – Students can choose the most efficient strategy (making a ten, doubles, near‑doubles) based on the numbers they encounter.

How to Show the Tens Fact You Used

When solving an addition problem, demonstrating the tens fact you relied on makes your thinking visible to teachers, peers, or yourself during review. Follow these steps:

Step 1: Identify the Addends

Look at the two numbers you are adding. For example, in 27 + 15, the addends are 27 and 15.

Step 2: Break One Addend into a Ten‑Friendly Part

Choose the addend that is easiest to work with. Often you pick the number that is closest to the next ten.

• 27 is 3 away from 30 (the next ten).
• 15 is 5 away from 20.

Step 3: Apply the Tens Fact

Use the known tens fact to create a ten, then add the remainder.

• Take 3 from 15 and add it to 27 to make 30.
• The tens fact used here is 3 + 7 = 10 (since 27 already has a 7 in the ones place, adding 3 completes the ten).
• After making the ten, you have 30 + (15 − 3) = 30 + 12.

Step 4: Write the Intermediate Equation

Show the tens fact explicitly:

27 + 15
= (27 + 3) + (15 – 3)      // using the tens fact 3 + 7 = 10
= 30 + 12

Step 5: Complete the AdditionAdd the remaining numbers: 30 + 12 = 42.

Step 6: State the Final Answer

Thus, 27 + 15 = 42, and the tens fact you showed was 3 + 7 = 10.

By writing each step, you make the tens fact transparent and easy to verify.

Writing the Difference

After you have shown the tens fact, the next instructional task is often to write the difference between the original problem and the tens‑based solution. This helps learners see how much they adjusted each number and why the final sum remains unchanged.

What Does “Write the Difference” Mean?

• Difference between addends: How much you added to or subtracted from each original number to create a ten.
• Difference between the original sum and the intermediate sum: Usually zero, because the adjustments cancel out, but showing this reinforces the concept of equivalence.

Procedure

1. Record the adjustments you made to each addend.
2. Express each adjustment as a positive or negative number (adding is positive, subtracting is negative).
3. Add the adjustments together; they should sum to zero, confirming that the total value did not change.
4. Write a short sentence explaining the net effect.

Example: 27 + 15

• Adjustment to 27: +3 (we added 3 to reach 30).
• Adjustment to 15: –3 (we subtracted 3 to keep the total unchanged).

Now write the difference:

(+3) + (–3) = 0

Explanation: The net adjustment is zero, which means the original sum and the tens‑based sum are equal. Therefore, 27 + 15 = 30 + 12 = 42.

Another Example: 46 + 28

1. Choose to make a ten from 46: it needs 4 to reach 50. 2. Take 4 from 28 → 28 − 4 = 24.
2. Tens fact used: 4 + 6 = 10 (the

Tens fact used: 4 + 6 = 10 (the 6 comes from the ones digit of 46).

Step 3 – Apply the tens fact
Add 4 to 46 to reach the next ten: 46 + 4 = 50.
Subtract the same 4 from the other addend: 28 − 4 = 24.

Step 4 – Write the intermediate equation ``` 46 + 28 = (46 + 4) + (28 – 4) // using the tens fact 4 + 6 = 10= 50 + 24

**Step 5 – Complete the addition**  
50 + 24 = 74.  

**Step 6 – State the final answer**  
Thus, 46 + 28 = 74, and the tens fact demonstrated was **4 + 6 = 10**.

### Writing the Difference for 46 + 28  

- Adjustment to 46: **+4** (added to reach 50).  
- Adjustment to 28: **–4** (subtracted to keep the total unchanged).  

(+4) + (–4) = 0

**Explanation:** The net adjustment is zero, confirming that the original sum and the ten‑based sum are equal. Therefore, 46 + 28 = 50 + 24 = 74.

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## Why the Tens‑Fact Method Works  

The technique rests on the additive identity: adding a number and then subtracting the same number leaves the total unchanged. By deliberately pairing a portion of one addend with the complementary part needed to reach a multiple of ten, we transform a potentially mental‑arithmetic‑heavy problem into two simpler steps—forming a ten and then adding the remaining, often smaller, numbers. This mirrors the way we naturally “make change” when handling money, reinforcing number sense and place‑value understanding.

### Benefits for Learners  

1. **Concrete visualization** – Students see exactly how much each number shifts.  
2. **Reinforcement of complementary pairs** – Repeated exposure to facts like 3 + 7, 4 + 6, etc., strengthens fluency.  
3. **Error‑checking** – Writing the difference (+ adjustment – adjustment = 0) provides an immediate sanity check.  
4. **Transferability** – The same reasoning applies to subtraction, multiplication (via distributive property), and even algebraic simplification.

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### Conclusion  

By breaking down addition into a tens‑fact step, recording the adjustments, and verifying that their net effect is zero, learners gain a transparent, repeatable strategy for mental math. The method not only yields the correct sum but also deepens comprehension of how numbers relate to one another through place value. Practicing this approach with varied pairs—such as 27 + 15, 46 + 28, or any other combination—builds confidence and prepares students for more complex arithmetic operations. Embrace the tens‑fact method as a reliable tool in the mathematician’s toolkit, and watch computational fluency grow.