Show How To Make A Ten To Solve 13 7

open up Subtraction Confidence: Mastering the "Make a Ten" Strategy for 13 - 7

For many young learners, the leap from simple, single-digit subtraction to problems like 13 - 7 can feel daunting. This isn't just a trick; it's a fundamental shift in number sense that builds a solid foundation for all future arithmetic. Consider this: the numbers are bigger, and the mental math isn't as immediately obvious. This is where a powerful, elegant strategy comes to the rescue: making a ten. But by learning how to strategically adjust numbers to create a round ten, we transform a tricky problem into a series of simple, manageable steps. This article will demystify the process, showing you exactly how to apply the "make a ten" strategy to solve 13 - 7 and empowering you to tackle countless similar problems with newfound ease.

Why "Make a Ten" Works: The Philosophy Behind the Strategy

At its heart, our decimal number system is built on tens. We group ones into tens, tens into hundreds, and so on. Problems involving numbers just above or below a multiple of ten (like 13, 17, 24, 38) are perfectly suited for this strategy because we can temporarily "borrow" or "regroup" to land on that comfortable, familiar landmark of ten.

Think of the number 13. It’s composed of one ten and three ones: 10 + 3. But the number 7 is seven ones. To subtract 7 from 13, we first need to deal with the three ones we have—we’re short. The "make a ten" strategy brilliantly asks: *What if we could turn those 3 ones into a full 10?But * To do that, we need to borrow 7 more ones. But where do they come from? They come from the 7 we are subtracting. We break the 7 into two parts: one part that completes our 13 to 20 (which is 7), and then we subtract the rest from that nice, round 20. This mental decomposition is the key.

Step-by-Step: Solving 13 - 7 Using the "Make a Ten" Method

Let’s walk through the process slowly and clearly. The goal is to make the subtrahend (the number we are taking away) fit perfectly to complete the minuend (the number we start with) to the next ten.

Step 1: Identify the Gap to the Next Ten. Look at your starting number, 13. The next multiple of ten above it is 20. How many do we need to add to 13 to reach 20?

• 13 + ? = 20
• The answer is 7. We need to add 7 to make a ten (in this case, 20).

Step 2: Decompose the Number You're Subtracting. We are subtracting 7. We just discovered that 7 is exactly the number needed to make 13 into 20. So, we break the 7 into two parts:

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1. The part that makes the ten: 7.
2. The remaining part: 0 (because we used the entire 7 to make the ten).

This is the most crucial insight. For 13 - 7, the number 7 is precisely the amount needed to reach the next ten. Because of this, we can think:

• First, use part of the 7 to turn 13 into 20. Even so, that uses up all 7. * Then, subtract what’s left from 20. Since we used the whole 7, 0 is left.

Step 3: Perform the Two Simple Subtractions. Now we execute the plan in two super-simple steps:

1. Make the Ten: 13 + 7 = 20. (We conceptually "add" the 7 to get to 20).
2. Subtract the Remainder: 20 - 0 = 20.

Wait—that gives us 20, but 13 - 7 is 6. Because of that, we’ve made a logical error in tracking. Let’s correct the framework. The standard "make a ten" for subtraction like 13 - 7 is often taught as a two-step process where you first make the ten in the minuend by borrowing, then subtract.

Corrected & Clearer Step-by-Step:

1. What do we need to add to 13 to make 10? This is a common point of confusion. 13 is already past 10. We actually want to make the next ten, which is 20. So, 13 + 7 = 20. The 7 from the subtraction problem is exactly what we need to add to get to 20.
2. Since we "used" that 7 to get to 20, we now subtract the leftover from 20. How much of the 7 is left? We used all of it to get from 13 to 20. So, 20 - 0 = 20. This still gives the wrong answer.

Ah, the flaw is in the final subtraction. The correct mental model is: **Start with 13. To subtract 7, we can think: "I'll add 7 to get to