Make A 10 To Subtract

Make a 10 to Subtract: A Key Mental Math Strategy for Elementary Students

Introduction

Subtraction is one of the foundational operations in mathematics, yet it can often pose challenges for young learners. Among the various strategies developed to simplify subtraction, "make a 10 to subtract" stands out as a powerful mental math technique that helps students solve problems more efficiently. This method leverages the familiarity of the number 10, which serves as a cornerstone in our base-10 number system, to break down more complex subtraction problems into manageable parts. By mastering this strategy, students not only improve their computational speed but also deepen their understanding of number relationships and numerical fluency.

The official docs gloss over this. That's a mistake Most people skip this — try not to..

The "make a 10 to subtract" approach is particularly beneficial for elementary students in grades 1 and 2, as it builds upon their existing knowledge of number bonds to 10 and introduces them to flexible thinking in mathematics. Rather than relying solely on counting backward or using physical manipulatives, this strategy encourages students to decompose numbers and rearrange them strategically, fostering a more sophisticated approach to problem-solving Simple as that..

Detailed Explanation

Understanding the Concept

The "make a 10 to subtract" strategy is rooted in the principle of decomposition, where a number is broken down into smaller, more convenient parts. But this method is especially useful when subtracting a single-digit number from a two-digit number, where the ones digit of the larger number is greater than or equal to the smaller number. The core idea is to adjust the problem so that it involves subtracting from 10 first, which is a fact most students have internalized through repeated practice.

Here's one way to look at it: consider the subtraction problem 13 - 8. They would then subtract 2 from 13 (leaving 11) and subtract the remaining 6 (since 8 - 2 = 6) from 11, resulting in the final answer of 5. Instead of immediately attempting to subtract 8 from 13, students using this strategy would recognize that 8 needs 2 more units to reach 10. This approach transforms a potentially challenging subtraction into two simpler steps, making the calculation more intuitive and less prone to error.

This changes depending on context. Keep that in mind.

Background and Context

This strategy is part of a broader set of mental math techniques known as "making tens", which also includes addition strategies like "make a 10 to add". These methods are emphasized in modern mathematics curricula because they promote number sense—the ability to understand numbers, their relationships, and their magnitudes. Number sense is critical for success in higher-level mathematics, as it enables students to approach problems with flexibility and confidence.

The "make a 10 to subtract" strategy is typically introduced after students have mastered basic subtraction facts and have developed a solid understanding of place value. It aligns with the Common Core State Standards for Mathematics, which encourage students to "add and subtract within 20 with mental strategies". By teaching this strategy, educators are helping students move beyond rote memorization toward a deeper conceptual understanding of arithmetic operations Most people skip this — try not to. Nothing fancy..

Step-by-Step Concept Breakdown

How to Apply the Strategy

The "make a 10 to subtract" method can be broken down into four clear steps:

Identify the ones digits: Look at the ones digit of the larger number and the smaller number you're subtracting.
Determine the difference to 10: Figure out how many more units are needed to turn the smaller number into 10.
Adjust the larger number: Subtract that difference from the ones digit of the larger number, which effectively subtracts from the tens place.
Complete the subtraction: Subtract the remaining part of the original smaller number from the result obtained in step 3.

Let's apply these steps to the problem 15 - 7:

Step 1: The ones digits are 5 (from 15) and 7 (the number being subtracted).
Step 2: To turn 7 into 10, we need 3 more units (10 - 7 = 3).
Step 3: Subtract 3 from 5, which leaves 2. This is equivalent to subtracting 3 from the ones place of 15, leaving 12.
Step 4: Now subtract the remaining 4 (since 7 - 3 = 4) from 12, resulting in 8.

Thus, 15 - 7 = 8 Took long enough..

Visual Representation

Visualizing this strategy can greatly aid comprehension. Teachers often use number lines or part-part-whole models to illustrate the process. To give you an idea, drawing a number line from 15 to 8 and showing the jumps of 3 and then 4 helps students see the relationship between the numbers and the steps involved No workaround needed..

Real Examples

Practical Application

Consider another example: 14 - 9.

Step 1: The ones digits are 4 and 9.
Step 2: To make 9 into 10, we need 1 more unit.
Step 3: Subtract 1 from 4, leaving 3. This represents moving from 14 to 13.
Step 4: Subtract the remaining 8 (since 9 - 1 = 8) from 13, resulting in 5.

Which means, 14 - 9 = 5.

This strategy is not limited to simple two-digit numbers. It can also be adapted for slightly more complex problems, such as 23 - 8:

Step 1: The ones digits are 3 and 8.
Step 2: To make 8 into 10, we need 2 more units.
Step 3: Subtract 2 from 3, leaving 1
Step 3: Subtract 2 from 3, leaving 1
Step 4: Subtract the remaining 6 (since 8 - 2 = 6) from 21 (1 from the ones place of 23), resulting in 15 Simple, but easy to overlook..

Which means, 23 - 8 = 15 Simple, but easy to overlook..

Additional Examples and Variations

The strategy works beautifully with larger numbers as well. For 47 - 9, students can:

Recognize that 9 needs 1 to make 10
Subtract 1 from 7, leaving 6
Then subtract the remaining 8 from 46, resulting in 38

It's the bit that actually matters in practice.

Teachers should make clear that this strategy develops flexible thinking and mental math abilities. Students learn to decompose numbers strategically rather than relying on counting backward, which becomes inefficient with larger values But it adds up..

Teaching Tips

When introducing this strategy, use concrete manipulatives like counters or base-ten blocks initially. Have students physically move objects to represent making 10, then transition to visual representations before moving to abstract thinking. Encourage students to explain their reasoning aloud, reinforcing the conceptual understanding behind each step.

Practice with varied problem types strengthens mastery. Include problems where the ones digit of the minuend is smaller than the subtrahend (like our examples), as well as problems where students must recognize when this strategy is most efficient compared to other methods And it works..

Conclusion

The "make a 10 to subtract" strategy represents a important milestone in elementary mathematics education. By moving students beyond basic fact memorization toward strategic reasoning, educators build the mathematical flexibility that serves as a foundation for more advanced concepts. This approach not only simplifies subtraction within 20 but also cultivates critical thinking skills essential for algebraic reasoning. In real terms, as students internalize this method, they develop confidence in their mathematical abilities and a deeper appreciation for the elegant patterns that exist within our number system. The investment in teaching such conceptual strategies pays dividends throughout students' mathematical journeys, creating capable, confident problem solvers who understand the "why" behind the "how.