Students learn to break two-digit numbers into different parts—such as tens and ones, or other combinations—to make calculation easier. For example, 25 can be seen as 20 + 5, or as 15 + 10, or as 24 + 1. This flexibility with numbers is crucial for mental math.
Use visual models like number lines, base-10 blocks, and part-part-whole diagrams. Practice writing different equations that show different decompositions of the same number.
You already know about tens and ones from place value: the number 37 is made of 3 tens and 7 ones, which you can write as 30 + 7. That is one way to break apart 37. Decomposing a number means breaking it into parts — and the standard tens-and-ones split is just the most obvious one. Numbers can be pulled apart in many different ways, and learning to see them flexibly is a superpower for mental math.
Think of 37 like a pile of building blocks you can divide however you like. 30 + 7 is one split. But 37 is also 20 + 17, or 25 + 12, or 36 + 1. All of these equations are true, and all of them mean the same total. You're not changing the number — you're just choosing where to cut it. Base-10 blocks help you see this physically: 37 blocks can be grouped as 3 rods-of-ten and 7 singles, or as 2 rods-of-ten and 17 singles, depending on what problem you're trying to solve.
This flexibility becomes useful when you want to add or subtract without pencil and paper. Suppose you want to add 37 + 25 in your head. You could decompose both numbers by tens and ones: 30 + 7 + 20 + 5. Then add the tens first: 30 + 20 = 50. Then add the ones: 7 + 5 = 12. Then combine: 50 + 12 = 62. You've turned a two-digit addition problem into two easier additions. The decomposition is the tool that makes this possible.
The key insight is that there is no single "right" way to decompose a number — the right decomposition depends on what makes the calculation easiest. Sometimes you want tens and ones. Sometimes you want to split a number so one part is a round number (like splitting 47 into 40 + 7, or into 50 − 3, if you're subtracting). As you practice, you'll start to notice which splits make problems simpler. That sense of number flexibility — seeing a number as a collection of different possible parts — is exactly what mathematicians call number sense, and decomposing is how you build it.