Arranging numbers in increasing or decreasing order (e.g., 3, 7, 12, 19 or 20, 15, 8, 1) develops understanding of number magnitude and sequence. Using a number line as a reference makes this concrete.
You already know how to compare two numbers — you can look at 7 and 12 and say that 12 is greater. Ordering takes that same comparing skill and applies it to a whole group of numbers at once. Instead of deciding which of two numbers is bigger, you arrange a whole collection of numbers from smallest to largest (or largest to smallest), placing each one in its correct position relative to all the others.
The number line is the clearest tool for this. Because numbers are arranged on the line in order from left to right — 1, 2, 3, all the way to 20 — any number's position tells you its relationship to every other number. A number that appears further right is always greater than a number to its left. So if you want to order the numbers 5, 14, 2, and 9, you simply find each on the number line and read them off from left to right: 2, 5, 9, 14. The number line does the work of holding all the comparisons at once.
Ascending order means going from smallest to largest — numbers climb upward: 3, 8, 11, 17. Descending order means going from largest to smallest — numbers come down: 17, 11, 8, 3. Both are just the same sequence read in different directions. A good way to check your ordering is to make sure each step is a move in the same direction: if you're going ascending, each next number should be larger than the one before it. If any number breaks that pattern, something is out of place.
Ordering numbers builds the foundation for later work with two-digit and three-digit numbers, where you'll use the same logic but need to compare tens digits before ones digits. Right now, with numbers up to 20, you can often just visualize the number line and place numbers by feel — and that mental picture of numbers arranged in a line, each in its rightful place, is one you'll use in mathematics for the rest of your life.
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