Ordering two-digit numbers means arranging a set of numbers from least to greatest or greatest to least. Students first sort by tens digit, then by ones digit within ties. This extends pairwise comparison to sequences and prepares students for reasoning about number position on a number line.
Give students sets of number cards to physically sort and re-sort in both directions. Start with three numbers, then build to larger sets. Require students to explain reasoning using place value language (tens first, then ones).
You already know how to compare two two-digit numbers: you look at the tens digit first, and whichever number has more tens is bigger. If the tens digits are the same, you compare the ones. That skill — comparing a pair of numbers — is the foundation for everything in ordering. Ordering just means applying that comparison skill to a whole group at once, arranging them from least to greatest or greatest to least.
Here is one way to think about it: imagine each two-digit number as a house on a street. The tens digit tells you which block the house is on (the 20s block, the 40s block, and so on). The ones digit tells you which house within that block. To arrange the houses in order, you first sort them by block — all the 20s together, then all the 30s, then the 40s. Within each block, you sort by house number. This two-step process (tens first, ones second) is exactly the rule for ordering numbers.
A useful strategy when you have a set of numbers is to group by tens first. Take the numbers 47, 23, 51, 38, and 29. Before putting them in order, notice: one is in the 50s, one is in the 40s, one is in the 30s, and two are in the 20s. That gives you the rough order immediately — the 20s come first, then 30s, 40s, 50s. The only careful decision is within the 20s: is 23 or 29 smaller? Since 3 < 9, 23 comes before 29. So the full order is 23, 29, 38, 47, 51.
When the direction is greatest to least, you are simply reversing this process — starting from the largest (highest tens digit, then highest ones) and working down. The comparison rules are exactly the same; you just read the result in the opposite direction. Practicing both directions builds a flexible sense of where numbers sit on the number line, which you will use throughout all of your future work with numbers.