Comparing quantities means determining whether one group has more, fewer, or the same number of objects as another. Children can compare by matching (one-to-one) or by counting both groups and comparing the numbers. The vocabulary 'more,' 'fewer,' and 'equal' describes these relationships.
Use physical matching: line up objects from each group in pairs and see if any are left over. Later compare by counting: 'I counted 5 red and 8 blue; 8 is more than 5.' Use the language consistently in daily contexts.
You already know how to count objects and how counting a group tells you how many are in it. Comparing quantities is the next step: instead of asking "how many?" about one group, you ask "which has more?" about two groups. This is one of the most fundamental ideas in mathematics — the ability to compare sizes is what turns counting from a memorization exercise into a reasoning tool.
The most natural way to compare is by one-to-one matching: line up objects from each group in pairs and see which group runs out first. If you have 4 apples and 7 oranges, match each apple to one orange — after pairing up 4 of each, you have 3 oranges with no apples left to match them. Those leftover oranges tell you: there are more oranges. This matching strategy works even before you know any number names, which is why it's so foundational. Mathematicians call this a bijection — a perfect pairing between two sets.
Once you can count reliably (your hard prerequisite), you can compare by counting both groups and then comparing the numbers. Count the red crayons: 5. Count the blue crayons: 8. Now the question "which group has more?" becomes "which number is bigger: 5 or 8?" Counting bridges physical objects to numbers, and comparing bridges numbers to the physical question of "more" and "less."
The key vocabulary — more, fewer, and equal — describes three possible outcomes of every comparison. Equal (also called "the same") is a special case: both groups have exactly the same count, so matching leaves nothing left over and counting gives the same number. Recognizing all three possibilities, not just more and less, is what makes comparison complete. As you move forward to ordering numbers and doing arithmetic, every step builds on this foundation: knowing that 8 is bigger than 5 is just another way of saying the group of 8 has more than the group of 5.