Exploring patterns is a fundamental activity in mathematics. Observing quantitative groupings is one way of making sense of patterns like tile arrangements. If we look for repeated groupings, we can use them to predict parts of patterns we can't see, and we can communicate our ideas by recording mathematically how we "see" those groupings.
Here's a simple tile arrangement.
We could count the tiles one-by-one very easily, but we want to use grouping methods that we can represent with mathematical statements. That way, we can communicate to others how we "see" the groups that make up the arrangement.
Either way, the total comes out to be fifteen. Each way of seeing, however is distinct, and reveals the thinking of the observers. We can understand how they see the groupings by reading their mathematical statements. See if you can picture the ways the students who wrote these mathematical statements saw the groupings:
(7 x 2) + 1
(2 x 4) + (2 x 3) + 1