Seedlings
A gardener plants seedlings in 6 rows of 8.
Here are two ways of representing the seedlings.
Both representations show 48 seedlings.
They differ in how those seedlings are arranged into rows.
How many seedlings are there altogether?
Both preserve what matters for this question: the total of 48 seedlings.
For this question, the arrangement into rows does not affect the answer.
How many seedlings are in each actual row?
Representation A preserves the actual row structure: 8 seedlings in each actual row.
Representation B preserves the total of 48 seedlings, but not the actual row structure.
For this question, that difference matters.
The seedlings did not change. The representations did not change. What changed?
In the first question, the representation only needed to preserve the total.
In the second, it also needed to preserve the actual row structure.
What a model needs to preserve depends on what you want to use it for.
A rectangular arrangement has 4 rows of 9 tiles.
Two possible representations show 4 × 9 and 9 × 4.
Either representation: How many tiles are there altogether?
The difference matters: How many tiles are in each actual row?
What a model needs to preserve depends on what you want to use it for.
You compared two representations and tested how well each one preserved what mattered for different questions.