Definition
Mathematical model
A mathematical model is a math-made version of a situation used to describe, solve, or predict.
Continue from this idea into connected AXIO math.
Boundary check: The model keeps selected relationships and assumptions; it is not the situation itself.
What it means
A model keeps the quantities and relationships that matter, then expresses them with mathematics. It might be a bar diagram, a table, a rule, or several of these together. Use the model to work something out, then check whether the answer makes sense in the original situation. A model can be useful without copying every real detail.
Remember it
Keep what matters, turn it into maths, then check it against reality.
Example
A box holds 6 apples. For b boxes, the model a = 6b connects the number of boxes to the number of apples. With 5 boxes, the model gives a = 30. It assumes every box is full and holds the same number of apples.
Watch for
A model is not the situation itself, and its conclusions are only as good as its assumptions and chosen relationships.
Common mix-up
A diagram can be part of a model; the model also includes what the parts mean and how they relate.
Exact meaning
A mathematical model is a representation of selected features and relationships in a real or imagined situation, made with objects, diagrams, tables, graphs, expressions, equations, or simulations. It is used to reason, calculate, explain, or predict within its stated assumptions.