Definition
Concrete model
A concrete model uses physical objects to show a mathematical quantity, structure, or relationship.
Continue from this idea into connected AXIO math.
What it means
You can touch the model, but the important part is what each object stands for. A counter may stand for one item, a ten-rod for ten ones, or a strip for one whole. Moving or regrouping the objects should keep the same mathematical relationships as the problem.
Remember it
Hands on, maths on: every piece has a mathematical job.
Example
Build 34 with three ten-rods and four unit cubes. The three rods stand for 30 and the four cubes stand for 4, so the model shows 34. Exchanging one rod for ten cubes changes the pieces, not the value.
Watch for
A pile of blocks is not a concrete model unless the blocks' features are linked consistently to the quantity or relationship.
Common mix-up
Concrete describes the physical representation, not an easier kind of mathematics; the same idea can later be shown with pictures or symbols.
Exact meaning
A concrete model is a mathematical representation made with physical objects whose counts, sizes, positions, or connections correspond to the mathematics being studied.