Definition
Multiple representations
Multiple representations are different ways of showing the same mathematical idea or relationship.
What it means
The maths stays the same while the way you see it changes. Seven can be shown with seven objects, a point at 7 on a number line, or the numeral 7. To check that representations match, compare the numbers, labels, scale, and relationships—not just how the picture looks.
Remember it
Change the window, not the maths: each view must show the same quantities and connections.
Example
To show 3 + 4 = 7, place three objects beside four objects, jump four steps from 3 to 7 on a number line, and write the equation 3 + 4 = 7. All three representations show the same addition fact.
Watch for
Two pictures are not matching representations when a count, label, scale, or relationship changes.
Common mix-up
A representation is not decoration; every important part must stand for something in the mathematics.
Exact meaning
Multiple representations are two or more mathematically equivalent forms—such as objects, drawings, words, tables, graphs, number lines, or symbols—that preserve the same quantities and relationships.