Definition
Mathematical representation
A mathematical representation is a form that shows a mathematical idea, quantity, relationship, or process.
Continue from this idea into connected AXIO math.
What it means
The same mathematics can wear different forms. Twelve can be shown as counters, a 3-by-4 array, the words 'three groups of four,' or 3 × 4 = 12. Each form makes some features easier to notice, but it must still tell the same mathematical story.
Remember it
Change the form, keep the relationship.
Example
For 3 groups of 4, place twelve counters in three equal groups, draw a 3-by-4 array, write 'three groups of four,' and write 3 × 4 = 12. The forms look different, but each keeps three groups, four in each group, and a total of twelve.
Watch for
A picture of twelve unrelated decorations may show twelve objects, but it does not represent three equal groups unless the grouping is visible or stated.
Common mix-up
Representation does not mean decoration or a copy; it must carry the mathematical meaning needed for the task.
Exact meaning
A mathematical representation is an object, picture, diagram, word statement, symbol, table, graph, or other form that expresses mathematical meaning while preserving the relationships needed for its purpose.