A useful representation makes the quantities, operations, and relationships in a problem visible through a drawing, number line, place-value model, array, bar model, table, or equation. The learner matches a representation to addition and subtraction situations within 1,000, comparison and equal-group situations, and explains how it preserves the problem’s meaning rather than assuming that one representation fits every situation; formal algebraic models and more complex representations are beyond this scope.
First, ask: What is happening in the problem? Then choose a drawing or model that shows that relationship clearly.
Example:
The school library has fiction books and nonfiction books. How many more fiction books are there than nonfiction books?
Notice the relationship.
This is a comparison problem. We are comparing two amounts to find the difference.
Choose a bar model.
A bar model is useful because it shows the two amounts and the extra part.
Fiction: [--------- 178 ---------][--- ? ---] = 245
Nonfiction: [--------- 178 ---------]
The two bars start together. The fiction bar is longer, so the last part shows how many more fiction books there are.
Find the missing part.
Count up from to :
Add the parts:
Write the answer.
There are more fiction books than nonfiction books.
The bar model helped because it showed the comparison: the larger amount was made of the smaller amount plus the difference.
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