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Choose a useful representation

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.

Detailed Explanation: Choose a useful representation

First, ask: What is happening in the problem? Then choose a drawing or model that shows that relationship clearly.

Example:
The school library has (245)(245) fiction books and (178)(178) nonfiction books. How many more fiction books are there than nonfiction books?

  1. Notice the relationship.
    This is a comparison problem. We are comparing two amounts to find the difference.

  2. 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.

  3. Find the missing part.
    Count up from (178)(178) to (245)(245):

178+22=200 178+22=200 200+45=245 200+45=245

Add the parts:

22+45=67 22+45=67
  1. Write the answer.

245178=67 245-178=67

There are (67)(67) 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.

Learn by doing: Choose a useful representation

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Base 10 Blocks - Less or Greater Than - Pictures to Symbol - Hundreds and Tens


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