Skill: 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 $(245)$ fiction books and $(178)$ 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 $(178)$ to $(245)$:

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

Add the parts:

$$22+45=67$$

4. Write the answer.

$$245-178=67$$

There are $(67)$ 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.