Through visualization, algebra-type word problems can be solved without formally introducing algebra. Here is a typical example of a non-routine word problem from a 4th grade Singapore Math workbook involving fractions:
⅓ of Amy’s money is equal to ½ of Bob’s money. Amy has $40 more than Bob. How much does Amy have?
A good visualization tool to solve such a problem is the bar model. For example,
Without explicitly representing any values with variables, students can easily visualize the problem and are able to understand there are 5 equal units involved. The extra unit that Amy has is exactly $40. So, since Amy has 3 of these units, she has 3 x $40 = $120.
Recognizing problems visually also makes them think algebraically. Without realizing it, students would be working with algebra through interesting word problems.
