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.
For more related resources, please refer to our Bar Models page.