Consider this problem:
Try to solve this problem using (1) algebra and (2) pictures. You may be surprised at how one method seems so much clearer than the other.
- Jane is 1/2 as old as Tom.
- Mary is 2/3 as old as Tom.
- How old is Jane compared to Mary?
Now, view the same problem using percentages instead of fractions:
Aren't the wording and language of mathematics a joy!
- Jane is 50% younger than Tom.
- Tom is 50% older than Mary.
- Does this mean that Jane is the same age as Mary?
Source: List serve for the Adult Numeracy Network, 2006
Hint: Use pieces of birthday cakes if you cannot think of any other pictures to use.
Solution Commentary: The necessary commentary has already been given within the problem's statement.
Students need to experience problems like this (though artificial) so that they can explore both the power of alternative solution techniques and the misleading aspects of mathematical language.