Student Reasoning about Percentage
Over the primary and middle school years it is likely that student understanding in relation to percent will develop in the following sequence.
Basic understanding of percent as a part-whole representation with the whole equal to 100%.
Appreciation of the relationship between percent and fraction and decimal representations, e.g., 75% = 3/4 or 75% = 0.75
Interpretation of percent in contexts, e.g., 15% risk of a rash
Use of percent calculations to work out a part from a whole, e.g.,
60% of 200 = □
Use of percent calculations to work out a “remainder” part from a whole, e.g., what is the price of an item with a 20% discount?
Ability to calculate the percent of a part to a whole, e.g.,
□ % of 200 = 150
[□% = 150/200]
Ability to use percent to calculate a whole given the part, e.g.,
60% of □ = 120
[□ = 120/0.6]
This sequence represents increasingly complex use of proportional reasoning. Throughout the middle years students should become increasingly able to interpret percents in media contexts and question those that appear without adequate justification.