In our last blog, Hello, Word Problems! Welcome to the 21st Century!, we contrasted the omnipresence of the use of percentages in our daily conversations and news reporting with the lack of examples in middle school math textbooks.
A classic problem in textbooks, likely dating back to the first percentage word problems found in petroglyphs on ancient stones.
In a class of 30 students, there are 18 boys and 12 girls. Calculate the percent of students that are boys. What is the value of calculating the percent? It is just another way to describe the already known boy-girl mix in the class.
To insult our students more, an even less meaningful calculation we often find requested in our current textbooks is:
Sixty percent of the students in a class of 30 are boys. How many boys are there? If the author knew 60% were boys, then they must have known how many were boys. The calculation of this problem is just “busy work.”
Teachers, if you have dedicated valuable time in your classroom to explain, illustrate and discuss the importance of knowing and calculating a percentage, then you have described how they are often a better descriptor than a ratio or number expressed as a decimal (18/30 or 0.60 in the above example).
Unlike decimals, in most contexts, percentages range naturally between 0% and 100%. They normally represent the share of a whole item, such as income or set of households.
For example, in U.S. reporting, households that spend more than 30% of disposable income on housing are classified as overburdened by housing costs. The U.S. Government Accountability Office (GAO) found that in 2017, 48% of renter households were cost burdened. They were paying more than 30% of their household income on rent. This is a six-percentage point increase from 2001, when 42% of renter households were cost burdened. Low-income households bore the brunt of this cost burden. The share of cost burdened extremely low-income, very low-income, and low-income renters in 2017 was 89%, 83%, and 54% respectively.*
Teaching our students that percentages are used for comparisons to explore issues of social justice and equity in diverse contexts will be invaluable to kickstarting their understanding of our society. This realization had special meaning to me this week as I worked with my granddaughter, Maytal, to solve mind numbing examples to compare two populations such as the percent of girls and boys who take AP calculus courses in high school to prove she was prepared. A problem calculating how a school reports the percentage of students testing positive for Covid-19 would be much more impactful.
Percentages also range from 0% to 100% when measuring performing on everything from personal achievement on an exam to manufacturing a batch of parts. Would you feel better about receiving a 100% score or a giant, red 1.00 at the top of the page? When 0% of a negative aspect is best, reporting 2% defective parts or 10% of high schools students drop out, seems more meaningful than a production run had .02 defects or a district had .10 students drop out (what is .10 of a student, anyway?).
Teachers, the next time you ask your students to calculate a percent stop, think, and refine the exercise so that the percentage adds insight to the work at hand. Afterall, the common goal of all of our work is to increase the percentage of examples in math classes that use meaningful contexts as reason for the mathematics calculation.
For examples of how the AMP21 curriculum can bring meaningful discussions about percentages to your classroom, download a FREE LESSON HERE.