Math Unmuddled: Percentages

Math Unmuddled: Percentages

The ‘Math Unmuddled’ series takes up topics that pose common difficulties for children and clarifies these to build strong conceptual foundations.

For students entering Grades 6, 7, 8 in 2021-22


A good grasp of basic Mathematics is important in today’s world, irrespective of the career one chooses to pursue. While Math is typically associated with Science and Engineering, it is hard to think of any line of work that does not involve an understanding of school-level Math (at least till grade 10). Unfortunately, many students struggle with the subject and even develop a fear of Math. The most common reason for this is that they attempt to remember many disconnected rules and procedures, and this makes Math seem more difficult than it is.


The GenWise team has seen many instances of this in their experience. For example, we have asked grade 2/3 students to perform a division like 391/17. After they answer this correctly and say ‘23”, we ask them to multiply 23 by 17. We find that there are always some students who start performing this multiplication instead of immediately seeing that the answer has to be 391 (because multiplication is the inverse of division). When underlying concepts such as these are understood, there is ‘less to remember’ and Math becomes simple and unmuddled. The ‘Math Unmuddled’ series takes up topics that pose common difficulties for children and clarifies these to build strong conceptual foundations.


Irrespective of whether the child goes on to become a DJ or a Historian or an Engineer, she will be in a much better place if she understands and can fluently apply the concept of percentages. This course in the series addresses student difficulties with Percentages at many levels. They often think that since the percentage is to do with “for 100,” the percentage value has to be less than 100.

  • Roshan, who was earning about Rs. 1500/- per day as a carpenter, is now doing a course to become an interior designer.  Once he sets up his business, he is hoping to earn about Rs. 3500/- per day. What would be the percentage increase in his earnings?

Another is that they get confused between an absolute increase and a percentage increase. For example:

  • What is 50 increased by 20%?

Some 23% of 9000 students who answered this chose the answer as 70.


Conversion can also make it more tricky. When students internalize the decimal-percent or percent-decimal conversion as a set of rules, rather than thinking about it using her sense of decimals on a number line, it can be confusing. Here is an example.

  • Based on a figure of a circle in which 9 parts out of 10 are shaded, the question asks, From the shaded portion of the figure, we can say that 0.9 is the same as...

When they had to do this problem, about 1700 students (of 13500) chose 9% as the answer even when they had a shaded figure to help.


They depend on the “moving decimal points” rule, but when they forget it, they get it wrong. The student is not able to use his/her knowledge of how close 0.9 is to 1.0 when he/she converts it to a percentage.


Students are also often unaware of the flexibility that comes from being able to convert fluently among Fractions, Decimals and Percentages as a way to approach a problem such as this one:

  • Sometime into a car journey of 600 km scheduled for 12 hours, Aryan’s father tells him that although 50% of the scheduled time is up, only one third of the journey is over because the drive was uphill so far on narrow winding roads. He said they would  cover the remaining distance in the scheduled time. 
  • How much longer do they have to drive? How much distance do they still have to cover?

This course will aim to clarify percentage, and its relationship to decimals and fractions; it will cover the following topics:

  • The concept of “per 100”
  • How percentages relate to fractions and decimals
  • Problem solving with very varied examples

References:

https://blog.ei-india.com/2015/03/24/super-test-and-common-misconceptions-in-percentages/

https://mr-mathematics.com/percentages/


Note:

The course is not a substitute for learning the topic in school. It is assumed that students already have some familiarity with the topic. Also, in the limited time available in this course, it is not possible to focus on practice. Students must internalize what they learn in the course through subsequent practice, under the guidance of a teacher or a parent.