Math Unmuddled: Ratios & Proportion

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

For children 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.


In this course, we address the important conceptual areas of Ratios and proportion. This topic, which has so much application in both real life and other areas of Math, causes real confusion among many children. This can be due to a number of reasons - one is that they often get introduced to it while they are still struggling with fractions. Fractions are related to Ratios of course, but are different and so the students get muddled. Here is a problem that shows this:

  • There are 2 girls and 3 boys in a group. Is the fraction of girls ⅔? Is the ratio of girls:boys in the group 2:3?

Also, the topic of ratios involves thinking in terms of multiples (multiplicative thinking) and not equal differences (Additive thinking).  Here is an example to illustrate this:

  • Salil, a 12 year old is thrilled to have his 8 yr old sister Sheena join his school. In Math class, he suddenly realises that the ratio of his age to Sheena’s  is 3:2. But he remembers that when he was 8 yrs old and joined this school, his sister was only 4 yrs old. How come the ratio was  2:1 then and it has changed now?

Another aspect that makes it tricky is that while working with Proportions, one has to notice changes in two or more things at the same time (Co-variational thinking). Here is an example.

  • Ria’s fruit punch recipe calls for 6 cups of fruit juice mix, 1 cup of sugar and 12 ice cubes for 4 people. She tries the recipe at home for her family of four and it tastes great. When Ria decides to make the punch for her Skating club party with a total of 12 people, she wants it to taste exactly the same. How can she change the recipe?

Inverse proportion only complicates things further when the basics are not clear to the student!


The course on Ratios and proportions will cover the following:

  • What the two numbers in a ratio represent and how they are related
  • What is the relationship between a ratio and fraction
  • Comparing ratios
  • Dividing a quantity in a given ratio
  • Notion of two things varying together, Equivalent ratios
  • Multiplicative thinking  and Direct Proportion
  • Inverse proportion

Reference:

  • Helping Students With Mathematics Difficulties Understand Ratios and Proportions, Barbara Dougherty, Diane Pedrotty Bryant, Brian R. Bryant, and Mikyung Shin, Teaching Exceptional Children, Vol.49, No. 2 pp 96-105

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.