Math Unmuddled: Fractions

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.

This course in the series addresses the difficulties that many children face while working with Fractions. When they learn the concept of Fractions as a set of rules without real understanding, it becomes a very challenging topic.

Here’s an example of two such “rules:”

Rule 1: To Convert a mixed number to a fraction, apply this rule:

Multiply the whole number part by the denominator and add the numerator to get the numerator. Use the common denominator as in the fractional part of the mixed number.

Rule 2: To Add Fractions with different denominators, apply this rule:

First find a common denominator by taking the least common multiple of the denominators. Then convert all the addends to have this common denominator. Then add using Rule 1.

When students really understand what fractions represent, they don’t need to memorise any rules!  Whether it is Equivalence or LCM, it makes logical sense once they are able to visualise what is going on.

Apart from being so much a part of life, Fractions form the basis of so much math that follows - ratio and proportions, percentages, decimals, and of course Algebra. It is all the more critical that they explore and understand fractions thoroughly.

This course is based on the gaps in student understanding of Fractions. Some of the topics that will be covered are:

• What a fraction is and how is it related to whole numbers
• What the numbers in a fraction represent and how they are related to each other
• Different representations of a fractional quantity and how they are related
• Fractions on a number line
• Equivalent fractions
• Four operations
• Translating English to Math - Word problems

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.

Reference:

• https://www.homeschoolmath.net/teaching/teaching-fractions.php