Fractions are easy to teach if they are taught in a simple, visual, manner first. This article is a step by step guide on how to bring a student from zero knowledge of fractions up to a higher level of competence. All of the best on-line math learning websites use the same core approach.
Teach Simple Fractions By Using Images and Examples
The first step in teaching fractions is to explain what a fraction is. Showing what a fraction is using an image is much more meaningful than trying to use an example like 3 / 8, and define the "numerator" as "3" and the "denominator" as "8". A useful tip when teaching fractions to someone with no knowledge, is to use the phrase "3 out of 8", instead of "three eighths".
It is important at this point to draw examples of fractions e.g. A rectangle split into eight parts, with 3 colored in, is 3 out of eight, or three eighths, see Figure 1.
Add and Subtract Fractions Of The Same Denominator
When the student is confident about what a fraction is, the next stage is to add and subtract fractions of common denominator. Drawing is still the best format. For example, draw two rectangles split into eight equal parts. Color in two of the parts from one rectangle, and five in the other. Below each rectangle, write the fraction (2 / 8 and 5 / 8). The student can then be asked to add the fractions. They will see that adding two parts from one rectangle to the five of the other gives seven parts.
At this stage, it is useful to introduce a very important concept: like can only be added to like. "Two dollars plus five dollars equals seven dollars"; "Two eighths plus five eighths equal seven eighths"; "Two eighths cannot be added to five dollars". See Figure 2.
Add and Subtract Fractions With Common Factors
Having explained how like can only be added to like, the student will be aware that two eighths cannot be added to five sixteenths. Somehow, the two rectangles need to be made in a way that they have the same "units". Placing the rectangles side by side, it can be seen that the eighths are exactly twice as large as the sixteenths. This is convenient - all that needs to be done is to split each of the eighths into two parts. See Figure 3.
Now that all of the units are consistent, they may be added or subtracted: two eighths is the same as four sixteenths, so two eighths plus five sixteenths equals four eighths plus five sixteenths equals nine sixteenths.
Add and Subtract Fractions With No Common Factors
Changing eighths into sixteenths so that fractions may be added was easy to understand, because eight divides sixteen exactly. Further examples of fractions like one half plus one third need to be taught though. One approach to teaching this type of fraction addition, is to state that multiplying the two (from the half) and the three (from the third) will give a unit that can be added. Drawing rectangles that each have six equal parts helps to understand this. One half is three sixths, and one third is two sixths. Adding these gives five sixths. See Figure 4.
The rationale for multiplying the two and three together is as follows:
- The fractions need to be in the same units before adding (or subtracting)
- In the example using eighths and sixteenths, only the eighths needed to be changed
- To add halves and thirds, they both need to be changed into a common unit - and multiplying two and three together will always give a common unit. For other fractions, multiplying the "bottom numbers" will give a common unit too, although it is easy to find the Least Common Multiple.
Teaching Fractions - Summary
Teaching fractions can be made very simple by a few simple ideas: use visual aids, start with simple examples, use real-life situations, emphasize that things may only be added when they are of the same type, and avoid using words like numerator and denominator until the student has some confidence. Every good math tuition book follows these rules, whether it is on-line math teaching or textbook for home-schooling.
Fractions References
There are many good on-line math teaching websites such as Teaching Ideas (teachingideas.co.uk)
Martin Bell - Martin holds a B.Sc. degree in chemical engineering, and an M.Sc. degree in electronics and computing. He has spent more than 25 years ...
Join the Conversation