| How to Teach Fractions | | | | Children learn order of operation, but does the order |
| Frank Ho | | | | of operation apply to a simple fraction operation? |
| Ho Math and Chess Learning Centre | | | | The operation of fraction is also from top to bottom, |
| | | | | not necessary from left to right, so how does the |
| Canada, BC certified math teacher | | | | order of operation apply to fraction? I have never |
| | | | | seen any math textbook address this problem. For |
| Vancouver, BC, Canada | | | | example, 18/3 times 6, should the student do 18/3 |
| | | | | first then times 6 or should student do 6 divided by 3 |
| | | | | first then do 18/2? Many children get confused on |
| The traditional way of teaching fractions addition is to | | | | this point. If you do order of operation then perhaps |
| tell children that if the denominators of two fractions | | | | one would do 18/3 then times by 6 from left to right |
| are different then they must be converted to the | | | | but it is much easier to reduce the “big” |
| same denominator by using LCD. Sometimes two | | | | number by reducing so 6/3 should be done first. This |
| diagrams of pie charts are drawn to show the reason | | | | kind of problem about fraction has never been clearly |
| why. It teaches the concept by drawing diagrams to | | | | mentioned to children in math book and the |
| show the reason and then the procedure is taught to | | | | complexity of having 2 operations born with fraction |
| children on how to do it. Why most students still get | | | | was never taught to children in a clear way. |
| confused by this way of teaching fractions? | | | | |
| | | | | The top to bottom operation of fractions is very |
| I was at shock the other day when a grade-8 | | | | unique which is very different from a normal |
| students did 2 fractions of multiplications by flipping | | | | operation of left to right and this was also not clearly |
| the second fraction in his test and he got all fractions | | | | taught to children. |
| multiplications wrong. This is a student who actually | | | | |
| understands concept and could do fractions | | | | Is it enough to just draw some pie charts to expect |
| operations well, I was really confused on what he did | | | | children to master fractions operations? Clearly from |
| and he simply said to me that he forgot that | | | | my explanation above, it is not enough. Inherently the |
| multiplication does not need to flip the second | | | | invention of powerful fraction has created a very |
| fraction. | | | | complexity of operations but the center of teaching |
| | | | | seems to only concentrating on how to get children |
| I have been giving a lot of thought and feel that the | | | | to understand why there are different denominators |
| notation of fraction is a great invention since it | | | | instead of also explaining the different of meanings |
| actually defines the meaning of what is a rational | | | | of the notation of p/q it self and how it should be |
| number. With the above said, fraction is also the | | | | operated correctly. |
| most confusing concept in elementary math and | | | | |
| continues to be confused when going to rational | | | | It is not enough we just try to teach children on the |
| equation in high school. | | | | concepts of how fractions are operated, it is equally |
| | | | | important we teach children on how a fraction is |
| Have we taught fraction clearly to children? Can the | | | | different from other math operation with its hidden |
| concept of fraction be expressed much more clearly? | | | | division and multiplication. Why p/q is not necessary a |
| My answer is that we have not been teaching | | | | fraction and what is unit fraction. How a sign is placed |
| children in a clearer way but thought it would be | | | | on a fraction? Where a negative sign is placed on a |
| understood if we simply explain the meaning of | | | | fraction and where is its preferred place -- top, |
| fractions to them by drawing diagrams. | | | | down, or in the front? To show its value we like to |
| | | | | place a “–“ in front of a fraction but to |
| A number written in the form of p/q is not | | | | calculate we like to place it on the top. |
| necessarily a fraction. Its meaning is not really clear | | | | |
| until the question is presented. So this is the first | | | | 2Y means 2 times Y. The number 23 does not |
| misconception on children to think that just because | | | | mean 2 times 3. So why does 2 2/3 mean 2 + 2/3? |
| a number is written in the form of p/q then it is a | | | | Have we explained to children all these different |
| fraction. p/q can be used to solve ratio, rate, %. | | | | meanings? If we have not, then no wonder they |
| Proportion, probability etc. problems so a number | | | | get confused. |
| written in the from of p/q is not necessarily always a | | | | |
| fraction. | | | | How is 3/2 related to how an expression can be |
| | | | | expressed in remainder form? |
| Should the denominators be always changed to the | | | | |
| same LCD? Look at the following example, ½ plus | | | | Is it true that we can not do fraction division? If this |
| 2/4. Its LCD is 4 but why not change 2/4 to ½ | | | | is true then how come when children go to high |
| and ½ plus ½ is 1. Here we did not use LCD, | | | | school then they can do polynomial division and its |
| which is 4. So clearly there is something missing here | | | | divisor is not a whole number? |
| that we continue to tell children to always change all | | | | |
| different denominators to the same LCD. What is | | | | We are at fault by not showing that we can actually |
| missing is the unit fraction concept. ½ has an unit | | | | do fraction division by using the same concept of |
| fraction of ½. 2/4 has 2 of unit fraction ¼ so | | | | whole number division. For example, 2 divided by |
| they can not be added together because they have | | | | ½ and use the regular notation of whole number |
| different unit fractions. By reducing 2/4 to ½ then | | | | division that we can do 2 divided by ½ and we get |
| they have the same unit fractions. | | | | quotient 4 since 4 times ½ we get 2 and the |
| | | | | remainder is 0. Why we did not tell children that we |
| One of 3/8 pie and 3 of 1/8 pies have different | | | | can do it? Why we decide not to do it this way? |
| meanings even though the final quantity are the | | | | This again is one of many reasons that children do |
| same. This can be understood by introducing the | | | | not understand fractions is that we have failed to let |
| concept of unit fraction. | | | | them see the reason but simply tell them not do |
| | | | | fraction division. |
| The most confusing about fraction is that the | | | | |
| fraction notation itself has 2 operations hidden. They | | | | I feel there are more work we need to do on how |
| are division and multiplication. So 2/5 can be thought | | | | we introduce fractions to children and let them |
| as 2 divided by 5 but it also can be thought as 2 | | | | understand its operations and see the result on what |
| times by 1/5. No wonder our children get confused. | | | | would happen if they do not follow the suggested |
| | | | | way. |