A Fraction Too Much?

Post date: Oct 20, 2013 7:20:10 PM

As I plan to start fractions with my fifth class this week, I thought I'd share some of my favourite resources.

Any teacher of first to sixth classes should consult A Guide to Teaching and Learning Fractions in Irish Primary Schools as their main resource/reference before starting fractions. This excellent and comprehensive guide from the PDST, divides up the targeted content into five levels:

    • Level A: Deals mainly with halves (first class) and quarters (second class)

    • Level B: Concerned mainly with halves, quarters, eighths and tenths (third class) but the methodologies could also be applied to thirds, fifths, sixths, ninths and twelfths (fourth class and fifth classes)

    • Level C: Equivalent fractions (fourth class) developing on to include improper and simplified fractions as well as mixed numbers (fifth class)

    • Level D: Operations and Fractions; D.1-D.3 for fifth class and D.4 & D5 for sixth class

    • Level E: Ratios (sixth class)

Therefore, I am going to start this week by looking at the relevant activities in Level B, moving onto those in Levels C and D when we're ready.

The particular things I like about this guide, is the emphasis it puts on the Concrete, Pictorial, Abstract (CPA) approach, how it highlights the importance of using different models in our teaching of fractions (area, linear and set), but most of all its teacher-friendly structure, giving examples of how the teacher can prompt and question the children.

A great accompaniment to the linear approach, is this great 5 min video clip, Introducing fractions and exploring equivalent fractions: that shows a teacher assessing what her class already know about fractions, and getting the children to explore equivalent fractions by producing their own fraction walls. This is the activity that I will be doing first with my class. It would also suit children in third and fourth (and perhaps even sixth) classes; the teacher can limit the pupils to the fractions for their class level or they can be allowed to include as many fractions as they can make. I usually do this activity with the class organised into ability groups; that way I can support those that most need it, while also allowing the more able to develop the fraction wall as far as they can.

Also worth mentioning from this video clip, is the teacher's use of the words numerator and denominator; children in fifth and sixth should definitely know and use this vocabulary when discussing fractions, and I wouldn't avoid using this terminology with fourth classes either. I usually explain the denominator as the part that names the fraction (eg sixth, tenth etc) while making connections with other words we know (eg nominate - to name; nom is French for name etc). The numerator (coming from Latin numerous, meaning number) tells us the number of equal parts (eg sixth, tenth etc) we are referring to. I have seen the denominator also being described as the number downstairs, and while mnemonics such as this can be helpful to children, it is important that they take second place to discussions that develop the children's understanding of fractions.

When is comes to operations with fractions, I would recommend fifth (and sixth) class teachers to check out Just a fraction: a Teachers TV video of how to teach addition, subtraction and multiplication of fractions. I use a variation of this approach every year, but using paper plates instead of the paper cups used in the video; this allows me to demonstrate addition, subtraction and multiplication with eighths, as well as halves and quarters, as shown in the clip.

By the way, the curriculum objectives for fifth class say we should enable the child to add and subtract simple fractions and mixed numbers; however most of the textbooks include all types of fractions, of every type of denominator. Using the paper plates approach, almost every child (if not all) will be able to add and subtract halves, quarters and eighths, and many will be able to further apply this understanding to operations concerning fractions with more complicated denominators.

Picture the scene; you pose this question: Three quarters of a number is 12; what is the number? and the answer you get is 9. And when asked how they got this answer, the usual response is I divided by the bottom, multiplied by the top. If this has been your experience then you should check out another favourite of mine; Thinking Blocks for Fractions. This free online tool, and more recently, iPad app, is a great way to encourage children to visualise the fractions and use this understanding to solve fraction problems.

To encourage children to recognise fractions in the world around them you could all look at Fractions out shopping: another 5 min video that could be used as a lesson starter.

Also worth checking out is my Fractions, Decimals & Percentages Board on Pinterest; a great, visual way to get some quick ideas.


While there are lots of other sites etc., that can be of great help when doing Fractions (or any topic), I would also urge educators to examine carefully the content and to evaluate the approaches suggested for themselves. For example, many of the US sites use the term reducing fractions interchangeably with simplifying fractions; however the PDST guide says that:

The phrase ‘reducing fractions’ when simplifying fractions should not be used because it implies that the fraction is being made smaller. This is not the case. Fractions are simplified not reduced.

I usually use the phrase "Same value, different appearance" to describe fractions that can be expressed in different forms, and explain that it is preferred to express a fraction in its lowest form, when possible.

Also worth noting is that some of these sites tend to focus on what to do, in a procedural way (eg do this, then do this, finally do this and you'll get the correct answer), rather than placing the emphasis on the children seeing patterns, making connections, and using what they know to solve what they don't know. As always, we need to teach them to understand the maths involved, not just teach them to do maths.