A Fraction as a Comparison as a Pizza as a Percent

This week in class we talked about fractions.                                            
We discussed the many ways of thinking about fractions and some different resources that can be used to teach fractions in order to adhere to different styles of learning and levels of comprehension.
           When I hear fractions, my immediate thought is ‘a part of a whole’ and the example I think of is a large pizza with one or more slices missing.

© CLASSWISH 2008-2016

No, that is not incorrect but it is also only a small part of understanding fractions. There are so many ways to describe a fraction…

A fraction as one thing compared to another

This explanation is not one I would think of when discussing fractions. However, after this week’s lesson it is probably one of the first I would teach my students.

          Why? Over the last few weeks we have discussed the importance of bringing real world scenarios and ideas into our lessons to encourage a deeper understanding. We are always making comparisons in real life.

Looking back at the pizza we can understand it as parts of a whole:

One part of the whole pizza is missing, the whole pizza has six slices so therefore there is 5/6’s of the pizza left.

Or we can look at it as a comparison:

If I’ve taken one slice of the pizza then there are five slices left for my friends. I am comparing my one to the other five in the box. If we add these up to create a total we have once again created fractions.

By demonstrating fractions as comparisons we are still teaching the ‘part of a whole’ definition but using the same steps one might go through with any day-to-day situation. The ‘fractions as comparisons’ definition might be one I would use to introduce fractions to my class or as review before delving deeper into the more complex aspects of the unit.

This concept was presented to us in class this week using Hershey’s Fraction Book. Hershey’s Fraction book is a children’s novel that uses the 12 portions of a Hershey’s classic milk chocolate bar to demonstrate fractions; one of the ways it does this is through comparisons. 

The book asks you to break the chocolate bar into pieces and compare how many you have in each group to create fractions (eg. If you break off 5 squares of chocolate you have 7 left, therefore providing you with one group of 5 out of 12 chocolates and one group of 7 out of 12 chocolates making your fractions 5/12 and 7/12). Children's books can be great resources for teaching math to students because they often break concepts down into very simple forms making them easier to grasp.  I would definitely use this book in my own classroom because it explains the big ideas in a very understandable way and uses an engaging topic (any excuse to use chocolate in the classroom is good with me!)

Once fractions have been introduced, we can provide phrases that show the connections between different arrangements of numbers:

              

A fraction as a ratio as a decimal as a percent

Just as we provide students with manipulative's as well as pencil and paper examples to help them grasp a concept, we can provide students with different ways of presenting fractions. Some students may really like the idea of comparisons and will prefer to look at fractions as a ratio and some students may find it easier to understand a fraction when it is converted to percent form. It is important we, as teachers, demonstrate that all of these arrangements are equal and as long as we can explain how to properly convert them students can choose the option that works best for them. Although this definition may be more applicable to students with a greater understanding, I chose to focus on it because I liked that it provided options. One of the things about math I struggled with most as a student was the idea that there was only ‘one way’. I think that if we show students they have options it will make math far more appealing and understandable to students of all learning styles and abilities.

Ensuring students have a strong grasp on fractions is very important as they are not only a vital part of basic math but they are used all the time in every day life. The ‘Exploring Fractions’ video is a great resource to show students to help them understand how often they will use fractions throughout their own lives.