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| Didax "Class Ideas" Newsletter Archive |
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With the school year coming to an end around here, kids are antsy to get outside and enjoy summer vacation. There are a few more weeks, however, and I hope this issue of Class Idea gives you some new ideas for working with Fractions in your classroom. And if this newsletter comes too late in the year for you, perhaps you can keep them in mind for next year.
This month's issue features an article detailing the three main models used in Fraction instruction, several information-packed website links, some downloadable activity pages to jumpstart your lessons, and of course, a Class Ideas subscriber-only special.
I love to hear your comments and suggestions. If you have an idea for a feature or topic you'd like to see covered in the newsletter, please send me an email. Thank you for reading!
Anna Mullen, Editor |
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| Teaching Fraction Concepts: Three Models |
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 Fractions are one of the most difficult mathematical concepts for students to master. It has even been found that college students studying to be teachers find it difficult to explain the meaning of fractions and generate appropriate fractional problems (Ball, 1990). However, using models to teach fractions is effective in giving students a base understanding and mastery of fraction concepts, allowing them to then move on to fraction computation.
The three basic models used to teach fractions are parts of a whole, parts of a set, and measurement. Being introduced to these three representations gives students a strong understanding of fractions. Introducing the models in the above order ensures a smooth learning progression.
Parts of a whole demonstrates fractions by dividing a whole into two or more pieces. This model divides a whole into sectors or regions, linking the more basic concept of division to fractions. Fraction circles, fraction squares, and even fraction strips are all good examples of whole models. A good real life example of this model is the popular pizza example, if a pizza is divided into four slices, each slice is 1/4 of the pizza.
Parts of a set differs from parts of a whole in that the entities in the model are distinct. For this model, almost any items can be used for demonstration as long as there are multiple items. An example of demonstration parts of a set is a bag of marbles divided among multiple children. If there is a bag of twelve marbles and four children to share them among, each child receives three marbles, or one-fourth of the marbles.
Measurement, at the most basic level, demonstrates fractions as students read a number line. Other measurement concepts used in teaching fractions are length, area, volume, weight, temperature, time and angles. An example of using a measurement model is determining how many minutes are in a quarter of an hour.
Tips for effective fraction instruction:
Demonstrate solving problems and allow students to observe you before assigning individual work.
Begin with concrete demonstrations (manipulatives), and progress to semi-concrete materials (such as pictorial representations), and finally introduce abstract problems (using numerical representation).
Allow for parts of a whole and parts of a set fair-sharing activities. This shows students that fractions are not always parts of a single whole, a very common misunderstanding. Fair-sharing activities also tend to promote meaningful discussion.
Provide guided practice before assigning independent work to ensure that skills are developing. This helps avoid frustration and reinforcement of incorrect skills.
Vary the types of problems you assign. Keep students interested in this difficult topic.
Allow time for lots and lots of practice. Fractions are a difficult concept and the more time students have to get comfortable with the concept the better their preparation for more advanced mathematical learning.
Be sure that students understand the concepts of operations and fractions very clearly before moving on to fraction computation. Understanding equivalence and fraction order are also important to master before performing operations with fractions.
References:
Ball, T.L. (1990). Prospective elementary and secondary teachers understanding of division. Journal for Research in Mathematics Education, 21, 132-144. |
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| Downloadable Fraction Activity Pages |
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 This month's downloadable activity pages come from two of our most popular World Teachers Press titles, The Fraction Book and The Early Fraction Book. These books explore the relationships between fractions, decimals and percentages, reinforcing the equivalences in these methods of expression. With activities in a range of grades, from 3 to 8, I hope you'll find some useful pages for your classroom! |
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| Fraction Internet Resources |
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 The Internet is a great resource for both lesson plans and background planning information. Here are a few websites to get you started on learning more about Fractions and teaching them in your classroom. From an article on the history of the Fraction concept, to ideas on using pattern blocks in your instruction, there's a lot of great information just a click away. |
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| July/August Theme: Back to School |
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 Look for the next issue of Class Ideas. This double issue will arrive in your inbox at the end of July, in time for your back to school planning. In addition to great ideas to get your 2005-2006 school year off to a great start, there will be a big subscriber-only special and lots of links to helpful websites. |
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