Fraction basics

Teaching Pre K-8, Aug/Sep 2002 by Naylor, Michael

Develop "fraction sense" at any grade level with these beginning activities.

Fractions can be children's most - or least - favorite math topic. If you'd like your students to love fi-actions, that result can be achieved with a little time and attention. Too often, students learn rules for manipulating written fractions before they've developed an understanding of fraction concepts.

So, for the next few months, we'll focus on developing students' intuition about fractions, an intuition that will serve as a base for later proficiency.

Fraction models

I believe we should always use manipulative models when teaching fractions. There are three main kinds of fraction models, and it's best if children gain experience with all three.

1 Length models, such as paper strips or Cuisenaire(R) rods, are easily connected to ideas about fractions on a number line.

2 Area models are usually portions of rectangles or circles (these are also known as pie fractions or pizza fractions, for obvious reasons!). Children respond to area models, which work especially well for the purpose of modeling operations with fractions. Geoboards also make excellent area models.

3 Set models, such as colored chips or counters, can be the most confusing, but work very well for developing algorithms later on.

Beginning fraction activities

These beginning activities can be used at different grade levels. I'll expand upon them in the next several columns. Is It fair? (Grades K-2) Show pictures of different shapes divided into portions. Some of the shapes should be divided into equal portions and some should be divided into unequal portions. Ask students to name which ones are fairly shared and which ones are not. Then give them paper shapes (rectangles, circles, etc.) and have them divide the shapes into fair shares by drawing lines and then cutting the shapes apart on those lines.

Fraction posters. (Grades K-2) Use the fairly-shared pieces from the previous activity to create posters of halves, thirds, fourths and other fractions. Be sure each poster includes different shapes and sizes so your students can see that fractions can look different depending on the size and shape of the whole.

Mixed fractions. (Grades 3-5) Students need to be able to conceptualize both proper and mixed fractions. Proper fractions, like 23/4, are expressed as multiples of one size fraction, while mixed fractions, like 1 and 1/2, contain a whole number and a fractional part which is less than a whole. Students sometimes develop their own algorithms for converting between mixed and proper fractions - that's great! Usually this means they've made sense of fraction concepts. In those cases, don't supply students with a different algorithm, as this may confuse them.

For practice with mixed fractions, try asking your students, "How can you make 2 and 1/3 using just one kind of fraction?" Give your students several challenges such as this and have them use fraction pieces to support their answers. Try moving from proper to mixed fractions, having students express proper fractions like 13/4 as mixed quantities.

Comparing fractions. (Grades 3-- 5) Give your students a series of comparison questions such as "Which is greater: 3/4 or 2/3?" Students should explain in writing which fraction is greater and why, and model the greater fraction with a line, area or set model (be sure they explain themselves first). Here are some other comparisons which work well: 1/6 or 1/8? 1/2 or 3/5? 4/9 or 5/9? 4/5 or 5/6?

Can It be done? (Grades 6-8) What fraction pieces can be used to make 1/2? Can it be done using only thirds? Fourths? Sixths? Have your students try to make 1/2, 1/3, 1/4, 1/5 and 1/6 using just one type of fraction piece. Have them sketch each solution they find. If the work is organized in a chart, you'll see some interesting patterns.

Congruent fourths. (Grades 6-8) Using geoboards, have students make fourths which are the same size and shape. Students should record their answers on dot paper or graph paper. Compare shapes as a class.

There's a geometric idea hiding in this activity - there are two very different methods of creating congruent fourths, as shown on the next page. Once your students know the methods, they'll come up with many more interesting pieces!

Here are two examples with fourfold rotational symmetry. In the first two examples, all of the pieces meet in the center.

In the examples below, the geoboard is first divided into rectangular halves, and then the halves are appropriately divided.

You can download geoboard dot paper FREE at www.wwu.edu/-mnaylor/ dotpaper

Michael Naylor is a professor of math education at Western Washington University, Bellingham, WA and a Teaching Editor of Teaching K-8. E-mail: mnaylor@cc.wwu.edu