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Teaching Fraction Operations: Methods & Manipulatives

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  • 0:04 Learning the Rules
  • 0:37 Context
  • 1:47 Addition and Subtraction
  • 5:07 Dividing Fractions
  • 6:03 Lesson Summary
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Lesson Transcript
Instructor: Matthew Bergstresser
Fractions are part of everyday life. Being able to add, subtract, multiply and divide fractions are important skills. In this lesson, we will discuss various methods to help students work with fractions.

Learning the Rules

Have you ever played a game, whether it was a sport, card game, or board game, that you have never played before? The first step in playing is to learn the rules. Sometimes the rules don't make sense until you actually play the game. This is often what it is like for students trying to learn how to work with fraction operations. Being told the rules alone may not be enough to understand what fractions are about. Let's discuss a few methods and use of manipulatives that will instill a deeper understanding of fraction operations in our students.

Context

Before students can add, subtract, multiply, or divide fractions, they have to understand what a fraction is. This process can begin with a lesson on ratios, which is what a fraction is. Using real world examples of ratios and how they translate into fractions is an effective method.

Start off by having the students count the number of girls in the room, then the number of boys in the room, and the total number of people in the room. For our purposes, let's say there are 8 girls and 12 boys, totaling 20 people including the teacher. Explain to them the ratio of girls to boys in the room is eight to twelve, which can be written as '8:12,' and the whole is 20 people. Then explain to them how to set this up as a fraction 8 girls divided by 12 boys, which can be reduced by dividing 4 into each number resulting in 2/3 or 2 girls for every 3 boys. When you feel they grasp the concept of a ratio and fraction, you can take the next step, which is adding and subtracting fractions.

Addition and Subtraction

Adding and subtracting can be quite challenging to students. The sticking point is having to get a common denominator and why. You can explain this by asking the students to add 3 apples and 2 bananas. It is common for them to answer 5, to which you say, '' 5 what?'' Let the students think for awhile and accept any answer that is correct such as 5 pieces of fruit. Explain to them this is what a common denominator is like. Both fractions share this value in common and it is put in the denominator. Let's look at some techniques for adding and subtracting fractions.

Fraction Models

Fraction models are similar to puzzle pieces. They consist of various rectangular pieces that are sized appropriately relative to the whole. For example, a rectangular whole can be broken down into as many parts as you want. Let's say you want it broken down into halves, thirds, quarters and fifths. These values are rectangles with lengths that total the whole.

These manipulatives can be used to teach students to add and subtract fractions. For example, add 1/5 + 1/5 + 1/5. Since there are three 1/5 fractions, the answer is 3/5. You can have the students determine the various combinations of fractions required to make a whole.

You can also have the students take a rectangular whole and see how many times they can fold it to represent fractions of the whole. Tactile learners really benefit from this activity because they get to work with physical models. Another method to add fractions that is very powerful is the grid method.

Grid Method

Make a grid on a transparency so the students can use dry erase markers to draw on the grids. The grid should consist of various numbers of boxes including twelve boxes, fifteen boxes, and so on. Give each student two grids. In our example, we have twelve boxes set up as four rows and three columns.

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