Visualizing Fractions Through Arrays

Too often students are shown only one image to illustrate the fraction-a pie. This limited visual representation may do little to help students grasp the basic concept of fractions or see how different fractions can be equivalent.

Arrays can be very useful in helping students understand fractions. Spreadsheets can be set up as arrays of any dimension (e.g., 1 row by 6 columns, 3 rows by 4 columns) and colored in order to show different fractions. This lesson allows students to see how the same fractional array can be manipulated to make different but equivalent fractions.

Classroom Discussion and Activities

Computer Lab Activities

Classroom Discussion and Activities

No doubt students have been introduced to the concept of fractions through pie diagrams. This is a good starting point for your discussion. Draw 1/2, 2/3, and 5/4 using pies. You can do this on the board or with a transparency.

The next and most important step is to link these pie representations with arrays. Thus, the array representations of fractions listed above could look like this.

 

Make sure that you discuss how these different representations-the pie and the array-stand for the same thing. Students may need practice in class drawing both representations and writing the fraction until they can explain how they are the same. Students can use graph paper and colored pencils for this purpose.

A second activity is to show how different arrays are equivalent. This will not be obvious to all students. Thus, students will need more practice seeing how the two fractions below-1/3 and 4/12-are the same. You will need to be careful to use arrays of the same overall size to show how, when one is superimposed over the other, the same area is colored.

 

In the Lab (Individual or Paired Work)

Make sure that the students leave plenty of space or rows when they create fractions. The spreadsheet fraction.xls shows what a spreadsheet could look like for the fraction 1/2.

• Students begin with a 6 x 2 array. They can use the Border icon to create a grid. Then they can use the Color icon to fill in two different colors. One half (or 6) of the arrays will be one color and 6 will be another color.

• From there on, students can create equivalent arrays in several ways. They can do it from scratch in the same way that they created the first 6 x 2 array or they can copy and paste the original array. If they copy and paste, they can "pull the array apart" by dragging cells after they have highlighted them. Try this yourself first before you have students use this technique.

• Encourage students to make and explain as many equivalent fractions as they can using the arrays. Have the students write the fractions for each of the arrays in the column where you are labeling the fractions. In fraction.xls, that is column A.

• Be sure to discuss how these fractions are all equivalent and use this exercise as a basis for further discussion in the classroom.