Eyes on Math: A Visual Approach to Teaching Math Concepts (0) by Small Marian

Author:Small, Marian [Small, Marian]
Language: eng
Format: epub
Publisher: Teachers College Press
Published: 2012-11-30T08:00:00+00:00

EXTENSION Ask students to draw three pieces of licorice where the length of one is about the length of another and where the length of one is about the length of another. Ask how else each length compares to the others and how the students know this.

FRACTIONS AS DIVISION

How much of an apple is each share?

AT SOME POINT, we want students to realize that the fraction can be interpreted as a ÷ b. This is used both when improper fractions are renamed as mixed numbers—for example, , since 6 ÷ 4 = —and when we have students divide a numerator by a denominator to determine a decimal equivalent for a fraction—for example, = 0.4 is determined by dividing 2 by 5. Thinking of fractions as division is addressed in Common Core State Standards 5.NF.

The picture provided here is designed to help students see that one way to model a ÷ b is to divide each of the a objects into b pieces, giving each of the b sharers a piece from each object. In this case, since 4 people are sharing, each of the 3 objects is divided into fourths. If each person gets one fourth from each of the three objects, the total share is . Since division describes sharing, this shows why 3 ÷ 4 = .

Another way to think about why = 3 ÷ 4 is to think of 3 ÷ 4 as asking how much of a 4 fits into a 3. This is what is called the “measurement” meaning of division, analogous, for example, to how many 3s make 9 for 9 ÷ 3. Cuisenaire rods make a good model. Clearly, the 3 is of the 4.

Download

Copyright Disclaimer:
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.