Number and Operations: Developing an understanding of and fluency with multiplication and division of fractions and decimals.

These resources offer support in explaining the difficult concepts underpinning multiplication and division of both fractions and decimals. Visual, interactive models are provided where possible. You will also find opportunities for your students to practice their skills in this area of arithmetic.

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Multiplication of Fractions http://nlvm.usu.edu/en/nav/frames_asid_194_g_3_t_1.html?from=category_g_3_t_1.html

Visualize and practice multiplying fractions using an area representation. With the “Show Me” option selected, the virtual manipulative is used to graphically demonstrate, explore, and practice multiplying fractions. A rectangular grid, representing a whole, shows the areas of two fractions to be multiplied, one fraction in red on the left and another in blue at the bottom. The area of the overlapping region, shown in purple, represents the product of their multiplication. The “Test Me” option provides problems to be solved using the same graphical representation. (From National Library of Virtual Manipulatives for Interactive Mathematics : all topics (grades 6-8) — MSP full record)

Multiplying Fractions http://www.visualfractions.com/multiply.htm

This tutorial site offers instruction as well as practice in multiplication of fractions. The fractions are modeled with either circles or lines (rectangular areas). The visual display matched with the numerical makes an effective demonstration. (From Visual Fractions — MSP full record)

Divide Fractions http://www.visualfractions.com/divide.htm

This tutorial site offers instruction as well as practice in multiplication of fractions. The fractions are modeled with either circles or lines (rectangular areas). The visual display matched with the numerical makes an effective demonstration. (From Visual Fractions — MSP full record)

Divide and Conquer http://www.utdanacenter.org/mathtoolkit/instruction/lessons/7_divide.php

This lesson is based on the idea that middle school students can better understand the procedure for dividing fractions if they analyze division through a sequence of problems. Students start with division of whole numbers, followed by division of a whole number by a unit fraction, division of a whole number by a non-unit fraction, and finally division of a fraction by a fraction. Activity sheets and guiding questions are included. (From Ohio resource center for mathematics, science, and reading — MSP full record)

Dividing Fractions http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=212

Students divide fractions using area models. They can adjust the numerators and denominators of the divisor and dividend and see how the area model and calculation change. Full access to ExploreLearning is available through an annual subscription, but you can apply for a month’s free access in order to test out the applets. MSP full record

Decimals http://www.aaamath.com/dec.html

This site has explanatory lessons and interactive practice on most aspects of decimals, including multiplying decimals and dividing them. MSP full record

Learning about Multiplication Using Dynamic Sketches of an Area Model http://standards.nctm.org/document/eexamples/chap6/6.1/index.htm

In this applet, a rectangle represents the familiar area model of multiplication. By changing the height of the rectangle, students can explore the effect of multiplying a fixed positive number, in this case 3, by decimal numbers greater than 1 and less than 1. The visual is powerful! MSP full record

Too Big or Too Small? http://illuminations.nctm.org/LessonDetail.aspx?id=L252

Of these three activities on developing number sense, go to Activity 3: Exploring the Effect of Operations on Decimals. Through playing the cleverly crafted game presented here, students explore the effect of addition, subtraction, multiplication, and division on decimal numbers. Students begin with the number 100 as they enter a maze. For each segment chosen on the maze, the student keys in the assigned operation and number; for example, “+ 1.2” or “? 0.8.” The goal is to choose a path through the maze that results in the largest value at the finish. A copy of the maze playing board is included. (From Illuminations, National Council of Teachers of Mathematics Vision for School Mathematics — MSP full record)

NCTM. (2006). Curriculum Focal Points for Kindergarten Through Grade 8 Mathematics: A Quest for Coherence. Reston, VA: Author

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Copyright April 2008 — The Ohio State University. This material is based upon work supported by the National Science Foundation under Grant No. 0424671. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

This work is licensed under a Creative Commons License.