What+it+means+to+multiply+fractions

Understanding Multiplication of Fractions
//The purpose of this activity is to provide a diagnosis and remediation strategy for students who have difficulty understanding what it means to multiply fractions.//

When using virtual manipulatives, third grade students can accurately interpret, display, and answer what is 1/4 of 4. However, they cannot interpret and answer what is 1/4 of 8. The student does not know where to start.

Step One: Ask the student to go back to the 4 block example and ask "Why is the answer 1 block?" Look for student to describe that 1 is 1/4th of 4. The student should be able to describe what the numerator and denominator of 1/4 represent. The denominator describes the number of equal parts in the whole group (4), and that the 1/4 represents 1 out of the 4 blocks.

Step Two: Ask the student "what is 1/3 of 3?", then ask "what is 1/3 of 6?" This will help determine whether it is an isolated event with 4 blocks.

Diagnosis: The student may not understand what a whole (denominator) represents.

Remediation: What we want students to understand is that 2 of 8 pieces in a whole is the same amount as 1 of 4 equal parts of that whole.

The [|Fraction Pieces] applet from the National Library of Virtual Manipulatives may help in visualizing this objective.

Another possible remediation activity is to have students get into a group of 8. Split the group of 8 into 2 groups of 4, and have a student say "1/2 of 8 is 4 students." Ask students to illustrate 1/2 group of 8 students, 4 students. Have the students model step 1 using manipulatives. Have the students model step 1 using the symbols 1/2 of 8 is (equal to) 4 and 1/2 x 8 = 4. The purpose of this suggestion is to make sure students are able to link symbols with appropriate terms.

Assessment: Students who understand what it means to take a fractional amount of a set of things will be able to accurately describe the question, and illustrate the result.