Unit 3: Fractions

Section 10: multiplying and dividing fractions

Goals:


Resources:

Word problems

Recognizing and analyzing word problems

You may want to print: the problems that are discussed in the videos
Watch:
Grouping multiplication and division with proper fractions
Grouping multiplication and division with mixed numbers
Multiplicative comparison multiplication and division with fractions
Rate multiplication and division with fractions
Assignment: 
Do thisAssn 52: Analyze some multiplication and division with fractions problems

Writing your own word problems:
Watch:
Writing multiplication word problems
Writing measurement division problems
Writing partitive division problems
Assignment:
Do thisAssn 53: Writing multiplication and division word problems

Multiplying Fractions

Multiplying fractions with materials

Watch:
Multiplying fractions with fraction circles
A variation on the previous manipulative algorithm
Assignment: 
Do thisAssn. 54: Fraction circle multiplication assignment

 

Multiplying fractions with arrays and the standard algorithm

Watch:
A subset array diagram for multiplying fractions
An area of a rectangle array diagram for multiplying fractions

Assignment
Do thisAssn. 55: Explain in a video
a. how to draw an array diagram for a product of two fractions (make sure your explanations of why your diagram is a sensible matches the diagram you draw.   This means if you are using an "of" interpretation, that you have a subset-type-diagram, and if you are using an "area of a rectangle" interpretation, you should use a symmetric diagram). 
b. Explain how to get from your diagram to the standard algorithm for multiplication of fractions.
Instructions for explanation videos about fractions

Note: I am looking for an explanation that includes all of these steps: *statement of the problem (fraction x fraction), * interpretation of the problem (in words), *diagram that shows the interpretation, *numerical standard algorithm with explanation of how to get it from the diagram.

Multiplying fractions with mixed numbers two ways:
Watch:
Multiplying mixed numbers
Assignment

Do
            thisAssn 56: Multiply mixed numbers two ways.


Dividing Fractions

Dividing fractions with materials
Watch:
Dividing fractions with fraction circles
Assignment: 
Do thisAssn 57: Dividing with fraction circles assignment

Dividing fractions with diagrams, measurement division:
Watch:
Modeling and interpreting example 1, example 2
Measurement division and the common denominator algorithm example 1, example 2

Read: an example of how to make a measurement division diagram

Web site: NLVM Fraction Bars

Assignment: 
Do thisAssn 58: Many problems having to do with measurement division.


Dividing fractions with diagrams, partitive division:
Watch:
Partitive division, bar/ratio diagrams and multiplication: part 1; part 2; another example
Assignment  
Do thisAssn 59: Diagrams for partitive division assignment


Understanding the standard algorithm;
Your assignment will be to explain out loud in a video, these ways of getting at the standard algorithm.
Watch:
Prerequisite ideas, and partitive division
Prerequisite ideas and an algebraic explanation

Assignment:
Do
          thisAssn 60: Watch the videos, practice, and ask questions until you understand how to make sense of the standard algorithm for dividing fractions using both a partitive division interpretation and an algebraic/fact family interpretation.  Then make a video, or write a detailed explanation for each way of explaining the standard algorithm).  You should be thinking about how you could explain the division of fractions algorithm to a class of students in a way that would make sense (grade level here is 6-8).  Your goal here is to make the connections between one of the informal ways of finding the solution to a division of fractions problem to the standard algorithm for dividing.
Instructions for explanation videos about fractions

[study the practice problems, and arrange to take the exam on or before Aug 8]