Unit 3: Fractions and Decimals

Week 9: multiplying and dividing fractions

Goals:

Resources: All of my fraction applets
A SMART Notebook with fraction circles in it
A SMART Notebook with grids for fraction squares in it, and a video showing how it works.
Instructions for explanation videos about fractions

Recognizing 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: Aug 7
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: Aug 7
Writing multiplication and division word problems

Multiplying fractions with materials
Watch:
Multiplying fractions with fraction circles
A variation on the previous manipulative algorithm
Assignment: Aug 7
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 Aug 10
Explain in either a video or a detailed written explanation, 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

Multiplying fractions with mixed numbers two ways:
Watch:
Multiplying mixed numbers
Assignment Aug 10
Multiply mixed numbers two ways.

Dividing fractions with materials
Watch:
Dividing fractions with fraction circles
Assignment: Aug 10
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

Web site: NLVM Fraction Bars

Assignment: Aug 10
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
Assignment  Aug 10
Diagrams for partitive division assignment


Understanding the standard algorithm;
Your assignment will be to explain out loud in a video 2 of the 4 presented ways of getting at the standard algorithm.
Watch:
Prerequisite ideas, and partitive division
Prerequisite ideas and measurement division part 1, part 2
Prerequisite ideas and an algebraic explanation
Fact families and getting there from the divide numerators and denominators algorithm part 1, part 2.
Assignment:
Watch the videos, practice, and ask questions until you understand 2 of the 4 above ways of making sense of the standard algorithm for dividing fractions.  Then make a video, or write a detailed explanation for each.  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 5-8)
Instructions for explanation videos about fractions Aug 11