Unit 3: Fractions and Decimals

Sectrion 10: multiplying and dividing fractions


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
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: July 30
Assn 58: Analyze some multiplication and division with fractions problems

Writing your own word problems:
Writing multiplication word problems
Writing measurement division problems
Writing partitive division problems
Assignment: July 30
Assn 59: Writing multiplication and division word problems

Multiplying fractions with materials
Multiplying fractions with fraction circles
A variation on the previous manipulative algorithm
Assignment: July 30
Assn. 60: Fraction circle multiplication assignment

Multiplying fractions with arrays and the standard algorithm
A subset array diagram for multiplying fractions
An area of a rectangle array diagram for multiplying fractions
Assignment Aug 1
Assn. 61: 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

Multiplying fractions with mixed numbers two ways:
Multiplying mixed numbers
Assignment Aug 1
Assn 62: Multiply mixed numbers two ways.

Dividing fractions with materials
Dividing fractions with fraction circles
Assignment: Aug 3
Assn 63: Dividing with fraction circles assignment

Dividing fractions with diagrams, measurement division:
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: Aug 3
Assn 64: Many problems having to do with measurement division.

Dividing fractions with diagrams, partitive division:
Partitive division, bar/ratio diagrams and multiplication: part 1; part 2
Assignment  Aug 3
Assn 65: 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.
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.
Assn 66: 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 (of your chosen 2 ways 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 5-8).  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 Aug 6

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