Unit 3: Fractions

Section 8: Representing, Comparing and Equivalence for fractions



Fraction models and representations


Different models for fractions (ways to approach the idea of fraction. Note: we are going to emphasize the repeated units model in this unit, which relies on the part-whole model)
Representations of fractions (how to draw part-whole and repeated unit fractions)
A few tips for explaining fractions using the repeated unit fraction model.

The main types of fraction representations and what they do best (follow all of the "next"s at the bottom of the pages.
Do this Assignment 40:
Fraction representations

Comparing fractions:
Fill out this exploration guide, using either fraction circle physical manipulatives you have cut out, or either the fraction circle or fraction bars applet (or some mixture of the two--experiment with the different representations to see what gives you the most useful insights). You may need wait a couple of minutes for the applets to start and/or reload the page.
Watch: My talking about the answers I "expect" you to get, and what good ways are of explaining them.  Also hints and
Do this Assignment 41: Write up your exploration guide stuff more carefully, and submit it.

Equivalent fractions:
Fraction Circles and Paper Folding
Array and non-array representations
The Array Strategy
Child-Invented Strategies: Equal Sharing and the Roots of Fraction Equivalence (D2L->Content->Readings)
Watch: Simplification strategies revisited
Do this Assignment 42: Explaining equivalent fractions 

Prime numbers: what they are; how to find prime factorizations
Watch: What to do with the web page
Do: See how well you can do with each of the applets on this page (note--this web page is giving some errors right now. I'm working on fixing it, but it might take a while).
Read: This assignment and exploration is inspired by the article "Ryan's Primes" in the May 1997 issue of Teaching Children Mathematics.  Read it in D2L -> Content -> Readings
Do thisAssignment 43:  Prime numbers and factorizations

Prime factorizations and equivalent fractions

Watch: prime factorizations
prime factorizations and equivalent fractions
more about equivalent fractions
more about prime factorizations and equivalent fractions
Read: Divisibility rules (useful but optional) Mathematics for Elementary School Teachers (Bassarear) section 4.1
Prime and composite numbers: Mathematics for Elementary School Teachers (Bassarear) section 4.2
Do this Assignment 44: prime factorizations and equivalent fractions

Factors and multiples: what is a factor, what is a multiple? How to find LCM and GCF two ways.
Watch: LCM, GCF
Read: Mathematics for Elementary School Teachers (Bassarear) section 4.3
Do this Assignment 45: Mathematics for Elementary School Teachers (Bassarear) 3rd edition pg 250 # 6 b,c.  Do each problem two ways: by writing lists, and by using a prime factorization. Do also  # 5, 7, 8, 9  (4th Edition, pg 252)