Unit 3: Fractions and Decimals

Week 7: Representing, Comparing and Equivalence for fractions

Resources: All of my fraction applets
Instructions for explanation videos about fractions

Fraction models and representations
Different models for fractions (ways to approach the idea of fraction)
Representations of fractions (how to draw part-whole and repeated unit fractions)
The main types of fraction representations and what they do best (follow all of the "next"s at the bottom of the pages.
Draw representations for 3/4 Aug 3

Comparing fractions:
Fill out this exploration guide, using either the 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 interesting insights)
Watch: My talking about the answers I "expect" you to get, and what good ways are of explaining them.  Also hints
Assignment: Write up your exploration guide stuff more carefully, and submit it. Aug 3

Early fraction work:
Watch: Fraction naming and  (first experiences in) adding in Montessori
Read: From Students' Problem Solving Strategies to Connections in Fractions (D2L->Content->Readings)
Approaches to teaching and learning fractions
Making up problems, and showing solutions for early fraction work Aug 3

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
Assignment: Explaining equivalent fractions  Aug 3

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
Assignment:  Aug 4  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) Bassarear section 4.1
Prime and composite numbers: Bassarear section 4.2
Assignment: Aug 4  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: Bassarear section 4.3
Assignment: Bassarear pg 250 # 6 a, b, c.  Do each problem two ways: by writing lists, and by using a prime factorization.  pg 250 # 5, 7, 8, 9 Aug 4