Unit 3: Fractions

Section 8: Representing, Comparing and Equivalence for fractions

• represent fractions using area, length, number line and discrete models
• understand and compare sizes of fractions by relating them to unit fractions and benchmark numbers
• write word problems for fraction addition
• add fractions with like and unlike denominators using manipulatives and diagrams
• know what a prime number is, and why 1 is not prime
  
• understand factors and multiples, and find least common multiples and greatest common factors using lists and prime factorizations.
  

Resources

Fraction models and representations

 Videos:

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.

Readings:

The main types of fraction representations and what they do best (follow all of the "next"s at the bottom of the pages.

Assignment 40:

Fraction representations

Exploration:

Do:

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
Assignment 41: Write up your exploration guide stuff more carefully, and submit it.

Watch:

Fraction Circles and Paper Folding
Array and non-array representations

Read:

The Array Strategy
Child-Invented Strategies: Equal Sharing and the Roots of Fraction Equivalence (D2L->Content->Readings)

Watch: Simplification strategies revisited

Assignment 42: Explaining equivalent fractions 

Exploration:

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

Assignment 43:  Prime numbers and factorizations

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

Assignment 44: prime factorizations and equivalent fractions

Watch: LCM, GCF
Read: Mathematics for Elementary School Teachers (Bassarear) section 4.3
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)