Unit3Section8

Unit 3: Fractions and Decimals

Section 8: Representing, Comparing and Equivalence for fractions

Goals:

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.

Instructions for explanation videos about fractions

Fraction models and representations

Videos:

Different models for fractions (ways to approach the idea of fraction)
Representations of fractions (how to draw part-whole and repeated unit fractions)

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 49:

Draw representations for 3/4 July 20

Comparing fractions:

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 interesting insights)

Watch: My talking about the answers I "expect" you to get, and what good ways are of explaining them. Also hints
Assignment 50: Write up your exploration guide stuff more carefully, and submit it. July 20

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)

A pproaches to teaching and learning fractions

Assignment 51:

Making up problems, and showing solutions for early fraction work July 20

Equivalent fractions:

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 52: Explaining equivalent fractions July 22

Prime numbers: what they are; how to find prime factorizations

Exploration:

Watch: What to do with the web page
Do: See how well you can do with each of the applets on this page

Assignment 53: July 22 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 54: July 22 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 55: Bassarear pg 252 # 6 a, b, c. Do each problem two ways: by writing lists, and by using a prime factorization. pg 252 # 5, 7, 8, 9 (3rd Edition, pg 250) July 22