# INTERMATH | Rational Numbers Workshop

 Atlanta Public Schools - September 19, 2007 to December 19, 2007

 Program: Rational Numbers - Wednesday Location: Atlanta Public Schools Instructor and Contact Information: Laurel Bleich LaurelBleich@gmail.com

WORKSHOP OBJECTIVES

The purpose of this course is for teachers to:

• Develop mathematical content knowledge
• Explore mathematical investigations using technology
• Become more proficient with technology for mathematical problem solving
• Align mathematical investigations with Georgia Performance Standards

The participants in this course will be expected to:

PERFORMANCE INDICATORS

As a result of this course, participants will demonstrate their ability to:

• Incorporate technology into the learning and teaching of rational number concepts.
• Communicate mathematical understanding of a variety of rational number concepts in the form of an online portfolio of investigation solutions.
• Plan middle school instructional activities based on InterMath experiences.

PARTICIPANTS

COURSE SCHEDULE AND SYLLABUS

Wednesday, September 19 - Week 1  Parts

1. Introduction to InterMath
2. Talking Points Quiz
3. Demo Problem: Introduction to Fraction Bars
4. Group investigations

Surrounding Numbers

5. Individual Investigation

Land Dispute
Musical Chairs
Fractional Parts
Pandigital Fraction
Those Fractions in Between

Wednesday, September 26 - Week 2  Parts of Parts

1. Demo Problem: Let's Operate on Fractions
2. Group investigations

Fraction Situations

3. Individual Investigations:

Exploring Multiplication with Fractions
What Happens When...
Can you tell?
Fraction Figures

Wednesday, October 3 - Week 3   Geometry, Fractions

1. Demo Problem: Dividing a Rectangle
2. Group Investigation
Double Trouble
3. Individual investigations

Equal Portions
Cutting the Cake

Wednesday, October 10 - Week 4  Pesky Parts I

1. Demo Problems

Cans and Containers
Exploring Division with Fractions

2. Individual investigations

The Meaning of 1/3
What does 3 divided by 1/2 look like?

Wednesday, October 17 - Week 5 Pesky Parts II

1. Group investigations

Division Pattern
Jacob's Idea
Natasha's Idea
Dueling Speakers

Wednesday, October 24 - Week 6 Decimal Concepts

1. Demo Problem: Approximate Digit Use
2. Group Investigations

Estimating the Point

3. Individual Investigations

Nonrepeating Decimals
Creating Integers
Unit fractions: Terminating, Repeating, or Never-ending
What coins?
Money Puzzle
Difficult Change

Saturday, November 3 (tentative) - Week 7  Decimal Models

1. Demo Problem: Representing Decimals
2. Group Invesigations

Moving the Point
Decimal Division
Modeling Multiplication

3. Individual Investigations

Spending it all
Library Fines
Decimal Products

Wednesday, November 7 - Week 8  Percents

1. Group Investigations

Beaker Comparison
Predicting the Value of a House

2. Individual Investigations

Discounting Cars
Raising Salaries
Choosing a Loan
It's on Lacey
Drinking Coca-Cola

Wednesday, November 14 - Week 9  Sum Difference

1. Demo Problem: Mathopia Farm
2. Group Investigations

Geometric Sequences and Series
Johnny's Rule

3. Individual Investigations

Making Unit Fractions
Proper Fraction Fury
Splitting Fractions in Two
What Happens When...

Wednesday, November 28 - Week 10 Ratios

1. Group Investigations

Which is Larger?
Jumping Monkeys
Ratio of a + b to b + c

2. Individual Investigations

Boys and Girls in the Class
Mathematics Football Players
Comparing Properties
Students in the Class
Building Roofs
Laurel's Muffins

Wednesday, December 5 - Week 11  Proportional Simulations

1. Demo Problem: Drink Mixes
2. Group Investigations

Proportions and Graphs

3. Individual Investigations

Maximum Capacity
Shopping for Soup
Which Movie is Best?
Fair Share

Wednesday, December 12 - Week 12  Inverse Proportions

1. Demo Problem: Inversely Proportional
2. Group Investigations

Exploring Rectangle Properties

3. Individual Investigations

Camera Lens Aperture
Volume and Pressure

Wednesday, December 19 - Week 13  Geometry & Rational Numbers

1. Demo Problem: Volume & Surface Area of a Cube
2. Group Investigations

Intersecting Chords
Paper Folding

3. Individual Investigations

Triangles in a Trapezoid
Proportional Rectangles

Week 14  Probability and Rational Numbers

1. Group Investigations

Getting Free
Varying Probabilities

2. Individual Investigations

Unfair Coins
Triangle Inside a Parallelogram
Medial Probabilities