Understanding Rational
Numbers
(Fractions, Decimals, Percents, Ratios)
Offered by: Looney Math Consulting
www.looneymathconsulting.com
looneyconsulting@comcast.net
What will educators learn from the course
Understanding Rational Numbers?
Educators (both regular and special ed) will:

enhance their own mathematics knowledge in the area of rational numbers:
fractions, decimals, percents and ratios.

better understand why children struggle understanding rational number
concepts and will learn how to move children forward.

create and interpret assessment tasks for common misconceptions and
implement targeted intervention plans.

learn how to integrate the use of technology in their classrooms.

gain comfort with wide-range of strategies and tools for teaching concepts
including the use of visual models and manipulatives .
Connecting Content and Pedagogy:






Content
Definition of rational
numbers
Representations of fractions
and decimal numbers
Comparison of fractions and
decimal numbers
Operations with fractions
and decimal numbers
Rates, ratio and proportions
Probability and Odds
Pedagogy






Use of models
Real World Applications
Development of concept
and meaning
Development of Learning
Communities
Assessments for Common
Misconceptions
Intervention plans
What is the grade span for this course?

Kindergarten through Grade 8:

Teachers who teach rational number concepts
(Grades 3 – 8)

Teachers wishing to enhance their own understanding
of rational number concepts and to make connections
to foundational concepts taught in early grades
(Grades K – 2)

Special educators, coaches, administrators
Details:

Staff: Taught by highly qualified teams of 3

Hours: 40 hours face-to-face instruction / 20
hours on-line (5 face-to-face days)

PDPs: 67.5 for course completion / 90 if taken
for graduate credit

Graduate Credits: 4 available through Endicott
College for $240
A Day in Understanding Rational
Numbers …….
Participants move between all of the following throughout
each day of the course:







Whole group instruction, small group, partners
Hands-on use of manipulatives
Games with a purpose
Reading and discussing research articles and case
studies
Analyzing student work
Creating lessons and assessments
Using technology
Sample Activity

Creating Concept Maps
Constructing Deep Understanding and Visual Models
How is division by one-half different than
division by 2?
Discuss the relationship
of ÷ 2 and x ½.
On-line Component

Participants required to obtain MassONE ID from district
technology coordinator prior to the start of class

Use of technology integrated throughout the course in a
supportive environment
On-line Assignments include:
 Readings
 Web-based activities
 Discussion forums
Sample On-line Session
Models for Fractions









In this session, you will look at various models for representing fractions. Please
complete the following assignments:
1. Visit the website PBS - the Fractionator and the Decimal Activities website.
2. Read the article Creating, Naming and Justifying Fractions and Teaching
Fractions.
3. Post to the discussion forums by Thursday evening. Respond to one other
post by Sunday evening.
Session 2 Assignments (Word document )
PBS - the Fractionator file (website)
Decimal Activities file (website)
Creating, Naming and Justifying Fractions (PDF document )
Teaching Fractions (PDF document)
Models for Understanding Fractions (Discussion Forum )
Resources to share back with district:






Workshop
Reference List
Alignment to textbook and standards
Assessments
Common Misconceptions / student work
Technology
Questions?
Please contact:
Dr. Susan Looney
Looney Math Consulting
looneyconsulting@comcast.net