Understanding Rational Numbers (Fractions, Decimals, Percents, Ratios)

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Understanding Rational Numbers(Fractions,
Decimals, Percents, Ratios)

• Offered by Looney Math Consulting
• www.looneymathconsulting.com
• looneyconsulting_at_comcast.net

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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 .

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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

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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

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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

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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

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Sample Activity

• Creating Concept Maps

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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.
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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

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Sample On-line Session

• Models for FractionsIn 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 )

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Resources to share back with district

• Workshop
• Reference List
• Alignment to textbook and standards
• Assessments
• Common Misconceptions / student work
• Technology

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Questions?

• Please contact
• Dr. Susan Looney
• Looney Math Consulting
• looneyconsulting_at_comcast.net