Course #11 Math-Grades 6-9


Thursday, March 9, 2017

Course #11 – Reasoning and Sense Making with Rational Numbers in Grades 6-9

by Paul Agranoff, MA, Creative Mathematics, Arcata, CA

About the Speaker
Agranoff Photo copyPaul Agranoff, MA,
recently retired from a 35-year career of teaching in the middle level classroom. Over the course of his career he taught various combinations of grades from 5th to 8th. In his last five years he was a full time 7th grade classroom teacher, a Mathematics Curriculum/Instructional Specialist for Pre K – Adult, and a district Mathematics
Curriculum Committee Chairperson. He has been a district level Teacher of the Year and recognized as a Minnesota Teacher of the Year candidate; twice a Minnesota Presidential Awardee for Excellence in Teaching Mathematics, and received the National Presidential Award for Excellence in Teaching Elementary Mathematics in 1993. He spent 13 years as a Board of Directors Member of the Minnesota Council of Teachers of Mathematics, and for 10 of those years he was the Minnesota NCTM Representative. Paul was a member of the writing team that authored the 2007 Minnesota Standards for Mathematics.  Paul has spoken at many state, regional, and national mathematics conferences. For the past 23 years he has traveled North America during the summer conducting professional development training for teachers of mathematics. His workshops help teachers grow professionally and personally in knowing and teaching mathematics beyond arithmetic. Disclosure: Financial- Paul receives speaking and teaching fees from Creative Mathematics, AIMS Education Foundation and various school districts and agencies. Nonfinancial- There are no nonfinancial relationships to disclose.

Target Audience (who should attend): General Education Teachers, Special Education Teachers, Resource Room Teachers, Math Teachers, Math Coaches, Math Tutors, Instructional Math Assistants and Paraprofessionals, and  Principals/Administrators

Target Age Range: Students Functioning at the 4th-9th Grade Math Level

Course Description: Student struggle with understanding and use of rational numbers undermines much of their future progress in both mathematics as well as the world beyond school. Researchers have even found where “fractional avoidance” in learning causes issues in student achievement. Participants will engage in instructional strategies that support student reasoning and sense making with critical number sense in rational numbers. Rational number concepts will be developed tactile/kinesthetically as well as spatial/visually. All operations with rational numbers will be developed in the same way as well.

What You Will Learn
Course Objectives- Participants will be able to:

  • Identify and describe all the different interpretations of rational numbers
  • Adequately describe how to make use of structure in numbers to develop student thinking about rational numbers
  • Describe relationships between rational numbers using structures in number and strategies
  • Demonstrate the ability to use manipulatives to explore mathematical relationships with rational numbers
  • Demonstrate the ability to build reasoning and sense making in operations on rational numbers through use of manipulatives and pictorial representations
  • Create and use manipulatives to explore mathematical relationships with rational numbers
  • Build reasoning and sense making in operations on rational numbers through use of manipulatives and pictorial representations


8:00-9:00 Multiple Interpretations of Rational Numbers and developing number theory concepts used in rational numbers

9:00-10:00 Deepening student understanding of structure in rational numbers

10:00-10:15 Break

10:15-12:00 Creating and using manipulatives to cognitively engage students in building understanding of rational numbers (including the operations of addition and subtraction)

12:00-1:00 Lunch- On your own

1:00-2:30   Using representations to build student understanding of multiplication with rational numbers

2:30-2:45 Review literature on vision issues

2:45-4:00 Using representations to build student understanding and meaning of dividing fractions

4:00 Complete program evaluations