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College Board

Homepage Home > Professional Development > Workshops & Summer Institutes > Mathematics & Computer Science > Pre-AP: Strategies in Mathematics—Accumulation

Pre-AP: Strategies in Mathematics—Accumulation

Expand your math teaching skills, techniques and knowledge in this workshop

Using a guided-exploration approach, teachers learn accumulation concepts for grades 6-12. Participants develop problems and learn instructional activities, assessment items, and cross-grade lessons for classroom use. They also learn diagnostic and assessment strategies that help teachers communicate with students and help monitor students' mathematical thinking.

Workshop topics include:

  • The concept of area
  • Accumulating distance when speed is constant, changes, or is a function
  • Velocity distinct from speed

The workshop conforms to the College Board's mission, particularly in promoting access and equity; National Council of Teachers of Mathematics (NCTM) standards; and to AP Calculus AB and Calculus BC topic outlines.


  • Understand AP mathematics standards and the role of Pre-AP in developing them
  • Establish connections between the presentation of accumulation concepts throughout the curriculum
  • Learn what students need for AP Calculus AB and Calculus BC
  • Appreciate issues and strategies critical to AP Vertical Teams in Mathematics


Accumulation and the Concept of Area
Accumulating Distance When Speed Is Constant
Accumulating Distance When Speed Changes
Accumulating Distance When Speed Is a Function
Velocity Distinct from Speed
The Big Picture of Accumulation

Workshop author

Jim Choike is a professor of mathematics at Oklahoma State University (OSU). He has been involved with the College Board for 20 years as an AP Reader, workshop presenter, curriculum developer, and professional development specialist. Mr. Choike has also worked on the College Board's: Pathways to Equity and Excellence, Pacesetter, CLEP, SAT, and SpringBoard programs. He teaches undergraduate and graduate mathematics courses at OSU and uses his summer months to work with middle and high school teachers and their students.

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