Home Browse Tutorials Instructor Resources Research Events About
Edition 1st

Scaling

Variant i Interactive tutorial lecture      

This tutorial helps students develop skill in reasoning about how surface area and volume scale for two-and three dimensional objects.

Topics   Mathematics / Scaling: graphs, models, proportional reasoning, rates of change, scaling, approximations, geometry, isometric growth, log-log plots, oxygen absorption & consumption, surface area, and volume

Jump to:

Materials

Materials by the UW team

  • Instructor SlidesTiIP_ITL_1stEd_SCL_tutorial_slides_instructor.pdfVerification required
  • Student Slides (no answers)TiIP_ITL_1stEd_SCL_tutorial_slides_student1.pdfVerification required
  • Student NotesTiIP_ITL_1stEd_SCL_tutorial_slides_student_notes1.pdfVerification required
  • Clicker Questions OnlyTiIP_ITL_1stEd_SCL_tutorial_slides_learning_catalytics.pdfVerification required
  • Instructor GuideTiIP_ITL_1stEd_SCL_instructor-guide.pdfVerification required
  • PretestTiIP_ITL_1stEd_SCL_pretest.pdfVerification required
  • Pretest for LMSTiIP_ITL_1stEd_SCL_pretest_qti.pdfVerification required
  • HomeworkTiIP_ITL_1stEd_SCL_homework.pdfVerification required
  • Homework for LMSTiIP_ITL_1stEd_SCL_homework_qti.pdfVerification required
  • Exam QuestionsTiIP_ITL_1stEd_SCL_exam.pdfVerification required
  • Equipment ListTiIP_ITL_1stEd_SCL_equipment.pdf


Instructor Slides
Slides presented by instructors when conducting Interactive Tutorial Lectures

Verification requiredLogin or register to see a preview and download

Tutorial details

The tutorial develops skill in reasoning about the scaling of objects in the context of the growth of an earthworm. Students use the concepts of surface area and volume to express the oxygen absorption and oxygen use rates of the worm. They then reason about the maximum size the worm can have while still absorbing enough oxygen to survive.

Section I: Absorption and consumption rates

Students first translate complicated units from verbal descriptions to expressions. They approximate the worm as a cylinder, then express the oxygen use and absorption rates of a worm in terms of a worm’s dimensions and mass. They then make calculations.

Section II: Modeling growth patterns

Students examine graphs of oxygen absorption and use for three different types of worm growth. They use these graphs to determine whether there is a limit to the worm’s growth (i.e., whether the oxygen use curve ever exceeds the absorption curve).

Section III: Approximations

Students determine how the endcaps of the worm affect the amount of oxygen it absorbs.

Section IV: Supplement

This section includes challenging questions involving log-log plots.

For instruction tips, login or register as a verified educator to see the Instructor Guide.

Prerequisites

None.

Equipment

List

  • tutorial instructor slides
  • tutorial student slides or worksheet

Discussion

Coming Soon! We hope to release the discussion section on each tutorial by the end of September 2024.