Rates of Change: Bottles and Divers

Source Institutions

Source Institutions

Add to list Go to activity
Activity link broken? See if it's at the internet archive
In this math lesson (page 2 of the PDF), learners use bottles of various shapes to explore the abstract concept of rate of change. Learners use a graduated cylinder to measure amounts of water, then add the water to their assigned container and measure the height of the water. After this data is collected, learners make a scatterplot of the their data. This lessons also includes other problems related to rates of change (optional).

Quick Guide

Preparation Time:
Under 5 minutes

Learning Time:
45 to 60 minutes

Estimated Materials Cost:
1 cent - $1 per group of students

Age Range:
Ages 14 - 18

Resource Types:
Activity, Experiment/Lab Activity, Lesson/Lesson Plan


Materials List (per group of students)

  • Graphing calculator with overhead unit
  • Overhead projector
  • Class data chart on newsprint or blackboard
  • Collection of various bottles, beakers, and flasks
  • Markers
  • Newsprint
  • Rulers
  • Measuring devices such as small graduated cylinders
  • Screening devices such as poster board or a box (optional)
  • Graphically Speaking activity sheet


  • Mathematics
    • Algebra
      • Equations and Inequalities
    • Data Analysis and Probability
      • Data Analysis
      • Data Collection
      • Data Representation
    • Measurement
      • Rate
    • Reasoning and Proof
    • Representation
  • The Nature of Technology
    • The Design Process
      • Problem Solving
  • Physical Sciences
    • Structure and Properties of Matter
      • Volume and Density


To use this activity, learners need to:

  • see
  • read
  • touch

Learning styles supported:

  • Involves teamwork and communication skills
  • Involves hands-on or lab activities


This resource is part of:

Access Rights:

  • Free access



  • All rights reserved, PBS, 2012

Funding Source:

  • US Department of Education