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Patterns and Functions: Fill 'er Up

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Patterns and Functions: Fill 'er Up

In this math lesson, learners predict, interpret, and sketch graphs of functions related to the shapes of bottles. A measure of water is poured into a container. Learners graph this as an ordered pair by using the number of the measure (x) and the resulting height of the water (y). Learners compare the ordered pairs of containers with various shapes, including irregular shapes.

Quick Guide

Preparation Time:
5 to 10 minutes

Learning Time:
45 to 60 minutes

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

Age Range:
Ages 11 - 14

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


Materials List (per group of students)

  • Two clear containers with different shapes
  • Six additional clear containers with different shapes and large graphs related to three of these containers
  • Container filled with colored water (rice or sand can be used instead of water)
  • 12-inch ruler
  • Graph paper
  • Measuring devices (i.e. cup, ladle, graduated cylinder)


  • Mathematics
    • Algebra
      • Patterns
      • Variables and Expressions
    • Data Analysis and Probability
      • Data Analysis
      • Data Collection
      • Data Representation
    • Measurement
    • Problem Solving
    • Representation


To use this activity, learners need to:

  • see
  • read
  • touch

Learning styles supported:

  • 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


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