In this activity, students gradually fill bottles of different shapes and graph the water level (height) versus the volume of water inside the bottles. Then they explore the relationship between the shape of a bottle and the resulting graph.

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A set of problems of many types.

A set of problems of many types.

A set of problems of many types.

A set of problems of many types.

A set of problems of many types.

### Lawrence O. Cannon

The article contains classroom enrichment suggestions related to Pythagorean triples. Topics discussed for student exploration can be adapted for any level from early algebra through early college.

A set of problems of many types.

A set of problems of many types.

### Colin Foster

Exploring even something as simple as a straight-line graph leads to various mathematical possibilities that students can uncover through their own questions.