There is a need, a time, and a place for building procedural fluency no matter what mathematical topics are being studied. However, moving students beyond procedural mathematics to developing true understandings of the mathematics with which they are engaging requires students to think. The Farmer Jones tasks for high school students requires students to investigate the relationships between the tangram pieces while working an open-ended problem. One activity requires students to maximize income and profit while the second asks for a minimization. Developing different options and presenting those options is required. Even though this is a contrived problem, students can make it more authentic by researching the crops and livestock options in their geographic region. Questions about moving the learning forward as well as extending the learning and reflecting are provided in addition to facilitation notes.
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Reproducible for the purchaser's classroom only.