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Here's a project I've done with my kids for several years. In groups, I assign a specific conic section then students create a physical "book" with chapters including history, applications, mathematical derivation of the conic from the distance formula, and for fun a poem they create.
Along with this group project, I also took kids to our computer lab where they had to individually go through a software program called Green Globs & Graphing Equations. They had to demonstrate ability to create equations when given graphs for lines, circles, ellipses, parabolas, and hyperbolas. I gave them a check-off sheet and I would sign-off when they show me their computer screens showing competencies.
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