# St. Patty's Day Rainbow Reconstruction: Circle Equations and Quadratic Systems

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Mason the Leprechaun is tired of granting wishes and is looking to retire in Ireland. He needs his magical, bottomless pot o’gold to buy his dream home. Sadly, Mason can’t remember where the gold is! He thinks he buried his treasure at the end of a beautiful rainbow, which has since disappeared. Lucky for him, a new business in town, “Rainbows ‘R’ Us”, specializes in finding pots o’ gold. However, they require a colored diagram along with equations for each arc of the rainbow.

Students work with equations of circles and a 2x2 system of quadratic equations to help Mason find his pot o’ gold.

The lesson is appropriate for Algebra 1, Geometry, and Algebra 2 students. This seemingly simple problem becomes fairly complex because students must solve a system of QUADRATIC equations. It is not an easy assignment, so I suggest giving it as a Problem of the Week. The lesson plan does provide an alternative for lower grade students who can’t solve the system of equations (or for teachers who want a quick activity).

The package includes a lesson plan, direction page, answer sheet with blank graph, and answer key with a detailed solution.

I am very excited about Common Core’s “Standards for Mathematical Practice,” which aim to make our students competitive in college and the workplace. This particular assignment addresses many of those standards:

1. Make sense of problems and persevere in solving them.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.

Of course, Domain Standards are also addressed (Algebra and Geometry). They are listed with the lesson plan.

Based on a work at www.uncommoned.com.
Total Pages
7 pages
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Teaching Duration
90 minutes
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\$3.00