Hotel Snap: Building for Profit Students will be required to build a high-profit yielding hotel using snap cubes. Building costs, rules and regulations, taxes, and income are all variables that students will be required to take into consideration.

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Want to use Illuminations resources but don't know where to begin? We've got you covered!

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Polynomial Puzzler: In this lesson, students explore polynomials by solving puzzlers. To solve the puzzlers, students factor polynomials and multiply monomials and binomials. The lesson includes ideas on how this format can be applied to other mathematical concepts.

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Polynomial Puzzler

Cutting Conics: Students explore and discover conic sections by cutting a cone with a plane. Circles, ellipses, parabolas, and hyperbolas are examined using the Conic Section Explorer tool. Physical manipulatives such as dough can optionally be used as well.

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There Has to Be a System for This Sweet Problem: We are confronted with problems on a regular basis. Some of these are easy to solve, while others leave us puzzled. In this lesson, students use problem-solving skills to find the solution to a multi-variable problem that is solved by manipulating linear equations. The problem has one solution, but there are multiple variations in how to reach that solution.

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There Has to Be a System for This Sweet Problem

Graphs from the Unit Circle: In this lesson, students use uncooked spaghetti to transfer lengths from the unit circle to a function graph on large butcher paper. In the process, they discover the key features of sine and cosine graphs. The activity is presented for students working in degrees, but another version of the handouts is provided for students working in radians.

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Graphs from the Unit Circle

Venn Diagrams & Logic: This lesson focuses on using Venn diagrams to explore direct, indirect, and transitive reasoning.

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Venn Diagrams and Logic

An Armstrong number is an n-digit number that is equal to the sum of the nth powers of its digits. In this lesson, students will explore Armstrong numbers, identify all Armstrong numbers less than 1000, and investigate a recursive sequence that uses a similar process. Throughout the lesson, students will use spreadsheets or other technology.

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Armstrong Numbers

Rise-Run Triangles: This lesson offers students a method for finding the slope of a line from its graph. The skills from this lesson can be applied as a tool to real-world examples of rate of change and slope.

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Rise-Run Triangles

The Regression Line and Correlation (4-lesson unit): Interactive computer-based tools provide students with the opportunity to easily investigate the relationship between a set of data points and a curve used to fit the data points. As students work with bivariate data in grades 9-12, they will be able to investigate relationships between the variables using linear, exponential, power, logarithmic, and other functions for curve fitting.


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Correlation and the Regression Line

Trigonometry for Solving Problems: This lesson offers a pair of puzzles to enforce the skills of identifying equivalent trigonometric expressons. Addtional worksheets enhance students' abilities to appreciate and use trigonometry as a tool in problem solving.

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Trigonometry for Solving Problems

Barbie Bungee: The consideration of cord length is very important in a bungee jump—too short, and the jumper doesn’t get much of a thrill; too long, and ouch! In this lesson, students model a bungee jump using a Barbie® doll and rubber bands. The distance to which the doll will fall is directly proportional to the number of rubber bands, so this context is used to examine linear functions.


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