Thank you for your interest in NCTM’s Illuminations. Beginning in mid-April, all Illuminations content will be moving to nctm.org/illuminations. Interactives will remain openly available and NCTM members will have access to all Illuminations lessons with new filtering and search options. We hope you will continue to utilize and enjoy these resources on nctm.org.

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Algebra

Building Connections

9-12
This lesson focuses on having students make connections among different classes of polynomial functions by exploring the graphs of the functions. The questions in the activity sheets allow students to make connections between the x-intercepts of the graph of a polynomial and the polynomial's factors. This activity is designed for students who already have a strong understanding of linear functions, some knowledge of quadratic functions, and what is meant by a polynomial function.
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Geometry

Counting Embedded Figures

6-8, 9-12
This grades 7-12 activity allows students to look for patterns within the given data. After looking at the pattern, the student should be able to form generalizations for the problem. Furthermore, this activity sharpens the algebraic skills of the students. The problem sharpens visualization skills.
Algebra

The Devil and Daniel Webster

9-12
Adapted from Navigating through Algebra in Grades 9–12, this lesson allows students to examine a recursive sequence in a game between the Devil and Daniel Webster.
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Data Analysis and Probability

Explorations with Chance

9-12
In this lesson, students analyze the fairness of certain games by examining the probabilities of the outcomes. The explorations provide opportunities to predict results, play the games, and calculate probabilities. Students should have had prior experiences with simple probability investigations, including flipping coins, drawing items from a set, and making tree diagrams. They should understand that the probability of an event is the ratio of the number of successful outcomes to the number of possible outcomes. This lesson was adapted from "Activities: Explorations with Chance," which appeared in the April 1992 issue of the Mathematics Teacher. 
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Data Analysis and Probability

Exploring Linear Data

6-8, 9-12
Students model linear data in a variety of settings that range from car repair costs to sports to medicine. Students work to construct scatterplots, interpret data points and trends, and investigate the notion of line of best fit.
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Data Analysis and Probability

Birthday Paradox

6-8, 9-12
This activity demonstrates the Birthday Paradox, using it as a springboard into a unit on probability. Students use a graphing calculator to run a Monte Carlo simulation with the birthday paradox and perform a graphical analysis of the birthday-problem function. This lesson was adapted from an article, written by Matthew Whitney, which appeared in the April 2001 edition of Mathematics Teacher.
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Data Analysis and Probability

Shrinking Candles, Running Water, Folding Boxes

9-12
This activity allows students to look for functions within a given set of data. After analyzing the data, the student should be able to determine a type of function that represents the data. This lesson plan is adapted from an article by Jill Stevens that originally appeared in the September 1993 issue of the Mathematics Teacher.
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Algebra

Allow Me 2 Reiterate

9-12
In this grades 9‑12 lesson, students use a computer software program to assist them in determining the square root of 2 to a given number of decimal places. From this, they will be able to study the repeating-decimal phenomenon of rational numbers and explore the system property of irrationality of numbers, such as 2.
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Algebra

Modeling Orbital Debris Problems

9-12
In this lesson, students examine the problem of space pollution caused by human-made debris in orbit to develop an understanding of functions and modeling. It allows the students an opportunity to use spreadsheets, graphing calculators, and computer graphing utilities.
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Data Analysis and Probability

Stick or Switch?

6-8, 9-12
This lesson plan presents a classic game-show scenario. A student picks one of three doors in the hopes of winning the prize. The host, who knows the door behind which the prize is hidden, opens one of the two remaining doors. When no prize is revealed, the host asks if the student wishes to "stick or switch." Which choice gives you the best chance to win? The approach in this activity runs from guesses to experiments to computer simulations to theoretical models. This lesson was adapted from an article written by J. Michael Shaughnessy and Thomas Dick, which appeared in the April 1991 issue of the Mathematics Teacher.