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### 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.### 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.### 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.

### 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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### 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. ### 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*.

### 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*.

### 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.
### 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.### 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*.