Calculus labs that generate in-depth learning in a cooperative group setting. Labs cover functions, limits, continuity, the derivative and its applications, Newton's Method, maximization and minimization, integration, comparison of methods and numerical integration.

It IS possible for students to find answers without their calculator! Sometimes, calculations are much easier than they seem. Other times, calculations are unnecessary when a good approximation can be enough to answer a question. Here are some ideas to get students to use the most high-tech gadget of all: their brain! These ideas are not only useful in the classroom, but also when dealing with the HSPA and SAT.

Let graph theory be the springboard for a unique context and to perk up some otherwise mundane computations. Combine network design, geometry and algebra to implement an investigation and problem set for second year algebra, precalculus, and beyond. The activities include the opportunity to use construction, special right triangles and rational expressions, and form the backbone of this activity. No calculator required, and some good opportunities for cooperative learning.

This presentation will take a look at the use of discrete mathematics (particularly graph theory) in games which can be used in the classroom. We will consider not only certain games like Sprouts and Instant Insanity which have a direct connection, but also the role of discrete math in scheduling contests and ranking the players based on the results.

"Should I assign a project?" "Is the project worthwhile?" "Will I have time to grade it?" "Is it on topic?" "Does it need to be?" "Why am I doing this, anyway?" These are several of the questions we often ask ourselves when we are contemplating assigning a project to our students. This session will explore a few projects (for Algebra, Geometry, and Pre-Calculus), some on, and some off topic, that provide students with an opportunity to demonstrate their talents in ways that are not usually available to them in more standard mathematics assignments.

The introduction of computer algebra systems (CAS) in the math classroom has made it challenging to create activities and assessments that test knowledge and understanding of precalculus topics while supplementing, rather than supplanting, traditional paper-and-pencil techniques. This workshop will introduce a variety of discovery-based activities and assessments that involve the use of the TI-89 calculator as well as Geometer's Sketchpad and Converge software.

In this session participants will look at several problems which will connect what is taught in the math classroom to real world applications. These activities are designed to help students visualize concepts, predict results, and make connections. Problems will be looked at from the graphical, analytic, numerical and verbal points of view and address the New Jersey Core Curriculum Content Standards in Mathematics. Bring your TI-83+ graphing calculator.

Come hear about creative ideas for alternative assessments for students in Algebra 1, Geometry, and Algebra 2. Examples and sample rubrics will be provided. These projects include daily, multiple day, and marking period projects. These ideas can be adapted to specific levels and some are appropriate for Precalculus.

This session will have participants doing hands-on activities that are motivating to students. The activities will use ready-made lessons that help prepare students for the NJ HSPA as well as integrate probability and data analysis concepts into the high school curriculum. Some time will be reserved for teachers in the audience to share their own successful lessons.

The mathematics of traffic flow is a fascinating exercise in reasoning. Braess' Paradox is a counter-intuitive analysis of what constitutes the best traffic pattern in a given situation, and of what results in the happiest drivers. This topic provides real-world applications of systems of equations, algorithms and logical reasoning.

Algebra students challenge you to explain "when are we ever going to use this stuff?". This interactive session presents lessons that use manipulatives and ideas from real world applications in engineering and computer science. The idea is to provide students with real world representations of the algebra they're learning to motivate their understanding of concepts such as linear equations and coordinate systems.

Participants will be shown how a slice of cake can be used as motivation to introducing the concepts of area and volume in Algebra 2 or Calculus. Each participant will receive a piece of graph paper and a slice of cake. After tracing the cake, a linear model will be found on the calculator. The area and volume will be computed geometrically and through the use of calculus. Yes, participants will be able to eat the cake at the end of the presentation! Please bring your TI-83.

Did you know that mathematical equations can create beautiful designs on a TI-83+, TI-89, TI-92, or Voyage 200 graphing calculator? Using any of these calculators, attendees will learn activities designed to help students quickly see and study graphs of functions encountered in pre- algebra through calculus courses, making connections between algebra and geometry. The activities encourage students to strive for greater depth and meaning.

An exploration via rational functions, as to whether a tin can manufacturing company is using the minimum possible surface area for their can. How "can" you make improvements? The discovery and development of volume and surface area of a cylinder. How the radius and height affect volume and surface area of a cylinder. Participants will actively derive a surface area function as it relates to the volume and radius of the cylinder. Using graphing calculators, participants will determine if their cylinder utilizes the minimum possible surface area for its volume. Using some of the same ideas participants will determine the maximum possible volume of a can given a fixed surface area. Bring in a canned food container and a graphing calculator and see what you "can" do.

PowerPoint Presentations are a very efficient way to present math lessons. There is no lost time while an example is erased and a new one written on the board. That lost time is time where students can lose their focus. An overhead is static while PowerPoint Slides can be very dynamic.

PowerPoint can be emailed to absent or homebound students. In the case where the student does not have access to PowerPoint and/or the Internet, slides can be printed out and photocopied.

Using the TI Graphlink an entire sequence of TI-83 Screens can be put on a PowerPoint Slide and brought up screen by screen. PowerPoint Presentations are a lot of work up-front but pay off with a lot less work later. Anyone can learn PowerPoint and teach math using it.

Computer science lends itself to lessons that promote student collaboration, class participation, and a whole lot of fun. No computers are necessary to teach numeracy, algorithmic thinking, and pattern-matching skills in the context of common algorithms, such as sorting and searching. The lessons are presented as games, which are easy to modify to fit any classroom, from kindergarten through college.

This session will focus on Sierpinski's triangle and its uses in Algebra, Geometry, Algebra 2, Precalculus, Calculus, and Discrete Math classrooms. Participants will use Pascal's triangle, a random experiment with dice, and the TI-83 program to construct Sierpinski's triangle. Participants will use hex paper to create Sierpinski's triangle. The hex paper will also be used to explain forest fire and oil-spill predictions. We will also build Sierpinski's pyramids (tetrahedrons). The tetrahedrons project can be used for classroom discussions on 3-D geometry, limits, and fractals.

Participants will use M&M's and graphing calculators to simulate radioactive decay. Exponential regression equations will be derived from M&M data which represents decay. Exponential growth problems will also be discussed. Bring along a graphing calculator and your appetite!

Solving cubic equations is quite a challenging task in Algebra, especially the ones that do not render themselves to the techniques of factoring. Many techniques have been devised to solve the cubic equations. This presentation will deal with the development of Cardan's Formulas in order to solve the cubic equation of the type x cubed + ax squared + bx + c = 0. The formulas will be derived from the first principle using some basic concepts from Calculus. Some cubic equations will be solved using the Cardan's formulas.

Ideas about rates of change and accumulation of rates of change are accessible to students before they have learned the details of calculus. Use those valuable five days to give your students a view of the ideas of calculus that will put them in a better position for organizing formal ideas later. In this workshop, we will take paper and pencil activities and extend them with the Geometer Sketchpad's dynamic tools. With these activities, students can ask and answer fundamental questions involving limits, derivatives, integrals, antiderivatives, and slope fields before they have even heard the words.

In precalculus, students who make connections between different representations of mathematical ideas build understandings that will firmly support future learning. See how to use the Geometer's Sketchpad to create unique exploratory environments where students visualize, verbalize, and symbolize trigonometry, complex numbers, vectors, and limits. Take a dip into fractals, chaos, and the third dimension in this multi-representational tour!

This presentation is specifically designed for new or newer precalculus teachers. A careful integration of technology and key concepts are the tools required to become an effective precalculus teacher. Unfortunately, many teachers fail to utilize the full capabilities of the TI-83. These same "capabilities" are also those required in most calculus classes. Therefore, the participants in this workshop will be presented with classic problems in precalculus and numerous ways to use the TI-83/ TI-89 to solve them.

With so much math software already available, how do you find just the right tool? How do you determine which technology really benefits your students? The Math Forum invites you to explore these questions with Math Tools, our new digital library for mathematics software.

We are creating a community digital library of software and applications for computers, calculators, PDAs, and other handheld devices. Currently available platforms include computers and graphing calculators, and the shelves are stocked with Java Applets, Flash, JavaScript and TI applications. Resources are categorized by course and topic, making it easy for you to find the perfect item to help demonstrate and teach whatever you're working on.

We're also looking for people who would like to help us grow the library, so whether you're interested in learning how to use it effectively or getting involved in the project or both, stop by to take a look and hear what's going on. Check out our website -- http://mathforum.org/mathtools/.

Following the September 11 attacks on the World Trade Center and the Pentagon, many scientists looked for ways to contribute to defense against terrorism. Surprisingly, mathematicians found they had a lot to offer. This talk will give some examples of how mathematics, statistics, and computer science are contributing to homeland security.

Fred Roberts is a Professor of Mathematics at Rutgers University. He is director of the Center for Discrete Mathematics and Theoretical Computer Science (DIMACS), a consortium of Rutgers and Princeton Universities, AT&T Labs, Bell Labs, NEC Laboratories America, and Telcordia Technologies, with partners at Avaya Labs, HP Labs, IBM Research, and Microsoft Research. He has been asked by Rutgers to coordinate all homeland security research on the campus. Professor Roberts has published widely on the uses of mathematics in such diverse areas as biology, psychology, transportation, communication, and energy use, and recently has been working on mathematical modeling in the defense against bioterrorism. He has also been active in the development of programs bringing new mathematical ideas to high school teachers and students. His awards include the National Science Foundation Science and Technology Centers Pioneer Award and, most recently, the Gold Medal of the Czech Union of Mathematicians and Physicists.

In this session, we will explore a number of problems that arise in different contexts but whose solutions are all similar to that of the "handshake problem", and connect their solutions to patterns in Pascal's triangle.

Rational functions exhibit unusual behavior for the beginning student of calculus. Studying this class of functions with the TI-89 helps students attain a clearer understanding of ideas such as asymptotes and limits. Misconceptions associated with rational functions will also be discussed. Please join us to witness the palatable marriage of functions and technology.

This session is designed for beginners to people who feel somewhat comfortable using the TI-8X. I've found (mostly through mistakes) that these puppies can do some neat things. Drop by and find out some neat window tricks, how to solve an equation 6 different ways, and why you have to take all your prescription tablets even though you feel better!

Break away from that structured textbook sequence. Mix Basic skills, Equations, Word Problems and Graphs in every lesson. Combine Arithmetic with Algebra. Add a spiral approach. Garnish with technology. Allow to simmer for 16 weeks. Enjoy the results. (All attendees will receive free tutorial software.)

Use cardboard, cellophane and scissors to help Geometry students understand the abstract concepts behind indirect and detour proofs. Bring along your scissors and tape for a fun exercise!