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In this unit, students will investigate a relationship between recursive functions and exponential functions. Math Content By the end of this unit, students will: Represent data using tables, graphs and rules Investigate patterns and make conjectures Express sequences with recursive and exponential rules Describe and interpret exponential functions that fit the patterns Individual Lessons Lesson 1 - Trains, Fibonacci, and Recursive Patterns In this lesson, students will use Cuisenaire Rods to build trains of different lengths and investigate patterns. Students will use tables to create graphs, define recursive functions, and approximate exponential formulas to describe the patterns. Lesson 2 - More Trains In this lesson, students will use Cuisenaire Rods to build trains of different lengths and investigate patterns. Students will use tables to create graphs, define recursive functions, and approximate exponential formulas to describe the patterns. Lesson 3 - Recursive and Exponential Rules In this lesson make connections between exponential functions and recursive rules. Students will use tables to create graphs, define recursive rules and find exponential formulas.

Another online graphing utility. Not as rigorous as Swivel, but offers a way of creating interesting venn diagrams. Great tool for teaching how to label and provide unit data so people can read the graph most effectively.

Another site to access already made charts/graphs or to have students create and share their own visual displays of information. 

Swivel is a great data source for students and teachers alike. You can create graphs right on swivel or download the data sources and create your own. The data set shown in the link is food expenditures at home and away from home by year since 1933. I really like the food expenditures away from home since 1947, it looks like a nice exponential decay function. It would be nice to have students analyze what happened in 1947 to cause the graph to change its behavior. If you are a SS or American History teacher, I think looking at the initial aspect of this data would be interesting given that the data mirrors the great depression and as America came out of the depression the amount of money spent on food items at home decreased, until the advent of WWII!

Easy to use graphing utility. No adds easy to setup different windows, graph multiple functions.

This is the kind of graph that students need to be interacting with as much as possible. Great example of different ways of expressing data. I would love to see questions that students could write based on this kind of graph.

Great free online graphing calculator. 

"28 tools for creating graphs, Gantt charts, diagrammers, calendars/schedulers, gauges, mapping, pivot tables, OLAP cubes, and sparklines, in Flash, Flex, Ajax or Silverlight." Not all free, but there is a free tool from Google that wasn't too hard to use.

Chris Harbeck's class blog from this last year. A great practitioner and great example of utilizing a blog for instructional purposes.

Great set of lessons for modeling, recursive functions, real-life application from NCTM Illuminations. The lessons include not only context, but applets that help students visualize the situation and  mathematical model. 

This is a great presentation. If you want to see how the best thinkers in the world are presenting their data, then take a look at this presentation by Hans Rosling. I think this presents a challenge to math teachers to have students look at data differently than we are now. I think the data on the income and child mortality rate is incredible. Such a powerful data set and it's a linear relationship!!

Powerful topic, poverty and patterns in data relationships over time, WOW. Hans Rosling uses some incredible statistical software to present the data, but the idea can be mimicked using some PP type technologies and creating graphs. The topic of poverty is explored in a very easy understandable way; I think high school students would understand the topic and love the idea. Make sure you listen to his use of the databases, and remember he is one of the premier statisticians in the world. He is changing how he presents data, and I think we need to listen to his message on this topic.

A simulation of the stock market. A great running application to use in algebra classes, as it allows students to use algebraic concepts to manage their portfolio. Not directly skill or concept related, but can utilize graphing, formula use (as simple as P/E ratio, to regression analysis, to derivatives). For those teachers who think a little outside the box. I would be glad to hear how others might envision using this in their classroom.

Great set of tools available online for free. I played with several and really like the ease of use, the nice conceptual nature of them (i.e. archimedi's bathtub is a great example of a graph that could be used to help students understand change).

I like Dave's blog for several reasons. He gives his students voice, he uses technology well, and he seems to find some interesting activities for his students. This post is right up my alley; he uses data that is relevent to his students, has them do some basic analysis and then in explore other data and compare/analyze the data with the original (relevant) data!

Neat tool for teachers. Need a quickly designed number line or graph paper. From NCTM and Illuminations, easy to use but not super easy to manipulate. Good for basic graphics needs.

s a software tool for detecting equations and hidden mathematical relationships in your data. Its primary goal is to identify the simplest mathematical formulas which could describe the underlying mechanisms that produced the data. Eureqa is free to download and use.

Allows you to make dynamic charts.

Statistics that lie! This is a great example of data that isn't reported correctly. The article decries the death of Netbooks, when in fact it is more about a stabalization of sales. I encourage math teachers to let students read the article and at least the first two responses. It's a great example of blatant misinformation.