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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.

I've always liked timelines as an educational tool. They offer the ability to show related threads compared to each other easily. I loved having students investigate a single topic, create a timeline for that topic, mash the timelines together in a BIG overarching timeine, and then have students start to look for connections. I stole the concept early in my career from the TV show Connections (too bad it didn't make it, GREAT GREAT show).

I've always liked timelines as an educational tool. They offer the ability to show related threads compared to each other easily. I loved having students investigate a single topic, create a timeline for that topic, mash the timelines together in a BIG overarching timeine, and then have students start to look for connections. I stole the concept early in my career from the TV show Connections (too bad it didn't make it, GREAT GREAT show).

What mathematical competencies must a teacher have to teach the subject well? This has proven difficult to investigate (1). A current view is that teachers' knowledge of mathematics "remains inert in the classroom unless accompanied by a rich repertoire of mathematical knowledge and skills relating directly to the curriculum, instruction, and student learning" (2). Unfortunately, there is no consensus on which "knowledge and skills" might activate teachers' inert knowledge. Two perspectives prevail, neither with a research base that enables strong claims about practice. The majority of current studies focus on explicit knowledge of curriculum content and instructional strategies. Such knowledge might be assessed directly through observation, interview, or written test (2), with a parallel research emphasis on the formal contents of teacher education programs [e.g., (3)]. A second school of thought, presented here, is that the most important competencies tend to be tacit, like skills involved in playing concert piano, learned but not necessarily available to consciousness.

A movable scale that goes from very, very small to universe. A sliding scale that allows you to investigate. 

A compilation of interactive resources. Very thorough and worth investigating. Most of the resources tend to be primary through middle. At least in math they are.

This applet allows the user to represent data about the states using colors. The state with the highest data value is darkest; other states are shaded proportionally. Investigate any of the data provided-or enter data of your own!

Great resource for math teachers to help them represent data.

Some nice online resources that might be useful in your classroom. I haven't investigated them all as of yet, but will be looking into them to make more specific recommendations. 

Interesting resource, worth investigating, but has a nominal cost involved $20 per year.

Virtual Science experiences. 

Physics applets from university of oregon. department of physics. 

Free falling body applet that gives you the option of dropping from a height or firing upwards from the ground. 

Applets are small, self-contained, interactive programs that can be run on your computer using code called Java (a free download from Sun Microsystems). All of the applets listed below are available for download from the web, but require Java to run. An Applet Search Engine can be used to find other available applets not found on this page.

Welcome to the Physlets resource page. Physlets, Physics Applets, are small flexible Java applets designed for science education.  You do not need to become a Java expert in order to use Physlets.  The links on the right contain tutorials, download instructions, and example problems to help you use Physlets in your teaching.

Fowler's Physics Applets. Michael Fowler - University of Virginia Physics

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. 

Interesting way to approach analysis of slope relationships.