This is a post that contains links, files, and a general description for each of the activities I hope we get to.
Each of the activities can be explored in one of two ways:
- Desmos (links provided)
- TI-Nspire (on the handhelds or click here to download the tns file)
Explorations
If you have seen any of these at one of my workshops before, feel free to jump down to the bottom of this page and explore one of the additional ideas.
The explorations we’ll be working on are:
- The Garden Fence Problem
- A Visual Quadratic Formula
- Simplifying Radicals Visually
- Dynagraphs
- Extras:
- Standard Form Quadratic Exploration of b
- Making connections using logarithmic transformations
Garden Fence Problem
- Desmos
- TI-Nspire pages 2.1-4.3
The maximizing the area of a garden given a 3-sided fence is a commonly explored problem. But technology offers some unique enhancements in terms of student thinking & generalizing, as well as for assessment.
A Visual Quadratic Formula
- Desmos
- TI-Nspire pages 5.1-6.2
The usual quadratic formula has a lot of embedded meaning, but it is difficult to see. We’ll explore an alternative formula that is much more visual.
Simplifying Radicals Visually
- Desmos
- TI-Nspire pages 7.1-7.2
The square root of n can be visualized as the base of a square whose area is n. This idea can be extended to visual the simplifying of radicals too! Click here for a more complete (but without technology) lesson.
Dynagraphs
- Desmos
- TI-Nspire pages 8.1-8.2
Dynagraphs are an idea invented by Paul Goldenberg, Philip Lewis, and James O’Keefe to help learners see the dynamic nature of functions better. An input value along one number line is mapped to an output value on a number line below it.
Extras
- Draw a graph of y=ax^2 + bx + c.
- Start with a=1 and c=0. Vary the value of b using a slider.
- Notice the vertex changes. What path does it follow?
- Change a and/or c. Explore the effect of b again.
- Adjust k and/or b to make the graphs equivalent.
- Generalize to determine an identity.
Diary of a Piman 