1 Overview (10 min)
This hands-on workshop is an opportunity for mathematics teacher educators to learn about our free online technology-based activities for teachers that focus on functions and geometric transformations.
The featured activities (and the lessons from which they come) are effective and easy to use in an online class. (They’re also effective in an in-person class, once those are running again.)
This workshop involves both full-group presentation and small-group breakout rooms in which you engage with the technology and discuss the activities with colleagues. We suggest using your favorite web browser on a computer or tablet so that you can be fully engaged in the workshop.
This workshop is based on materials developed by the Forging Dynamic Connections project, supported by the National Science Foundation under NCSU IUSE award 1712280 (July 2017 through June 2019). The preparation for and presentation of the workshop itself was supported by NSF Supplemental Funding under the same award.
2 Introduce Transformations as Functions (45 min)
This lesson introduces geometric transformations from a function point of view. Students experience geometric points as the variables and explore how dragging the independent variable (the pre-image) affects the dependent variable (the image). Students describe the relative motion (rate of change) of the two variables and distinguish between examples and non-examples of functions.
In the breakout section you will explore the Examples and Non-Examples activity from this lesson.
3 What is Web Sketchpad? (2 min)
Web Sketchpad (WSP), derived from The Geometer’s Sketchpad, is a web-based dynamic mathematics software that strives for simplicity (for instance, no menus) and configurability (tailoring the toolbox to the task at hand).
The objective of WSP is to reduce the emphasis on the technology in order to put the main focus on mathematical ideas.
4 The Reflect Family (20 min)
This lesson introduces the Reflect Family of functions. Students warm up by exploring a reflection maze.
In the body of the lesson they dance a reflection dance, construct their own reflect functions, find the rule connecting given independent and dependent variables, play a variety of games in the reflect arcade, and finish with more function dances (both physical dances in the classroom and virtual dances on the screen).
In the breakout section you will explore the Find the Function Rule activity from this lesson.
5 Transformations and Congruence: Mystery Transformations (20 min)
In this lesson students apply five function families to triangles. They transform one of two given triangles, trying to superpose its imnage on the other given triangle..
In the process they refine their understanding of each of the families, and they come to understand that two triangles are congruent if and only if an isometric transformation of one can be superposed on the other.
6 Connect Transformational Geometry and Algebra (10 min)
In the Construct a Dynagraph lesson students restrict the domain of geometric transformations to a number line, identify which transformations fit most cleanly into the new domain, connect the transformations to their corresponding algebraic operations, create linear functions via transformations, and use their resulting dynagraphs to play a dynagraph arcade game.
7 Questions, Answers, and Comments (10 min)
The floor is open for questions and comments. (Please use the Chat window to ask your question or to make a comment.) With such a large number of participants in this workshop, please keep your questions and comments relatively brief, to allow us to respond to as many of them as possible.
8 Resources and Follow Up
The Forging Connections lessons are available here: Forging Dynamic Connections. Most of the lessons are reasonably complete and ready to use, but please be aware that some are not as complete, or not as polished, as the lessons you have seen today.
Within a few days we will email all participants, including links to additional resources and providing responses to some of the questions and comments we didn't have time to address during the workshop.
This article from the February 2016 Mathematics Teacher provides a more detailed exposition of the value of connecting geometric transformations and functions in algebra: Connecting Functions in Geometry and Algebra