These activities are drafts. They all include student worksheets and websketches, and a number of them include performance-based assessment games. None of them yet incorporate teacher-support materials, though we hope to be able to provide those soon. We are revising the worksheets, websketches, and assessment materials as we we continue using them with students and observing students' successes and challenges. Please contact the webmaster with your questions, comments, and suggestions for improvements, or for information about our field-test program.

Each activity below is expected to require one or two class periods. The first activity is a review activity from the introductory unit to prepare students for the rest of the activities. Click any blue header below to go to that activity's web page.

1. The Dilate Family: This activity comes from the Introducing Transformations unit, and is included here so that students can review important prerequisite understandings about geometric functions and so they can practice working with Web Sketchpad tools.
2. Reduce the Dimension: Students begin with the already-familiar geometric functions in Flatland and figure out how to move each function into Lineland by restricting the domain of the independent variable to a line and adjusting the function so that the range of the dependent variable lies on the same line.
3. Number the Domain: Once the functions are in LineLand, students turn the restricted domain into a number line, measure the values of the independent and dependent variables, and figure out the numeric operation that corresponds to each geometric function.
4. Compose on a Line: Using a number line as a restricted domain, students compose two geometric functions and examine the behavior of the resulting composed function both geometrically and numerically.
5. Create a Dynagraph*: Students shift the output variable vertically to create a Dynagraph* representation of their linear function. They drag the independent variable to study the behavior of various linear functions and to solve puzzles in which they adjust the scale factor (for dilation) and the vector (for translation) to match given mystery functions.
6. Connect to Cartesian: Students rotate the output variable of their composed dilation/translation function by 90° and use the resulting Cartesian axes to create and analyze their function’s Cartesian graph, and to solve puzzles in which they adjust the original dilation and translation functions to match given mystery graphs.
7. Cartesian Games: Students play a series of games designed to help them understand the Cartesian graph of a linear function in terms of the relative rate of change of the independent and dependent variables. In each game, students control scale factor s and translation vector v to adjust function T(D(x)) so that it matches mystery function ??(x). Each successive game moves a bit further in the direction of abstraction. The first major step is fading the role of the dependent variables and encouraging students to use instead the plotted points (x, T(D(x))) and (x, ??(x)), and the second major step is to move toward using the graph itself, and to extract from the shape and location of the graph the needed information for adjusting s and v.