In Geometric Functions activities students create, manipulate, and experience function concepts by treating geometric transformations as functions with points as their variables.
In this activity students use Sketchpad’s locus construction to create the range of a function with a restricted domain. They then use this constructed range as a tool to investigate function behavior. For instance, students can change the angle of a rotation or the center of a dilation while observing the effect on the range. In the process, students experience functions as mappings that take a set of input points to a set of output points, and use functions as objects to be combined, edited, and animated.
In this activity students will:
(1) Make sense of problems and persevere in solving them; (2) Reason abstractly and quantitatively; (3) Construct viable arguments and critique the reasoning of others; (4) Model with mathematics; (5) Use appropriate tools strategically; (6) Attend to precision; (7) Look for and make use of structure; (8) Look for and express regularity in repeated reasoning.
8.F1,2; 8.G1; F-IF1,2,9; G-CO2; G-SRT1