Activity Overview
Students use the interactive TI-nspire file and support video to gain an understanding of slope fields and differential equations. Students use a slope vector to manually produce a slope field and specific solution followed by the more automated option using the inbuilt calculator functionality. Students solve differential equations by hand and on TI-Nspire.
Objectives
Understand slope fields and differential equations by hand and using technology.
Vocabulary
Slope field, Differential equation, Initial conditions, specific solution, isocline
About the Lesson
Students begin using a differential equation to identify specific slopes for given coordinates. Students then use the interactive TI-Nspire file that contains a responsive slope vector providing instant feedback whilst focusing on a single set of coordinates. This understanding is then used to progressively produce a slope field where slope vectors are added as the student moves the point around the Cartesian plane. A range of differential equations are then used to explore slope fields including solutions by hand and using the CAS functionality of TI-Nspire. A support video is linked to this document so that students can prime their understanding before the lesson or as a follow up.