Examining Students’ Practices in Algebra and Function > Module 2
ESP_AF Module 2-Algebraic Equivalence
This module uses two different technologies, polypad virtual algebra tiles and CAS, to explore completing the square. Teachers will examine students using both technologies to build a conceptual understanding of the procedure for completing the square and compare and contrast the affordances of each approach. Teachers will build on their understanding of noticing student thinking on technology-enhanced tasks and practice posing purposeful questions.
This module could be used alongside a chapter from Teaching Algebra materials:
Chapter 4: Equivalence and Equality
Overview Documents
Module Elements
| 2.1 Completing the Square with Algebra Tiles Teachers will engage with a Desmos Activity in which they use virtual algebra tiles to determine a generalized procedure for completing the square |  Instructor Materials |
| 2.2 Completing the Square with CAS Teachers will engage with an activity that uses Geogebra’s CAS tools to determine a generalized procedure for completing the square | Class Materials Instructor Materials |
| 2.3 Noticing Student Thinking: Completing the Square with Virtual Algebra Tiles Teachers engage with noticing one pair of students’ mathematical thinking as they are making sense of completing the square with virtual algebra tiles. | Class Materials Instructor Materials |
| 2.4 Posing Purposeful Questions: Completing the Square with Virtual Algebra Tiles Teachers practice posing purposeful assessing and advancing questions to pairs of students who have used virtual algebra tiles differently to model the same expression. | Class Materials Instructor Materials |
| 2.5 Noticing Student Thinking: Completing the Square with CAS Teachers practice noticing student thinking and posing purposeful assessing and advancing questions, for a pair of students who are using a CAS to develop an understanding of completing the square. | Class Materials Instructor Materials |