# 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 Chapter 4: Equivalence and Equality of the PTMT Teaching Algebra Materials.

For more details see the Module Overview document.

## 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.### 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.### 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.### 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.### 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.Last modified: Saturday, January 28, 2023, 12:16 AM