Course Guide - USAID Teacher Education Project

• The idea of a pattern rule• The distributive property of multiplication over addition [x (trunk shapes +leaf shapes) + 1 top shape]• The idea of equivalent expressions, that [x (trunk shapes + leaf shapes) + 1 topshape] is equivalent to (x trunk shapes + x leaf shapes + 1 top shape).Early attention to equivalence and equivalent expressions is important because it willbe featured in later sessions of this unit.e) End the session by having students refer back to the article and read through thephoto scenarios of the teacher's observation of individual students. What was theteacher thinking about student thinking?If you were the teacher in this classroom and heard all these student ideas, how wouldyou prepare an end-of-class summary that moved from rudimentary to moresophisticated thinking about growth patterns?5. Assignments (to be determined by instructor)Faculty NotesUnit 2 AlgebraWeek 2: Variables, Coordinate Graphs, Multiple Representations, EquivalenceWeeklong Overview:Session 1: Developing an understanding of x as an unknown and as a variable,coordinate graphing, discrete graphsSession 2: The importance of multiple representations in algebra, continuous graphsSession 3: Introduction to symbolic representation and mathematical equivalenceFaculty Preparation for Upcoming Class (1-2 hours)• Read the following articles and look through these websites that addressvariables, multiple representations, coordinate graphs, and equivalence:• The College Preparatory Mathematics teaching guide for its MultipleRepresentations chapter. You'll note on page 17 that high school students aregiven the same "tree growth" problem that 7 year-olds worked on in theMarilyn Burns article last week. There are also excellent diagrams of growthpatterns linked to how they can be represented in various formats:http://www.cpm.org/pdfs/information/conference/AC_Con_Mult_Rep.pdf(Also available at: http://tinyurl.com/Algebra-Mult-Rep)• Introduction to Mark Driscoll's Fostering Algebraic Thinking. Note the list ofquestions on page 3 that you can use as discussion prompts during class toraise issues about the teaching of algebra with your pre-service teachers: