Course Guide - USAID Teacher Education Project

Session 2 continues the idea of multiple representations in algebra by adding quadraticexpressions to the tables and graphs that students produced in the prior session. Thus theywill need to bring the prior session's work back to class to extend the work they did with tableand graphs.Session 2 will show how the expanded format for a quadratic equation (y = ax 2 + bx + c) andthe factored format are two different ways to express the same function.The session will also relate these two formats to the table of values, graph, and algebra asgeneralized arithmetic. This will be an opportunity for students to revisit the partial productsmethod for multiplication that they studied in the Number and Operations unit, noting howthis method relates to quadratic equations.A key aspect of this session will be the introduction of a manipulative called Algebra Tiles tomodel how the partial product method applies to quadratics, showing the link between theexpanded and factored forms. It is imperative that you read through the Algebra Tileshandouts and websites to prepare for this session.Session 3 will end this Algebra unit where most algebra textbooks begin: solving for "x theunknown."Imagine the confusion of this student who says to his teacher: But yesterday you said ‘xequals 2.’By this time your students will have experienced x as a variable for over three weeks. Now itis time to shift to the other meaning for x, and deal with the symbol manipulation.Phrases such as "like terms," have not been specifically noted during this unit. However, bythe time students have reached the end of this unit they should have an intuitive grasp ofthem. When combined with their understanding of equations from the Number andOperations unit, students should be well positioned to use the commutative, associative,distributive, and identity properties to solve for x.This final session of the unit will also ask students to reflect on what they can do as teachersof young children in the early and middle grades to foster the algebraic thinking thatyoungsters will need in middle grades and in secondary school.