Course Guide - USAID Teacher Education Project

Unit 2 AlgebraWeek 4, Session 2: Introduction to Quadratics (2): Equations, ConnectingAlgebra and Arithmetic1. What are the important concepts?a) Quadratic Functions can be represented by equations in the form of y = ax 2 + bx +c.b) The coefficients a, b, and c in y = ax 2 + bx + c determine the shape of theequation's parabolic graph.c) The "second differences" on a table of values indicate a "second-degree equation,"where the greatest power of x is 2. (Similarly, a "first difference" indicates a "firstdegree"or linear equation where the power of x is 1.)d) A quadratic equation can be expressed either in its expanded form or its factoredform.e) Quadratic equations can be modelled by a manipulative called Algebra Tiles.f) The partial products method of multi-digit multiplication, introduced in theNumber and Operations unit, can be directly linked to Algebra Tiles.2. How do children think about these concepts?a) Because Number and Operations is the major focus of early education, youngstersneed strategies to help them link their number sense to algebra concepts.Youngsters who are visual learners need ways to link algebra to their geometricsense.Children who are tactile learners need to work with manipulative materials, movingthem around in space, in order to make sense of mathematical concepts.All these different kinds of learners can benefit from using Algebra Tiles to connectalgebra to what they already know, as well as how they need to learn it.b) When presented with various representations of a quadratic function, youngstersneed their teacher to make connections among various representations.For example, students may not notice that the maximum or minimum of a graph isevident from the table of values. Or that the "c" in the expanded form of y = ax 2 + bx+ c is the y-intercept.Rather than telling youngsters about these characteristics teachers need to ask probingquestions that force their students to look for patterns. This means that teachers mustfind specific examples to elicit youngster's thinking about quadratic patterns.