Course Guide - USAID Teacher Education Project

Bring to class:• Graph paper• Rulers• ScissorsRead through the plans for this week's three sessionsWeeklong Overview:Session 1 starts by students developing a table of values and a graph for what they probablyanticipate is another linear function activity.Unlike in past sessions where you were asked not give students guidelines about parametersand scaling, you will need to be quite directive about this so that students can focus on theattributes of the resulting graph without considering conflicting images.Regarding their data table: it will have more than four columns, and you will need to tellstudents which two columns to use when setting up their graph.Once they have used their table of values to construct the graph they may be in for a surprise:it's not a line. It's a parabola!At this point you and the students will do two things that will occupy the rest of the classperiod: 1) analyse their graphs and then 2) analyse their table of values.When analysing their graphs, listen to the features that students notice and be prepared to askfollow-up questions and comment about intersection with the x axis, a line of symmetry, theparabola's orientation (opening up or opening down), etc.When analysing their table of values, students will discover that what they learned about "firstdifferences" for linear equations no longer holds true. What does a "second differences"mean?Students also should notice patterns in their tables with regard to symmetry, similar to thischart:x -5 -4 -3 -2 -1 0 1 2 3 4 5y 25 16 9 4 1 0 1 4 9 16 25It is important to ask a variety of questions about how their table relates to their graph.(A note about limited time: Last week when introducing slope, the focus was on positiveslope because there was not enough class time available to discuss negative slope andnegative y-intercepts. The same holds true here for quadratic graphs. There will be ahomework assignment with a handout so that students can see that some parabolas are"upturned" whereas others are "downturned," some have a line of symmetry on the y axis (asthe above table implies) whereas others do not, etc. This is a good opportunity for them touse the free online graphing calculator (http://tinyurl.com/Graph-Calc-Free ) to explorethe eight different quadratic graphs on the homework sheet. This approach to usingtechnology, where students spend time analysing eight computer-drawn graphs, may be amore valuable learning experience than having them hand-draw each one. The homeworksheet has equations in a format that allows students to enter them into the online calculatorand see not only the graph but also the corresponding table of values.)