advertisement

Modeling Algebra Harshbarger & Yocco Fall 2007 1 Chapter 3 Suggestions: (Week 7) Lab Day: Interactive Software. With this activity we are accessing software intended for use with our previous textbook. An Activity Page that accompanies this software is available on the VISTA site under the Chapter 3 Activities link. It’s a single file called Interactive Software Activity. Ask students to download, print, and bring to class this file. You might want to make a few copies to bring with you on lab day. Pleas guide students through these directions to open the software: 1. Students can access the website by going to their MATH 11009 VISTA site, click on Chapter 3 Activities, then on the Interactive Software link. (This same link is on the Instructor site for you, under Chapter 3: 3.1: Website.) 2. Once on the site, Click on Interactive Software for PC* . (This is the SECOND link.) 3. Click on Download the Interactive Software for PC (ZIP Format) 4. When prompted with the dialogue box, click on Open. (If for some reason you get an error message, try clicking on Save first, then try again to open it. ) 5. Click on the exponential&log.exe file. The first activity uses E3: y Ca x Sliders so click on that one and Enjoy! Day 1: Sec. 2.3. Piecewise Functions Day 1 Goals for students Understand the need for piecewise functions in certain contexts Find function values given a piecewise function Sketch a graph of a piecewise function given a real-world scenario Write a function rule for a piecewise function given a real-world scenario For this first day, you might have students working in groups on the activities available on Instructor Site under Chapter 2: Piecewise Functions: Opening activity; The Earthworm problem presents a nice introduction to piecewise functions. When most students are finished with this piece, we usually discuss it, thus bring to the surface some significant issues with piecewise functions: evaluating them, using function notation, and domain restrictions. Then I plan to simply let students work on the other activities, discussing them as the need arises. This will probably take most of the time. When most students are finished, you might have them come to the board and sketch their graphs and write their formula. OR you might make an overhead transparency of the grids, thus facilitating a meaningful discussion as one student works on the overhead and others clearly see what s/he’s doing. Suggested homework: Finish the Activity Sheets Modeling Algebra Harshbarger & Yocco Fall 2007 2 Day 2: Sec. 2.3. Piecewise Functions Day 2 Goals for students: Given the graph of a piecewise linear function, student can write its function rule Given the rule for a piecewise linear function, student can sketch it Given a real-world scenario using a piecewise function, student can write the function, evaluate it at given values, and interpret the meaning The focus today is on graphing piecewise functions and writing a function rule given its graph. Ideally, we’d like students to be able to write a piecewise function for a real world scenario, but our book simply does not demand that of students, so we’ll have to skim over that part. Our book is weak on exercises here, so there’s yet another piecewise function practice sheet on the Instructor site. It’s called “Graphing Piecewise Functions.” This file is NOT on the VISTA site, so you’ll either have to email to your students or make copies. Suggested homework: Graphing Piecewise Functions worksheet: odds; Also in text p. 189-92: 9 – 12 all, 23 – 26, 49, 50 Day 3: Sec. 3.0. Algebra Toolbox Goals for students: Explain the meaning of negative exponents and a zero exponent Simplify expressions with negative and zero exponents Understand the need for scientific notation Work accurately with scientific notation This is pretty traditional stuff. Be sure to intuitively derive the notation for negative exponents: e.g. you might ask students. x3 . Using the usual rules for exponents, what do we get? [x -7 ] x 10 x x x Now if we spell out the meaning of the exponents, what do we get? x x x x x x x x x x 1 Which = 7 , etc. etc. x Suppose we wanted to simplify Please again emphasize understanding NOT rote memorization of the rules. I have a discovery worksheet on exponents somewhere….if I find it I’ll post it on the instructor site. Follow with plenty of traditional examples and/or student work at the board. Suggested homework: p. 280: 1-38 odds, 24, 26, 28. Day 4: Sec. 3.4 . Exponential and Log Models Given a real world scenario, student can write an exponential model Student understands, and can explain, the difference between a growth (or decay) factor and a growth (or decay) rate. Modeling Algebra Harshbarger & Yocco Fall 2007 Given an exponential model, student can identify the growth (or decay) factor, rate, and initial value. Student can recognize exponential data given a data set in a table. The purpose here is to introduce students to exponential growth in context. You might start with a problem for them to discuss in small groups: Suppose over Christmas break you had a choice of two jobs. Company A will pay you $1,000,000 for 30 days work. Company B will be willing to pay you a penny on the first day, two cents on the second, and continue doubling the amount until the end of the month. On day 30 you would receive the final doubled amount (not the sum of all days). Which job should you take and why? Create, with the students, the math model to represent the above scenario. Then you might continue with problems from the book, eg. #14, 16. After students feel (somewhat) comfortable writing exponential models, you might want to look at the corresponding data set and note that there’s a constant percent change and this is what characterizes exponential functions. Time permitting, you might compare exponential growth to linear. Suggested homework: p. 328: 1,2,5,7, 13 – 21 odds, 14, 16 (if not done in class) 3