1. As Class Convenes l Find your team’s table and have a seat l Pick up Team’s Modeling Folder l Remove Chapter 1 Assignment l Place your Chapter 2 Assignment and Excel Assignment Corrections in Team’s Folder and return in alphanumeric order before end of Contact Before Work u Start up your computer and download today’s class presentation from the U drive modeling/class/mcneill5.ppt

2. Agenda Contact Before Work5 min Introduction5 min Task 1 and Report Out40 min Break10 min Task 2 and Report Out45 min Out of Class Work5 min

3. Hidden Slide Which Contains More Detailed Comments About The Reporting Out Activity

4. Begin With the End in Mind u Chapter 3 of HTMI –algorithm –jumping in the deep end –notation –representation types –upper and lower bounds

5. Resubmitted Work Products Resubmissions should consist of the following ( in the order specified ! ) : ¶ The original checklist with check marks on those items you believe you have improved or corrected. · The improvements you have made to the original work product; ONLY the improvements; NOT a complete, new work product. ¸ The original work product

6. Clarification for the Modeling Class The Problem Solving Heuristic ( based on the McMaster Five-Point Strategy ) u Define the Problem ( COMPLETED ! ) u Generate Solutions u Decide the Course of Action ( MODELING CLASS STARTS HERE ! ) u Implement the Solution u Evaluate the Solution

7. How To Model It : Chapter 3 Structure Before Task u Please CLOSE YOUR BOOKS and PUT THEM AWAY for now; Thank you ! u Each INDIVIDUAL, read the problem statement on the next SLIDE;( 5 min) make notes on questions, anything that needs clarification, etc. ( N.B. Please limit your questions to words you don’t understand, etc.; this is not an opportunity for a discussion of the problem. ) u Clarification, if any( 2 min) u Each INDIVIDUAL, read the description of the first task on a(20 min) subsequent slide; discuss in your SUBteam and follow the directions on the slide u Reporting out by teams of (10 min) (1) the REPRESENTATION or MODEL you developed, (2) the list of questions you would like to ask, or (3) the assumptions you would like to make.

8. slide 8 Problem Context There are several diseases of the heart where it is critical to monitor, twice a year, the liquid volume inside the heart to see if the volume is changing

9. The Problem It is proposed to inject, for a limited amount of time, at a constant rate, a dye tracer into the vein that moves blood into the heart. Small samples of blood are withdrawn at regular intervals from the artery that pumps blood out of the heart. These samples are stacked, labeled, and subsequently analyzed to determine what concentration of dye they contain. How could you use the results to determine the volume of blood stored in the heart?

10. How To Model It : Chapter 3 Structure Before Task u Please CLOSE YOUR BOOKS and PUT THEM AWAY for now; Thank you ! u Each INDIVIDUAL, read the problem statement on the next SLIDE;( 5 min) make notes on questions, anything that needs clarification, etc. ( N.B. Please limit your questions to words you don’t understand, etc.; this is not an opportunity for a discussion of the problem. ) u Clarification, if any( 2 min) u Each INDIVIDUAL, read the description of the first task on a(20 min) subsequent slide; discuss in your SUBteam and follow the directions on the slide u Reporting out by teams of (10 min) (1) the REPRESENTATION or MODEL you developed, (2) the list of questions you would like to ask, or (3) the assumptions you would like to make.

11. slide 11 The Task (20 minutes) é In your SUBteam take about 10 minutes to prepare a plan ( remember think and plan BEFORE you ‘do’ ) and then come up with a REPRESENTATION or MODEL that helps you explain your plan to others. é Use an overhead transparency to document your results for presentation. é Your representation could be a diagram, a set of equations, a flowchart, an algorithm, or whatever format (or representation type ) you choose ! é If you find it difficult to develop a representation, then make a list of questions you would like to ask, or assumptions you would like to make. Remember the heuristic ‘Any answer is better than none’ ! é Do NOT actually try to solve the problem at this time. Also remember that the decision to use dye has already been made; you may have thought of using other methods, or have had other bright ideas, but that is NOT the problem you have been asked to solve.

12. slide 12 Reporting Out u When your name is called: –quickly come to the overhead –present your plan (model), questions you have, or any assumptions you made

13. Break Be back with your team, ready to work, in 10 minutes : remember our class Code of Cooperation !

14. Chapter 3 (continued) Structure Before Task u Each SUBteam, reflect on, discuss and make notes on (10 min) (1) how you actually developed the REPRESENTATION or MODEL, (2) what heuristics you used, and (3) what ideas you had about the problem. u ( N.B. this is a ‘reflection’ on the PROCESS, NOT the PRODUCT ! ) u Reporting our by teams on the PROCESS ! (10 min) u Please RETRIEVE and OPEN YOUR BOOKS; Thank you !  Each INDIVIDUAL, read pp. 10Y - 12Y ( N.B. only TO the (15 min) FIRST hollow 3); discuss in your SUBteam and check each other for ‘understanding’. u Clarifying Expectations and Process Check ( 10 min)

15. Chapter 3 (continued) Structure Before Task u Each SUBteam, reflect on, discuss and make notes on (10 min) (1) how you actually developed the REPRESENTATION or MODEL, (2) what heuristics you used, and (3) what ideas you had about the problem. u ( N.B. this is a ‘reflection’ on the PROCESS, NOT the PRODUCT ! ) u Reporting our by teams on the PROCESS ! (10 min) u Please RETRIEVE and OPEN YOUR BOOKS; Thank you !  Each INDIVIDUAL, read pp. 10Y - 12Y ( N.B. only TO the (15 min) FIRST hollow 3); discuss in your SUBteam and check each other for ‘understanding’. u Clarifying Expectations and Process Check ( 10 min)

16. Chapter 3 (continued) Structure Before Task u Each SUBteam, reflect on, discuss and make notes on (10 min) (1) how you actually developed the REPRESENTATION or MODEL, (2) what heuristics you used, and (3) what ideas you had about the problem. u ( N.B. this is a ‘reflection’ on the PROCESS, NOT the PRODUCT ! ) u Reporting our by teams on the PROCESS ! (10 min) u Please RETRIEVE and OPEN YOUR BOOKS; Thank you !  Each INDIVIDUAL, read pp. 10Y - 12Y ( N.B. only TO the (15 min) FIRST) hollow 3); discuss in your SUBteam and check each other for ‘understanding’. u Clarifying Expectations and Process Check ( 10 min)

17. Assessment Expectations for Chapter 3 Tasks That DO Need to be Completed to Meet Expectations for This Chapter (U:\MODELING\ASSESSMT \...\I_EXPECT.DOC, \EXPECT_3.DOC, and \CHKLST3.DOC) u Complete the following tasks : –pp.13 (CM): As suggested in the text, calculate the numerical answers for the models –Enter ONE of the MODELS on the EXCEL spreadsheet ( i.e, see OUR FIRST MODEL on pp. 14(CM) and 36- 39(HTMI) and OUR SECOND MODEL on pp. 15 (CM) and 39-41(HTMI ). You may select either model. Consider having each SUB team construct a separate model. Present your results in a graphical form comparable to Figures 3.4 or 3.5.(HTMI)

18. Assessment Expectations for Chapter 3 Questions That DO Need to be Completed to Meet Expectations for This Chapter (U:\MODELING\ASSESSMT \...\I_EXPECT.DOC, \EXPECT_3.DOC, and \CHKLST3.DOC) Specifically define and describe the terms ‘Algorithm’, ‘Control Heuristics in Problem Solving’, ‘Jumping in the Deep End’, and ‘Salami Tactics’, in terms of YOUR model for purging a gas storage tank. Finish reading the entire chapter and make a list of heuristics found in this chapter which you found useful, or believe may be useful in the future. The list should meet the relevant standards established for the answers to questions.

19. Assessment Expectations for Chapter 3 Submit answers to the questions below. The answers must meet the expectations established in the ‘Assessment Expectations’ document. –pp. 34HTMI, The representation in Figure 3.2H overestimates the amount of dye and provides an upper bound. Why? –pp. 35HTMI, What are the heuristics that might have been used (either consciously or subconsciously) to make the ‘cognitive leap’? –pp. 16-20CM, Summarize in a few sentences the discussion of ‘More and Less Useful Approaches’ to problem solving and modeling. –Note at the bottom of pp. 20CM, ‘These are questions about control and we learn control strategies by experience. We learn them faster if we criticize and analyze that experience, if we ask questions like those suggested by Schoenfeld. A good apprenticeship provides both the experience and the analysis. That is what we are trying to accomplish in this book. –Note at the bottom of pp. 21Y and the heuristic that CRITERIA are required to make DECISIONS ! Do you depend on your opinions, intuition, etc. to make important decisions? Can you make the transition to criteria based decisions?

20. slide 20 Process Check - Plus Delta u On a Post-it (WebNotes), write one thing in today’s class that helped you learn the material u On a Post-it (WebNotes), describe how we could improve your learning of this material u Post on wall as you leave