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					Day                  Student Skills                            Instructional Strategies                                                       Probing Questions                                                                                           Assessment Process
                                                                                                                                                                                                                 Student Product/Behavior                                            Feedback
      1.Identify real-world problem associated          Classroom discussion about real-world                 What is your experience with banking? (Do you have a bank account?)                        Students brainstorm the probing questions in      Based on student responses, teacher asks more questions about
      with standards-based concept(s)                                 problem:                                What do you look for in a bank?                                                            teams and share results with class                         banking and how it can affect each student.
                                                                                                              What types of savings accounts are offered?
                                                           What is my best banking option?                    What do you look for in a savings plan?                                                    Students answer the questions based on their
                                                                                                              How do people make money? vs. How do people lose money?                                    experiences with banking
                                                                                                              What has happened in the nation recently concerning wealthy people?

      2.Develop background skills and knowledge           a.    Students research interest for                  What are some different banks in Colorado?                                                    a.    Students complete worksheet on             a.    Oral feedback on bank presented and written feedback
          Perform background research                          savings accounts on various bank                What is interest?                                                                                   savings account research and                     on completed worksheet
          Develop content understanding of key                 websites                                        What does it mean for interest to compound?                                                         present one to the class
           variables                                      b.    Students investigate simple and                 Given a choice, would you take a salary of $1,000,000/year for 25 years or $1.00 the                                                           b.    Answer questions while completing worksheets and
          Conduct investigations (labs) to gather              compound interest through the                 first year, $2.00 the second year, $4.00 the third year, $8.00 the fourth year, and so on        b.    Students complete all worksheets                 activities in class. Also, provide written feedback on all
           data                                                 penny activity, worksheets, and               for the next 25 years? Why?                                                                            and activities relating to simple                completed assignments.
          Learn to use a modeling tool (e.g.,                  double your money activity                      What is the difference between simple and compound interest?                                        and compound interest
           STELLA)                                        c.    Students learn to use STELLA                    In your opinion, is simple or compound interest better? Why?                                                                                   c.    Answer questions during model tutorial and check to
                                                                through a sample population                     What do the different symbols in STELLA mean?                                                 c.   Completed population tutorial in                  make sure that the model works correctly for each
                                                                model tutorial                                  How do you build a model using STELLA?                                                             STELLA                                            student
      3.Simplify real-world problem                       a.    Discuss the ways that banks                     How do the banks that you researched compound interest? How often do they pay                 Discuss as a class the bank research             Oral feedback on opinions about banks and compound
                Determine applicable                           compound interest                             interest?                                                                                        and compound interest                            interest
                 principles/laws/procedures                                                                     How did you compound interest in the Double your money and investigating
                Explain assumptions                      b.    Discuss how to model simple and               compound interest activities?
                                                                compound interest so it matches                 How often should you compound interest in your models?
                                                                the activities                                  Why should we compound the interest annually?

      4. Identify variables and                           a.    Use cut outs of arrows, blocks,               Why would you use the block, circle, or arrow for that particular part of the model?          Groups make flowcharts of simple and          Oral feedback to particular groups while they are creating their
        interrelationships                                      and circles to identify the flow of           Why does that flowchart not make sense?                                                       compound interest using cut out tools         flowcharts
           Make a diagram or flowchart                         the simple and compound interest              Why does that flowchart make sense?
            connecting ideas from research                      models

                                                          b.    Work in groups to complete the
      5. Defend the identified relationships and                                                              Why does that flowchart make sense?                                                        Class discussion of the groups flowcharts and               Student response to teacher posed questions
      assumptions                                         a.    Groups present flowcharts to the              Why does that flowchart not make sense?                                                       the class decides which flowchart to use
          Present and defend in groups                         class on the overhead                         Which flowchart should we use? Why?
                                                                                                              What is the difference between the simple and compound interest flowchart?
                                                          b.    Discuss variations of the                     Why are the two flowcharts different?
                                                                flowcharts on the overhead to
                                                                decide which ones are correct

      6.    Represent relationships in terms of           a.    Teacher uses student work to pull             What math equation are we going to use in this flowchart?                                    Class participation in groups working with      Class comprehension check of both equations during explanation
            mathematical equations                              out math from students                        How would you represent the relationships in your own language?                              flowcharts while the teacher explains the
           Use diagrams and relationships to                   flowcharts                                    How can we represent the material using mathematics?                                                        mathematics                                   Yes/no approval of the equations used
            Derive mathematical equations                                                                     What relationships form between the shapes of the flowchart?
           Determine theoretical numbers in              b.    Teacher directs groups in writing                                                                                                            Write equation based on the flowcharts
            absence of real figures                             of mathematical equations

      7.Translate variables and relationships into   Simple Interest/Compound Interest                        What do your results look like? Were they what you expected? Why or why not?                 Changes made to model when necessary                       Yes/no approval of changes made to model
      computational model:                                a.    Students build simple interest and            Was your graph linear or exponential?
          Translate model into computational                   compound interest model using                 Was there a mistake in your model? How can you fix it?                                      Student responses to questions about their       Formative evaluation of model (does it work? do the results look
           process                                              the data from the investigation or            If you change a number, does it change your model? How?                                                      model                               like what was expected? what needs to be changed?)
          Review math equations                                activities and the mathematical               How can you make more money at a quicker rate? What would you want to change?                                                                          Yes/no approval of changes made to model
          Run the model                                        equations from 6                              What happens if you begin with a smaller amount in your bank? Bigger amount?                           Peer review of model
          Get results                                                                                                                                                                                                                                                     Monitor participation of peer review
          Explore range of validity                      b.    Students run model, review their                                                                                                             Compare results to investigations and
          Run check cases                                      mathematical relationships,                                                                                                                 activities and discuss changes that occur                 Student responses to teacher posed questions
                                                                explore results, and run check                                                                                                                      when numbers are changed

                                                          c.    Students switch computers and
                                                                compare results
      8. Interpret findings                              Students use models to explore what                  Is there a better way to explore this data?                                                    Responses to teacher-posed questions                       Informal evaluation of student responses
                Evaluate results                    happens when interest rates are changed and              What do the graphs mean?
                Draw conclusions                     to decide what is a reasonable interest rate            What happens to the graph when interest rates are changed?                                 Short written report on recommendations for         Read and respond to short written report. Provide comments
                Make recommendations                            for banks to charge                          Do your results match the data that you investigated previously? Why or why not?           banks and explanation of why students think            about why their recommendation is reasonable or not.
                                                                                                              What would be a reasonable interest rate for banks to charge?                               banks should offer a particular amount of
                                                                                                              How do you think banks decide on interest rates?                                                              interest

      9. Communicate findings                        Students research two different banks to find         Why did you choose that savings account?                                                          PowerPoint presentation that includes        Rubric scoring of presentation and answers to teacher and student-
          Presentation, letter, essay, etc.          information about savings accounts that are          How much do you have to have in the account to begin? How long will it take to make           information on the two banks, the particular                              posed questions.
                                                        offered. They will prepare a PowerPoint             money?                                                                                        savings account, why the savings account is
                                                     presentation on the savings account that they         How did you compare and contrast the banks?                                                     better than the others, graphs of how the
                                                                    would invest in.                       How did you use your STELLA models to decide which account to use?                            money grows, and a recommendation to the
                                                                                                           What else does the bank offer for customers?                                                  class about why their savings account is the
                                                                                                           Did you talk with anyone in the bank? What did they say about their business?                                      best.

                                                                                                                                                                                                             Teacher and student-posed questions.

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