1. Common Core High School Mathematics: Transforming Instructional Practice for a New Era 4.1

2. Agenda Homework review and discussion The frog and the paddlewheel Reading MP3 and MP5 Break Modeling temperature Reading F-TF.1, 2, 5 Homework and closing remarks 4.2

3. 4.3 Homework Review and Discussion Activity 1: Table Discussion: Discuss your write up for the day 3 math task Rumors: Compare your strategies with others at your table. Reflect on how you might revise your own solution and/or presentation.

4. 4.4 The Frog and the Paddlewheel Draw a graph (envisioning 2 ways students might draw it), that shows the location of the frog from 0 minutes to 12 minutes. Assume the frog stays on the paddle wheel even when it gets carried under water. Activity 2: While swimming along, a frog reaches out and grabs onto the rim of a paddle wheel with radius 1 meter. The frog, clinging tightly to the wheel, is immediately lifted from the surface of the river. The wheel spins counterclockwise at a rate of one rotation every 6 minutes.

5. 4.5 The Frog and the Paddlewheel What is the height of the frog after 0 seconds? 30? 45? 60? 90? Discuss: what type of model (linear, exponential, trigonometric,...) would best fit this situation? Why? Construct a specific model of your suggested type that, in your opinion, best fits the data. How might you verify the accuracy of your model on a graphing calculator? Activity 2:

6. 4.6 The Frog and the Paddlewheel Work out as many additional times and corresponding heights as you can, up to a time of 12 minutes. Does your model still work over this longer period of time? Activity 2:

7. 4.7 Reading MP3 and MP5 Read the Standard for Mathematical Practice. MP3. Construct viable arguments and critique the reasoning of others. Turn and talk: how did you see this practice standard in the activity you have just completed? As a table group, chart student behaviors and corresponding teacher behaviors that are implied by this practice standard. Activity 3:

8. 4.8 Reading MP3 and MP5 Read the Standard for Mathematical Practice. MP5. Use appropriate tools strategically. As a table group, build a list of tools that you would consider as being relevant to this practice standard. Activity 3:

9. Break 4.9

10. 4.10 Modeling temperature Use the temperature data on the handout to construct a model which will give the average temperature in Milwaukee on any given day of the year. You should make a statplot of the data on a graphing calculator, and verify your model by graphing it on the same screen as your statplot. Activity 4:

11. 4.11 Modeling temperature How did you see MP3 and MP5 in this activity? MP3. Construct viable arguments and critique the reasoning of others. MP5. Use appropriate tools strategically. Activity 4:

12. 4.12 Modeling temperature Homework reading: How did you see the Modeling conceptual category in this activity? Activity 4:

13. 4.13 Reading F-TF.1, 2, 5 Read these content standards from the Functions conceptual category. Turn and Talk: How did you see these content standards in the activities you have completed today? Activity 5:

14. 4.14 Homework and Closing Remarks Activity 6: Homework (to be included in journal): Day 4 Math Task: Foxes and Rabbits (or alternate) Day 4 Class Reflection Reading California Draft Curriculum Framework Appendix: Mathematical Modeling (lines 1-60, pp.1-4)