1. Welcome to the Summer Institute Day 2 Thursday, August 7 Please sit in lesson study teams Today’s Agenda Homework follow-up Mathematical Modeling Coach’s meeting Functions

2. Plant Growth Examine cards that were given to your group. Discuss any similarities and differences See if you can make any connections All plants are growing…so what is different about them?

3. Matching Graphs to Tables Consider the different tables given Find the graph that best matches each table Explain

4. Homework Follow-Up Take out the article, Functions and the Volume of Vases and turn to Figure 1 In your table group, discuss verbal descriptions for each of the graphs Compare answers with another table group

5. Observations? We have completed 3 activities: Plant Growth, Matching Graphs to Tables, and Matching Graphs to Verbal Descriptions Any ahas?

6. Filling a Container Video http://www.faculty.umassd.edu/adam.h ausknecht/temath/TEMATH2/Examples /VideoImageSequences/FillingVaseMode l.htmlhttp://www.faculty.umassd.edu/adam.h ausknecht/temath/TEMATH2/Examples /VideoImageSequences/FillingVaseMode l.html This afternoon you will investigatethe relationship between the height of the water in the container and the amount of water in the container

7. Filling a Container Examine the container that has been given to your group. Do you expect the relationship between the height of the water in the container and the amount of water in the container to be linear or non-linear?

8. Filling a Container On your handout… Sketch a picture of your container. Sketch a graph that represents how you think the height of the water will change with each cup poured in.

9. Filling a Container Now for the experiment… Add a fixed amount of water to the container. Measure the height of the water and record the data in the table given. Repeat this process until the container is full.

10. Filling a Container Accurately graph the data collected on grid paper. Compare the sketch of your predicted graph with the actual graph that you obtained from your data.

11. Filling a Container Work with your group to draw your graph on poster paper. Draw a cross section of the container next to the graph. Prepare to share your graph with the whole group

12. Filling a Container Follow-Up Questions Is the relationship linear? Why or why not? What is the domain and range of the function?

13. Filling a Container Follow-Up Questions Suppose the bulges of your container were replaced by narrow parts, and the narrow parts were replaced by bulges. Draw the new container and a graph that would represent the height of the water as a function of the number of times the water was added.

14. EVALUATIONS Please complete the evaluation form. Let us know … what you learned. what you valued. what you would like more information about. and any other comments that can help us improve our professional development days.