Welcome to the

1

• Welcome to the
• Summer Institute Day 2
• Thursday, August 7

• Please sit in lesson study teams
• Todays Agenda
• Homework follow-up
• Mathematical Modeling
• Coachs 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 growingso 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 ContainerVideo

• http//www.faculty.umassd.edu/adam.hausknecht/tema
  th/TEMATH2/Examples/VideoImageSequences/FillingVas
  eModel.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.

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