4251

0011 0010 1010 1101 0001 0100 1011

Welcome to theSummer Institute Day 2

Thursday, August 7

•Please sit in lesson study teams•Today’s Agenda•Homework follow-up•Mathematical Modeling•Coach’s meeting•Functions

4251

0011 0010 1010 1101 0001 0100 1011

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?

4251

0011 0010 1010 1101 0001 0100 1011

Matching Graphs to Tables

• Consider the different tables given• Find the graph that best matches each

table• Explain

4251

0011 0010 1010 1101 0001 0100 1011

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

4251

0011 0010 1010 1101 0001 0100 1011

Observations?

• We have completed 3 activities: Plant Growth, Matching Graphs to Tables, and Matching Graphs to Verbal Descriptions

• Any ahas?

4251

0011 0010 1010 1101 0001 0100 1011

Filling a ContainerVideo

• http://www.faculty.umassd.edu/adam.hausknecht/temath/TEMATH2/Examples/VideoImageSequences/FillingVaseModel.html

• This afternoon you will investigatethe relationship between the height of the water in the container and the amount of water in the container

4251

0011 0010 1010 1101 0001 0100 1011

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?

4251

0011 0010 1010 1101 0001 0100 1011

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.

4251

0011 0010 1010 1101 0001 0100 1011

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.

4251

0011 0010 1010 1101 0001 0100 1011

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.

4251

0011 0010 1010 1101 0001 0100 1011

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

4251

0011 0010 1010 1101 0001 0100 1011

Filling a Container

Follow-Up Questions• Is the relationship linear? Why or why

not?• What is the domain and range of the

function?

4251

0011 0010 1010 1101 0001 0100 1011

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.

4251

0011 0010 1010 1101 0001 0100 1011

EVALUATIONSPlease 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.