Name: ____________________________ Hour: _____________
Fill It Up – Part I
Student Project Instructions
Objectives: Students will explore and discuss the key
features of a linear function including the y-intercept
and the rate of change and how they relate to the
function rule in slope-intercept form. Students will also
analyze the steepness of each graph and discuss the
meaning of “steep” vs. “flat” in terms of the context and
appropriate units.
Materials:
Ruler
Various sizes of cylindrical vases (must create a linear
pattern)
Sand (or beads, or water if you are brave!)
Scoop
Funnel (You can have students make funnels out of
paper)
Student hand out
Introduction
As a container fills with a substance of some sort,
an observer can watch as the height of the
substance visibly moves up the sides of the
container. Certainly, the rate at which the height of
the material changes is related to how fast the
volume is changing or to how fast the substance is
poured into the container. Are there factors that
will also affect the rate of change of the height? In
the following experiment, you and your classmates
will investigate what happens to the height of the
substance when the containers of various sizes are
filled at the same rate.
Process
1. Within your group, assign the following
roles:
a. The pourer: scoops and pours the sand
into the vase
b. The measurer: measures the height of
the sand after each scoop
c. The recorder: records the height for
each number of scoops
d. (if needed) The project manager: makes
sure the scoops are level and consistent
and double checks the measurements.
2. Using a piece of scratch paper and a piece
of tape, make a funnel.
3. Make sure you have all materials.
4. Place your vase in the center of your table
(or on the floor if you do not have a flat
table).
5. Record your first measurement on the table
below. At zero scoops of sand, the height of
the sand in the vase is __________ units.
6. The pourer scoops one level scoop of sand
(be sure the sand goes all the way to the
rim of the scooper. Use a ruler to level it if
needed.) Question: Why do you think
consistency is important when scooping
the sand?
____________________________________
____________________________________
___.
7. The pourer will pour the scoop of sand into
the vase. The measurer and the project
manager need to make sure the sand is
level in the vase before measuring.
8. The measurer will now measure the height
of the sand in centimeters and the project
manager will confirm the measurement.
9. The recorder will then record the
measurement on the table below.
10. Repeat steps 6-9 until either your vase is
full or until you run out of sand.
Name: ____________________________ Hour: _____________
Representing Data Using a Table:
Number of
Scoops of Sand
Height of Sand
in Vase (in cm)
Representing Data Using a Graph:
Graph the results you recorded in your table. Be
sure to label your independent and dependent
variables and create an appropriate scale for both.
Discuss these things with your group before
starting.
Discussion Topics:
Before we begin our class discussion, talk with your group about the following items, fill in the blanks and be
prepared to offer your answers to the class discussion. Remember, your vase is a little different from the
others, so your group’s input is very important. Please be prepared to discuss the following:
1. Is the data discrete or continuous? ______________________ Explain your choice? ____________________
__________________________________________________________________________________________
2. What is the y-intercept of your graph as an ordered pair? _________ What does this ordered pair mean in
when you are discussing your variables? _______________________________________________________.
Will each group’s y-intercept be the same for this activity? _________
3. What is the relationship between the number of scoops and the height of the sand? _________________
Explain. _________________________________________________________________________________.
Name: ____________________________ Hour: _____________
4. Is your data linear? ______________ If you answered yes, explain how you know. If you answered no, do
you think it is intended to be for this activity? Why or why not?
_________________________________________________________________________________________
_________________________________________________________________________________________
5. How can you determine the rate at which the vase is filling with sand? Use the space below to show the rate
of change using which ever method your group determines to be effective.
* Use this space to add any additional information from the class discussion that is relevant to question #5.
6. Can you write an equation to express the height of the sand as a function of the number of scoops of sand?
Use the space below to show your group’s equation and explanation of how you came to your answer.
* Use this space to add any additional information from the class discussion that is relevant to question #6.
Name: ____________________________ Hour: _____________
Fill It Up Part 1 – Closing Assignment
1. As we wrap up this part of the activity, please list two things that you are going to remember about
what we learned and discussed today. Please be specific and as detailed as you can be.
1.
2.
2. Finally, list one thing that we discussed today that you may still have some questions about. Again,
please be as detailed and specific as you can be.