|
1
|
- Interactive Mathematics Program
- Shadows Unit
|
|
2
|
- Jamie Holnick
- Resides in Perkasie, PA
- First year math teacher
- Currently teaching Algebra II and Geometry at Pennridge High School
|
|
3
|
- Pennridge School District is approximately 30 miles north of
Philadelphia in Upper Bucks County.
- Our district covers approximately 95 square miles with a total
population of 45,000 people.
- There are seven elementary, two middle, and one high school with a total
enrollment of approximately 7,000 students.
|
|
4
|
|
|
5
|
|
|
6
|
|
|
7
|
- What formula can be used to express S as a function of the variables L,
D, and H? That is, how can you
get a formula for a function f so that S = f (L, D, H)?
|
|
8
|
- Your task is to collect data by focusing on one of three variables:
- The height of the light source (L)
- The distance from the object to the light source (D)
- The height of the object (H)
|
|
9
|
- Each group will need the following:
- An electric candle
- Meter stick
- Unifix cubes
- Books, folders, or textbooks
- Chart paper & markers
|
|
10
|
- Only change one variable and keep the other two variables constant
- Measure in millimeters
- Record all variable measurements including constants
- Record at least 10 trials
- Accuracy is very important
|
|
11
|
- Each group must turn in one report on their experiment.
- This should include:
- Purpose
- Materials used
- Procedure
- In/Out Table
- Diagram
- Constants
|
|
12
|
|
|
13
|
- Set room up ahead of time by having extension chords ready for each
groups use and designate areas for each group to work. Try to have stations around the
perimeter of the room.
- Organize groups by having students pick playing cards (put students in
groups of four).
- Have students read “Shadow Data Gathering” (IMP Year 1 – Shadows Unit)
aloud by calling on one student.
That student must read at least one sentence, then at the end of
any sentence they may call on another student in the room to continue
reading. A bonus point may be
awarded when a fellow student is called on and they do not know where
the group is in the passage. The
student called on that does not read will incur a point deduction.
|
|
14
|
- Review the slides included in our slide show with your students.
- We recommend using electric candles (see your nearest dollar store) with your shades closed and
lights off instead of using flashlights.
We found the electric candles cast an easier shadow to measure
and they are free standing so its easier to adjust the height of the
light source.
- Explain to students that they can stack textbooks and put the candle on
top to vary the height of the light source.
- Assign at least two groups to each variable. Post these on the board.
- Send students to their stations.
- The write-up has been put into lab form to help organize their findings.
- As students are working, go around to each group to remind them again of
ACCURACY and to keep the two variables constant while only changing the
variable they’re assigned.
- Assign Homework 4 – “An N by N Window”.
For lower functioning classes you might advise them to start with
a 1 by 1 window and work their way up to help find a formula.
|
|
15
|
|
|
16
|
- Discuss solutions to the homework with your group
- Have each group member model a different sized window using the
toothpicks
- Use your models to verify your In/Out tables are accurate
|
|
17
|
- Let’s take a look at a specific example of an N by N Window…
|
|
18
|
|
|
19
|
|
|
20
|
|
|
21
|
|
|
22
|
|
|
23
|
- Allow students to spend about five minutes sharing their homework
results in their groups. At this
time go around to assess if any students were able to find a
formula. There are three ways
that students may have solved this problem:
- Just by looking at the table.
- Analytically, by looking at the
wood pieces.
- By putting the data into a
graphing calculator and using the calculator to generate an equation.
- If any student found the formula analytically have them explain their
findings to the class first. We
recommend reinforcing the students work with the slide show. If the technology is not available, we
suggest that you have a 3 by 3 window prepared using overhead
transparencies.
|
|
24
|
|
|
25
|
|
|
26
|
- To Enter the Data into the Calculator
- Select Start
- Select #1 for Exit
- Enter the x data into list 1 (L1) and the y into list 2 (L2). You must hit enter after typing in
each number in order to get to the next line. If you make a mistake you can go back
to line using the arrow keys.
- To See the Graph with your Data Plotted…
- Select 2nd Stat Plot
- Select #1
- Move the Cursor to On
- Make sure that the first graph is highlighted under type in order to get
a scatter plot
- Hit Zoom and select #9 for Zoom Stat
- To Get a Regression Equation:
- Select Start
- Move the cursor over to Calc
- Select the appropriate regression (ie: linear, quadratic, exponential,
etc.) and hit enter.
- Hit 2nd List to get L1, L2 (for
example: QuadReg L1, L2)
|
|
27
|
|
|
28
|
- Each group will analyze the data to come up with the best equation that
fits.
- Begin at your groups’ station. As
a group, try to find an equation that best fits the data. Tape this
equation face down at the bottom of the chart paper. If your group decides that no
reasonable rule fits the data, then no card is needed.
- After five minutes, each group will travel together clockwise to the
next groups station. Continue until you’ve seen every groups’ work.
|
|
29
|
- Have students begin by discussing Homework 5 – More About Windows. Have the club group members from half
the groups put their homework up on the board. Have the remaining club group members
explain the work on the board for the class.
- Have students read Looking for Equations using popcorn reading format
(as used in Shadow Data Gathering).
- Have groups continue rotating clockwise upon your command after 5 minute
intervals until they return back to their starting points.
- Have each group turn the cards for their data over and discuss in their
groups which equations are valid or not.
Have the diamond cards share their groups discussion with the
class.
|
|
30
|
- After teaching the Shadows Unit, we felt that certain classroom
structures and visual enhancements would expand the learning process for
our students. We have
incorporated our evaluations in this project. This presentation has enabled us to
grow as educators. We are happy
to offer it to other educators as a tool that will be easy to use and
will be received well by their students.
|
Notes
