| Short Description: |
A set of introductory self-paced lessons using the Motion Detector |
| Duration of Lesson: |
Multiple Class Periods |
| Grade Levels: |
Middle 6-8 |
| Subjects: |
Mathematics |
| Technologies used in Lesson: |
Computer, Probe |
|
Online Tutorial: |
|
Walk this Way
MathLab Lessons for Grades 7 and 8
Kara Louise Imm,
Greenwich Village Middle School
Goals for 7th grade Students:
N
To
learn how to use a motion detector to collect data
N
To
set up and take apart all parts of the lab without assistance from an adult
N
To
explore how various types of movements are represented on a position-time graph
and table
N
To
understand the effect of changing direction on the graph and table
N
To
understand the relationship between the steepness of a graph (slope) and the
relationship between the variables (position and time)
N
To
predict the shape of a graph with accuracy before a student walks in a
particular way towards or away from the motion detector
N
To
interpret the meaning of various types of lines on position-time graphs (horizontal,
vertical, very steep, less steep, etc.)
N
To
understand the effect of changing the scale along each axis
N
To
begin to explore velocity graphs and determine their relationship to
position-time graphs
N
To
articulate glessons learnedh verbally and in writing to an outside audience
Goals for 8th grade students (all of the above and):
N
To
represent linear relationships in a table, graph and equation
N
To
interpret the meaning of slope in a table, graph and equation
N
To
find and interpret a point of intersection of two lines (idea of a meeting
point)
N
To
find and interpret a Y-intercept of any line (idea of a ghead starth)
N
To
interpret the meaning of parallel lines (similar slope, different starting
point)
N
To
begin to explore the idea of exponential relationships as they appear on a
position-time graph
Related texts:
Connected
Math Projectfs Variables and Patterns (7th grade)
Connected
Math Projectfs Moving Straight Ahead (8th grade)
Materials:
N
8
motion detectors (7 for student groups and 1 for demo station)
N
8
Vernier computer interfaces
N
Logger
Pro software (to be installed on GVMS I book computers)
N
One
IBook with projector for demo station (GVMS has this)
N
Masking
tape
N
Pencils
N
Graph
paper
N
Meter
sticks
DEMONSTRATIONS
and CLASS MEETINGS
I imagine that I will begin both MathLabs
with a demonstration for all classes.
We will explore the actual pieces of technology and take some time as a
group to explore a few lines together.
Then I will divide students into groups of 4, assigning roles and
responsibilities to each member of the team. The groups can work at
their own pace. In fact I
will encourage them at first to explore the technology on their own before they
proceed to a series of situation and questions that I provide.
I will begin each session with a class
meeting in circle. The purpose of
these sessions will be to:
N
address observations, questions
and problems from students
N
allow students to share new
discoveries with each other
N
help struggling students to
make new discoveries
N
make connections between new
knowledge of student groups
N
create a ever-expanding base of
classroom knowledge (K-W-L chart)
SELF-PACED LESSSONS
Once students are comfortable
with the technology, I will ask them to explore a variety of situations. My 8th grade students have
some exposure to the motion detector, but I will ask them to start at lesson 1
as a review of last yearfs material.
The 7th grade students have never used the motion detector
(or for that matter, any technology) in a math classroom. Listed here are the types of activities
I will ask students to move through:
LINEAR GRAPHS (CHANGING SLOPES)
1A. Start
at the 1/2 meter mark and walk away from the motion detector in a slow and
steady way. Record the data with paper and pencil,
and store the data on LoggerPro.
1B. Select
a different walker and have them start at the ½ meter mark and walk away from
the motion detector in a faster and steady way. Record the data with paper and pencil,
and store the data on Logger Pro.
As a group
study the data, then answer the following questions and record your results in
the Word template provided:
Describe the
difference between a graph of a slow, steady speed and one with a faster, but
still steady speed. Predict what
would happen if the student walked away even slower or even faster than the two
students in this experiment. Defend
your prediction.
GRAPHS
with DIFFERENT DIRECTION
2A. Start
at the 1/2 meter mark and walk away from the motion detector at a medium
speed.
Record the data with paper and pencil, and store the data on LoggerPro.
2B. Start
at the 4 meter mark and walk towards from the motion detector at a
medium speed. Record the data with
paper and pencil, and store the data on LoggerPro.
As a group
study the data, and then answer the following questions and record your results
in the Word template provided:
Describe the difference
between a graph walking away from and towards the motion detector. Predict what would happen if a student
stood at the ½ meter mark and did not move at all. Predict what would happen if a student
stood at the 4-meter mark and did not move at all. Draw those predictions on the screen,
and then test both predictions.
LINEAR GRAPH (HORIZONTAL
SECTION and SAME SLOPE)
3A. Using
paper and pencil have each member of the group predict the graph for a person
who starts at the 1-meter mark, walks away from the motion detector slowly for
5 seconds, stops for 5 seconds, then continues walking away at the original
speed for another 5 seconds.
3B. Have
each member of the group show their graphs. Discuss as a team and convince each
other of the graph that makes the most sense. Draw that group prediction using
LoggerPro software.
3C. Choose
a student to walk the graph a few times and compare the predictions with the
actual data.
As a group study the data, and then answer the following questions
and record your results in the Word template provided:
Was your group prediction
the same as the actual data collected?
If not, what part of the graph did not match and why? Make a list of the specific pieces of
information you would need to make an accurate prediction of a personfs walk.
LINEAR GRAPHS (HORIZONTAL
SECTION and DIFFERENT SLOPES)
4A. Using
paper and pencil have each member predict the graph for a person who starts at
the 4-meter mark, walks towards the motion detector very slowly for 5 seconds,
stops for 5 seconds, then continues walking towards the motion detector at
twice the original speed for another 5 seconds.
4B. Have
each member of the group show their graphs. Discuss as a team and convince each
other of the graph that makes the most sense. Draw that group prediction using
LoggerPro software.
4C. Choose
a student to walk the graph a few times and compare the predictions with the
data.
As a group study the data, and then answer the following questions
and record your results in the Word template provided:
Was your group prediction
the same as the actual data collected?
If not, what part of the graph did not match and why? If you found this graph more difficult
to predict, describe what factors made it more difficult.
PREDICTING GRAPHS 1
5A. Open
the file called gPosition Match 1.h
Study the graph that appears and write down individually what you would
have to do to be able to reproduce the graph shown.
5B. Choose
one student to share how they will try to match the graph. Record their data and compare it to the
original. Store this data and label
with the studentfs name.
5C. Have
two other members of the group also try to replicate the graph. Save each studentfs graph on the screen
and label with their name.
As a group, write down how
you moved to create the three sections of the graph (the horizontal section,
the less steep section, and the more steep section)
PREDICTING GRAPHS 2 (PEAKS and VALLEYS)
6A. Open
the file called gPosition Match 2.h
Study the graph that appears and write down individually what you would
have to do to be able to reproduce the graph shown.
6B. Choose
one student to share how they will try to match the graph. Record their data and compare it to the
original. Store this data and label
with the studentfs name.
6C. Have
two other members of the group also try to replicate the graph. Save each studentfs graph on the screen
and label with their name.
As a group, write down how you moved to create the gpeaksh in the
graph. What does a peak tell you on a
position-time graph?
PREDICTING GRAPHS 3 (STUDENT-GENERATED)
7A. Have
one student in the group draw a possible graph using the prediction tool on
Logger Pro.
7B. Choose
one student to share how they will try to match the graph. Record their data and compare it to the
original. Store this data and label
with the studentfs name.
7C. Have
other members of the group try to replicate the graph, making note of new
strategies. Save each studentfs
graph on the screen and label with name.
Give each member of the group a chance to design a challenge
graph. Then discuss as a group, Which graphs were easy or difficult to
replicate and why? Did any student
design a graph with a vertical section?
IS this possible to walk?
Why or why not?
WHOLE-CLASS DISCUSSION and INFORMAL ASSESSMENT
8A. We
will take half of a class session (45 minutes) to discuss what we have learned
so far as a class. I will have
various graphs stored on LoggerPro to present to students on an IBook with
Projector. Together we will
interpret and test the possible motion that created them.
8B. We
will make a list of lessons learned to date and keep that poster in the
classroom for reference.
8C. I
will send students home with an at-home assessment to determine how deeply each
student understands the material. I
will make changes to the curriculum or groups accordingly.
FINDING RATES
9A. After
students have worked extensively with the motion detector in general, I was ask
them to create some sample graphs and determine their rate (if it is steady),
and average rate (if the speed varies).
9B. Determine
your rate, then calculate how far you could travel if you walked with the same
pace for 60 seconds, 5 minutes?
EXPLORING SPEED and VELOCITY 1
10A. By clicking on the Y-Axis variable,
change gpositionh to gvelocity.h
10B. Start at the 1/2 meter mark
and walk away from the motion detector in a slow and steady way. Record the data with paper and pencil,
and store the data on LoggerPro.
10C. Select a different walker and have
them start at the 1/2 meter mark and walk away from the motion detector in a faster
and steady way. Record the data
with paper and pencil, and store the data on Logger Pro.
As a group
study the data, then answer the following questions and record your results in
the Word template provided:
Describe the difference between a velocity graph of a slow, steady
speed and one with a faster, but still steady speed. Predict what would happen if the student
walked away even slower or even faster than the two students in this
experiment. Defend your prediction,
then test it.
EXPLORING SPEED and VELOCITY 2
11A. Start at the 1/2 meter mark and
walk towards the motion detector in a slow and steady way. Record the data with paper and pencil,
and store the data on LoggerPro.
11B. Select a different walker and
have them start at the 1/2 meter mark and walk towards the motion detector in a
faster and steady way.
Record the data with paper and pencil, and store the data on Logger Pro.
As a group
study the data, then answer the following questions and record your results in
the Word template provided:
Describe the difference
between a velocity graph walking towards and away from the motion
detector. Is it possible to have a
negative speed? Is it possible to
have negative velocity? What do
each of these ideas mean? Test a
few more graphs walking away from the motion detector at various speeds.
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