MATH 136: Mathematics for Elementary Teachers, Course II
Summer, 2011
Instructor: Ke Wu Norman
Office: MATH 201
Email: ke.norman@mso.umt.edu
Class time/location: 1:30-3:30 P.M, MTWRF (May 23- June 24, 2011)
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Class location: LA 235; Lab location: LA 206
Prerequisites: Open to Elementary Education or (pre-ED) majors only. Math 135.
Text: A Problem Solving Approach to Mathematics for Elementary School Teachers (10th
Ed.), by Billstein, Libeskind, & Lott
Supplies: You need to have a ruler, protractor, and a good compass. A graphing calculator
is highly recommended
Course Agenda: Chapters 9 – 12
The following course schedule is subject to modifications:
Temporary Schedule (Refer to the updated schedule on Blackboard)
Monday
Tuesday
Wednesday
Thursday
Friday
Finish 11.4
Q/A for
Exam 1
Week 1, May 23-27
11.1/11.2
11.2/11.3
11.3/11.4
Field trips for
project 1
Lab 1
Exam 1
Project 1 due
Lab 2
Week 2, May 30-June 3
Holiday
12.1
12.2
12.3
Project 2 due
Lab 3
Exam 2
Week 3, June 6-June 10
12.4
12.5
13.1
13.2
Project 3 due
Lab 4
Exam 3
Week 4, June 13-June 17
13.3
13.4
13.5
14.5
Project 4 due
Week 5, June 20-June 24
14.1
14.2
14.3
14.4
Exam 4
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Course Goals: (1) To understand the concepts in geometry and to solve elementary
geometry problems. (2) To model the logic of arguments and to explore, conjecture, and
prove mathematical ideas and theorems.(3) To understand concepts of measurement such as
length, area, and volume. (4) To explore motion geometry including translation, rotation,
reflection, and size transformations.
Course Assignments (grading distribution):
(1) Homework/Participation (15%): Homework is given daily. Each class’s participation
counts as 2/5 of that day’s homework. Homework is collected on Fridays at the
beginning of the class.
(2) Projects (10%): There are four projects that you will either work with a group or on
your own.
(3) Four Exams (75%): Exam 1 (chapter 9); Exam 2 (chapter 10), and Exam 3 (chapter
11), and Exam 4 (chapter 12)
* Late homework will not be accepted. No makeup test/exam will be given without permission prior to
the schedule test/exam.
Grading scale:
Letter grades will correspond to the following percentages (+/- grades may be assigned
when deemed appropriate):
A: 94–100% A-: 90-93%
B+: 87-89%
B: 84-86%
B-: 80-83%
C+: 77-79% C: 74-76%
C-: 70-73%
D+: 67-69%
D: 64-66%
D-: 60-63%
CR:  60%
F: 0-59%
Students with Disabilities or special needs: Please feel free to discuss accommodations with me.
Academic Honesty: All students must practice academic honesty. Academic misconduct is
subject to an academic penalty by the course instructor and/or a disciplinary sanction by the
University.
Student Conduct Code: All students need to be familiar with the Student Conduct Code. You
can find it in the “A to Z Index” on the UM home page.
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[skip Project 1-3]
M 136, Summer 2011
Project 4
This Project has two components that your group (group of 3 or 4) will work
together.
Part I: Calculate the Velocity, Area, and Discharge of a Stream in Missoula or
Surrounding Area
Materials needed for each team
Meter stick or yardstick
20 ft tape measure
5-10 sticks of equal size
Stopwatch
String/yarn 50 ft
Each student will need:
Graph paper
Pencils
Colored pencils
Getting started
•
•
Use a map or your knowledge about Missoula and surrounding area to find a
stream that usually has flowing water, preferably with a few bridges on it to
take measurements from.
Bring all materials to fieldtrip site.
Taking measurements
1. Use the 20 ft tape measure to measure the wet perimeter edge of the
stream, from left to right, looking downstream. This can be done from a
bridge if the bridge is a level surface. If the bridge is not level have two
students pull the string tight over the stream and the rest of the team take
measurements.
2. Use the meter or yard stick to take depth measurements. Take 5-7
measurements (depending on stream width). Lower measuring stick to
water's edge 1 and 2, and 3-5 equally spaced locations between
measurements recorded left to right as one looks downstream. Record each
of these measurements.
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3. Use the 20 ft tape measure to measure a distance of 20-100 ft downstream.
Split team apart. At least two members stay at start point of distance, at least
one team member stands at end point of distance (20-100 ft). Team member
A drops a stick in an area of the stream with the maximum velocity and
minimum obstructions. Team member B starts the stopwatch exactly when
the stick hits the water. Team member C holds hand in the air until the stick
passes, then lowers hand. Team member B stops the stopwatch at that
moment. Record the time, do this procedure 3-5 times.
Analyze the data
• Using graph paper, graph the x-axis (the width of the stream) and the y
axis (measuring stick depths).
• After the distance points have all been plotted, divide points into
geometric shapes to find areas and add them together to get cross-section
total.
• Calculate the mean time for stream velocity.
• To find discharge, multiply the velocity and the cross-section area.
• Calculate discharge of the stream in one month assuming that the velocity
and cross-section area stay the same during the month.
Part II: Water Sustainability
•
•
•
•
•
As a group, pick one topic that relates to WATER (e.g. water pollution, water
conservation, water consumption, ice melting due to global warming, etc.).
Do a brief research on the topic (e.g. why the topic is important, what is the
current situation/concerns relates to this topic, what is the status of this
topic in the United States, and if you can find information, what is the status
on the state of Montana on this topic)
Research on “water footprint” (what is it (the definition)? How this concept
was developed? How to calculate it?)
Each member of the group calculate his or her water footprint and include
the calculation/results in your group report
Reflect on the impact of individual person on the WATER issue
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Timeline and Expectation of the Project
1. By Monday, June 13, your group needs to submit a Group Contract that every
group member agrees upon: What is the location of the stream that your group
is going to measure the velocity and discharge? What will you do if a member
misses a scheduled meeting, does not finish part of assigned work, etc.? What
are the times that you can meet together? All members must sign the contract.
2. The class time on Thursday, June 16, will be arranged for your group to have a
field trip to the stream and do the measurement. (We might be able to make
part of the class time on Wednesday, June 15, for your group work, and you are
welcome to plan your fieldtrip on Wednesday or any day before).
3. Group Report will be due on Friday, June 24. The report should be typed,
double-spaced, with 1-inch margins, and 12 point front. The report needs to be
pages. In your report, please include:
(1) Background about the stream that your group picked (where it is, any history
or background of this stream, etc.)
(2) Drawing of the cross section of the stream and the measure.
(3) Calculation of the velocity and discharge of water in one month
(4) Report on Part II
4. Individual reflection will be due on Friday, June 24. Reflection on group work:
How the each group member contributes to the project. Do you want the
grading of your group work be adjusted? Do you like the idea of working with
group on project(s) from a student perspective? Will you or how will you use
group work in your future teaching?
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