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College of Natural, Mathematical and Health Sciences
MATH 104 Geometry and Measurement (3, 2)
Day/Time: MW 10:00 – 10:50 a.m. and TR 9:30 – 10:45 a.m.
Spring 2011
4 Credits
Location 119 CAS
Prerequisites: Mathematics ACT score > 23 or a grade of “C” or better in MATH 102.
Instructor(s):
Office Hours:
Monday
9:00 a.m.
Sherry Duesing
206C CAS
Tuesday
1:00 p.m.
635-2150 (work)
[email protected]
Wednesday
11:00 a.m.
Thursday
1:00 p.m.
Friday
10:00 a.m.
Required Texts: 1. Billstein, Libeskind and Lott. (2010). A Problem Solving Approach to
Mathematics For Elementary School Teachers. Tenth Edition. Pearson
Addison Wesley.
2. Dolan, Williamson and Muri. (2010). Mathematics Activities for
Elementary School Teachers: A Problem Solving Approach. Seventh
Edition. Pearson Addison Wesley.
Course Description: Basic notions of geometry for elementary teachers including constructions,
congruence and similarity, motion geometry, symmetry and tessellations. Concepts of
measurement, coordinate geometry, probability and data analysis.
Course Goals: This course is designed to prepare prospective elementary school teachers:
1. In the mathematics content they will be expected to be able to teach including
instructional issues, national and state standards, manipulatives, problem solving, and
hands-on learning.
2. To develop a deep understanding of the mathematics taught in elementary school, not just
getting the correct answer.
3. To develop and use a variety of problem-solving techniques.
4. To communicate mathematically, in both the oral and written form.
Course Objectives
Upon successful completion of this course, students should be able to:
1. Describe and represent mathematical relationships; use mathematical modeling to
solve real-world problems, and apply a variety of problem solving strategies to solve
problems in data analysis, measurement, and geometry.
2. Apply concepts and interpret probability in real-world situations, construct sample
spaces, model and compare experimental probabilities with mathematical
expectations, and use probability to make predictions.
3. Use counting methods including combinations and permutations to enumerate sets
and model problem situations.
4. Use descriptive statistics to analyze data, make predictions, and make decisions
(collect, organize, represent, analyze, and interpret data).
College of Natural, Mathematical and Health Sciences
MATH 104 Geometry and Measurement (3,2)
Spring 2011
4 Credits
5. Use terminology, concepts and relationships from Euclidean geometry to describe and
model mathematical ideas and real-world constructs and use these concepts for
solving problems.
6. Compare and contrast Euclidean, coordinate, and transformational geometry.
7. Apply the process of measurement to two- and three-dimensional objects using nonstandard, customary and metric units.
8. Use the properties of geometric shapes to make and verify conjectures such as
relationships between figures including congruency, similarity, symmetry, etc.
9. Use a variety of physical and visual materials for exploration and development of
mathematical concepts used in grades K-8, including geometric concepts and spatial
visualization; measurement concepts and procedures; logical conjectures and
conclusions using words such as all, some, and none; and concepts of probability and
elementary data analysis.
10. Develop mathematical relationships across disciplines and connections within
mathematics, describe these relationships, and use geometric concepts and
relationships to describe and model mathematical ideas and real-world constructs.
11. Communicate understanding of basic mathematical concepts used in grades K-8 by
means of written and oral discussions and explanations.
12. Use appropriate technology to support the learning of mathematics. This technology
includes, but is not limited to, computers and computer software, calculators,
interactive television, distance learning, electronic information resources, and a
variety of relevant multimedia.
13. Examine the historical development of mathematics that includes the contributions of
under-represented groups and diverse cultures.
Grading Scale and Policies:
Point Values:
6 (100 points each) exams . . . . . . . . . . . . . . . . . . . . . . . . . . 600 points
Final Examination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200 points
Chapter Assignments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 points
Problem Assignments. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 points
Project/Portfolio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 points
Communication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 points
Total . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1000 points
Grading Scale:
98-100
92-97
90-91
88-89
82-87
80-81
78-79
A+
A
AB+
B
BC+
72-77
70-71
68-69
62-67
60-61
0-59
C
CD+
D
DF
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College of Natural, Mathematical and Health Sciences
MATH 104 Geometry and Measurement (3,2)
Spring 2011
4 Credits
Evaluation
In addition to the usual class evaluation of tests and final examination, assessment of your
work will include the following: problem assignments, chapter assignments, resource
manual, and communication.
Exams: Six exams will be given throughout the semester and a cumulative final
examination will be given during final exam week (Thursday, April 28, 7:30 – 9:30 a.m.,
119 CAS).
Problem Assignments: A few “Ongoing Assessment”, “Now Try This” or other problems
will be assigned regularly which will be completed for the next class day. These will be
submitted for a grade and included in your resource manual. Plan to spend at least one
hour each day preparing these problems for the next class session. You are encouraged to
ask questions about the problems to facilitate your understanding of the concepts.
Chapter Assignments: Each week you will be participating in hands-on activities and
working on problems that relate to the topics and objectives for the week. Approximately
two reports will be completed for each chapter. Assignments will include the writing of
objectives, vocabulary definitions, problems from the text as well as response questions
from the text and the laboratory text. A grading rubric will be included with each report.
Resource Manual: Throughout the semester, you should collect interesting problems (not
worksheets) that could be used in your classroom in the future. (These problems could
be used to introduce a lesson, used for the entire lesson, used as an assessment, etc.)
Include problems from class, the lab manual, and other outside sources. These will make
a great resource for you later as you are preparing your lesson plans for your internship
and/or your teaching. To organize your collection use a 3-ring binder and create sections
labeled by content topic. Include problems relating to 1) probability, 2) data analysis, 3)
geometry, 4) constructions, 5) motion geometry, and 6) measurement. This resource
manual will be used and extended later for use in EDUC 420: Mathematics Methods for
Elementary Teachers.
Communication: This part of your grade will be based upon how you communicate
mathematically.
1. Participation in class (oral communication)
Presenting and explaining at least one problem in class.
2. Expressing your understanding of mathematical ideas in written form (written
communication)
Your written communication reflects the pride you have in your work. Even though this
is not an English grammar course, it is expected that you will write in a professional
fashion. Be proud of everything you produce. Your students will be watching you
someday and mimicking your written behavior.
Ground Rules:
Absences: You are expected to be an active participant in this class; thus, regular
attendance is expected. If you have more than two (2) unexcused absences during the
semester, you can expect your grade to be affected adversely. Unexcused absences during
an exam will result in a zero. Contact me prior to class regarding an absence that cannot
be avoided. Make-up of any exam will be at the discretion of the instructor.
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College of Natural, Mathematical and Health Sciences
MATH 104 Geometry and Measurement (3,2)
Spring 2011
4 Credits
Lab Sessions: Although you have registered for both a class and a lab, most sessions
will seem like labs. We will be solving problems, using manipulatives, and doing other
hands-on activities regularly (lab activities). Problem solving is described by the
National Council of Teachers of Mathematics (NCTM) as both a goal of learning
mathematics and a major means of doing so. Problem solving means engaging in a task
for which the solution is not known in advance. Therefore, you will be learning
mathematics using problems and hands-on activities. Since solving problems is a major
focus in this course, it is important that you develop your own answers to problems. Be
sure you can justify why you think your answer is correct rather than relying on the
book’s answer or the instructor’s answer.
Group Learning: Most class sessions will focus on group learning experiences. You
are responsible for your own learning as well as helping others in your group. To make
the most of group learning, you need to be sure you understand what the others in your
group are doing and your group’s solutions to the problems assigned to be discussed.
Some actions that will help you make the most of your experiences in your learning group
include: making eye contact, encouraging fellow group members, using quiet voices,
disagreeing without hostility, contributing your ideas, respectfully listening to others’
ideas, giving everyone a chance to speak, asking all teammates for help before asking the
teacher, using consensus to settle disputes, sharing personal understandings and resources
with other group members, and interactively designing and redesigning solutions through
honest debate, disagreement, discussion, research, and development.
If you do not understand, let the others in your group know. One advantage of learning
groups is that you may get your question answered before having to listen to the teacher
answer a lot of questions to which you know the answer. If you are still not sure when
class is over, be sure to see the instructor or meet with a tutor before the next class
session.
Communication: Because mathematics is, in part, a language, communication skills are
stressed in this course. As with any language, the more you use it, the more proficient
you become. Thus, you will be expected to take part in classroom discussions of the
course material and make verbal as well as written explanations of mathematical ideas.
You should be able to justify a mathematical procedure, rather than simply use it. This
aspect of the course will provide you an opportunity to practice skills you will need as a
teacher.
University/Departmental Class Policies: Please read the attached Class Policies
document regarding Mathematics Departmental policies.
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College of Natural, Mathematical and Health Sciences
MATH 104 Geometry and Measurement (3,2)
Tentative Course Outline
Spring 2011
4 Credits
Date
1/10
Monday
Introductions
Syllabus
Tuesday
9-1 How Probabilities Are
Determined
Read pages 515 - 533
Wednesday
9-1 How Probabilities Are
Determined
1/17
9-2 Multistage Experiments
with Tree Diagrams and
Geometric Probabilities
9-3 Using Simulations in
Probability
Read pages 555 - 564
1/24
9-5 Using Permutations and
Combinations in
Probability
Read paged 575 - 587
10-1 Displaying Data: Part I
Read pages 592 – 614
9-5 Using Permutations and
Combinations in
Probability
9-4 Odds, Conditional
Probability, and Expected
Value
Read pages 564 - 575
Review – Chapter 9
10-2 Displaying Data: Part II
Read pages 615 – 629
10-3 Measures of Central
Tendency and Variation
Read pages 630 – 657
10-3 Measures of Central
Tendency and Variation
2/7
10-4 Abuses of Statistics
Read pages 658 – 671
11-1 Basic Notions
Read pages 678 – 697
Review – Chapter 10
Test 2 – Chapter 10
2/14
11-1 Basic Notions
11-2 Polygons
Read pages 697 - 709
11-3 More About Angles
Read pages 710 – 726
11-3 More About Angles
2/21
11-4 Geometry in Three
Dimensions
Read pages 726 - 740
11-4 Geometry in Three
Dimensions
Review – Chapter 11
Test 3 – Chapter 11
1/31
Thursday
9-2 Multistage Experiments
with Tree Diagrams and
Geometric Probabilities
Read pages 534 - 555
9-4 Odds, Conditional
Probability, and Expected
Value
Test 1 – Chapter 9
2/28
S P R I N G
B R E A K
3/7
12-1 Congruence Through
Constructions
Read pages 747 - 768
12-1 Congruence Through
Constructions
12-2 Other Congruence
Properties
Read pages 768 – 779
12-3 Other Constructions
Read pages 780 - 792
3/14
12-3 Other Constructions
12-4 Similar Triangles and
Similar Figures
Read pages 793 - 809
12-5 Lines and Linear Equations
in a Cartesian Coordinate
System
3/21
Review – Chapter 12
Test 4 – Chapter 12
12-5 Lines and Linear
Equations in a Cartesian
Coordinate System
Read pages 810 - 831
13-1 Linear Measure
Read pages 837 – 854
3/28
13-2 Areas of Polygons and
Circles
13-4 Surface Areas
Read pages 894 – 906
13-5 Volume, Mass, and
Temperature
Read pages 906 - 928
4/4
13-5 Volume, Mass, and
Temperature
13-3 The Pythagorean Theorem,
Distance Formula, and
Equation of a Circle
Read pages 876 - 893
14-1 Translations and Rotations
Read pages 935 - 953
Review – Chapter 13
Test 5 – Chapter 13
4/11
14-2 Reflections and Glide
Reflections
Read pages 954 – 967
14-3 Size Transformations
Read pages 967 - 977
14-4 Symmetries
Read pages 978 - 990
14-5 Tessellations of the Plane
Read pages 990 – 1003
4/18
Review – Chapter 14
Test 6– Chapter 14
Review – Final Exam
Review Final Exam
13-2 Areas of Polygons and
Circles
Read pages 854 - 876
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College of Natural, Mathematical and Health Sciences
MATH 104 Geometry and Measurement (3,2)
(Topical Outline for Instructor Only)
Topical Outline for MATH 104
(4 credits)
Spring 2011
4 Credits
Percent of Time Spent

Probability and counting techniques
20

Graphical interpretations
15

Geometric terminology
15

Geometry constructions
20

Measurement in a variety of dimensions
15

Transformational geometry
15
Total
100%
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College of Natural, Mathematical and Health Sciences
MATH 104 Geometry and Measurement (3,2)
CHAPTER SECTONS
9-1
9-2
9-3
9-4
9-5
10-1
10-2
10-3
10-4
11-1
11-2
11-3
11-4
12-1
12-2
12-3
12-4
12-5
13-1
13-2
13-3
13-4
13-5
14-1
14-2
14-3
14-4
14-5
Spring 2011
4 Credits
HOMEWORK
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