Download Informal Geometry Math 304 Summer 2011 Syllabus Web page: http

Informal Geometry
Math 304
Summer 2011 Syllabus
Meeting in MacLean 269
Section #000150
Instructor: Dr. Tim Harms
Office: MacLean 375H
Office Phone: 218-477-4016
Office hrs: 1:00-2:00 M – F along with additional hours available by appointment
e-mail: [email protected]
Web page: http://www.mnstate.edu/harms
Required Text & Supplement:
Text: Problem Solving Approach to Mathematics for Elementary School Teachers, A, 10/E
Rick Billstein, Shlomo Libeskind, Johnny W. Lott
Required Supplies: Activity Packet (Distributed on June 27th), three ring binder, colored
pencils, protractor, ruler with both cm and inches, compass, & scientific calculator
Prerequisites
Students enrolled in this course should have completed two years of high school algebra or its
equivalent and one year of high school geometry. Students must have successfully completed
Math 303 or its equivalent with a C - or better prior to taking this course.
Course Description:
This course will focus on a review of algebraic reasoning, statistics, probability, measurement,
and geometry. You should strive to find many ways of solving these problems. A good
solution is one that can be followed by others and deals with the problem in a clever or concise
way.
Learner Outcomes:
 Development of a multitude of problem solving skills and strategies.
 Increased understanding of algebraic reasoning, statistics, probability, geometry,
measurement and better ways to communicate that understanding.
 You will continually be asked to show how you went about solving the problems in this
class.
Course Outline:
Unit 1 – Probability & Statistics, Chapters 9-10, Test 1
Unit 2 – Geometry, Constructions, Congruence, & Similarity, Chapters 11-12, Test 2
Unit 3 – Measurement, Motion Geometry & Tessellations, Chapters 13-14, Comprehensive Final
Exam over Chapters 9-14
Class assignments with due dates are posted
and regularly updated on the Web page listed
above under the Math304 link.
Student Expectations:
 Regular and active classroom participation.
 Use appropriate tools (paper pencil, ruler, protractor, calculator, computer, other
manipulatives) when solving problems.
 Work cooperatively in small groups in the discussion of individual homework and the
completion of study guide activities.
 Solve problems in mathematics by formulating problems, use different strategies to
verify and interpret results, & communicate results.
 Please turn off your cell phone while in class.
 Students will act in an honest and trustworthy manner in class and on all assignments.
Attendance Policy:
 An absence will result in no credit for that day’s ticket in/out.
 Late work will lose 50% of its value for each weekday beyond its due date.
 No make-up on missed quizzes or tests if prior arrangements have not been made with
Dr. Harms.
Evaluation:
1. Daily ticket in/ticket out 3 pts each
2. Weekly quizzes worth 10-15 pts. each
3. Select problems from the activities, textbook, & handouts 5 -10 pts. each
4. Measurement project - 80 pts.
5. Two unit tests worth 100 pts each
6. Comprehensive Final July 29th - 200 pts.
Grading Scale:
-98 A+; 97-93 A; 92-90 A89-88 B+; 87-83 B; 82-80 B79-78 C+; 77-73 C; 72-70 C69-68 D+; 67-63 D; 62-60 D59%- F
Assistance Available:
If you are having trouble please see Dr. Harms during office hours or make an appointment. The
Math Department offers drop in tutoring M-F in MacLean 362A 383 M – F from 8:00 – 3:00.
Special Accommodations:
Students with disabilities who believe they may need an accommodation in this class are
encouraged to contact Greg Toutges, Coordinator of Disability Services at 477-5859 (Voice) or
1-800-627-3529 (MRS/TTY), CMU 114 as soon as possible to ensure that accommodations are
implemented in a timely fashion.
Math 304 – Informal Geometry
Problem Solving Approach to Mathematics for Elementary School Teachers, A, 10/E
Rick Billstein, Shlomo Libeskind, Johnny W. Lott
9. Probability
9-1 How Probabilities are Determined
9-2 Multistage Experiments with Tree Diagrams and Geometric Probabilities
9-3 Using Simulations in Probability
9-4 Odds
9-5 Using Permutations and Combinations in Probability
10. Data Analysis/Statistics: An Introduction
10-1 Displaying Data: Part I
10-2 Displaying Data: Part II
10-3 Measures of Central Tendency and Variation
10-4 Designing Experiments/Collecting Data
10-5 Abuses of Statistics
11. Introductory Geometry
11-1 Basic Notions
11-2 Polygons
11-3 More about Angles
11-4 Geometry in Three Dimensions
11-5 Networks
12. Constructions, Congruence, and Similarity
12-1 Congruence through Constructions
12-2 Other Congruence Properties
12-3 Other Constructions
12-4 Similar Triangles and Similar Figures
12-5 Lines and Linear Equations in a Cartesian Coordinate System
13. Concepts of Measurement - manipulatives include geoboard
13-1 Linear Measure
13-2 Areas of Polygons and Circles
13-3 The Pythagorean Theorem, Distance Formula, and Equation of a Circle
13-4 Surface Areas
13-5 Volume, Mass, and Temperature
14. Motion Geometry and Tessellations - manipulatives include Mirras & Pattern blocks
14-1 Translations and Rotations
14-2 Reflections and Glide Reflections
14-3 Size Transformations
14-4 Symmetries
Math 304- Key concepts:
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Probability using a Tree Diagram (Activity 9‐ 7) Designing and conducting a simulation (Activity 9‐8) How many arrangements (Activity 9‐10) Display and compare data using box‐and‐whisker plots (Activity 10‐5) Interior angle measurements of polygons (Activity 11‐5 pattern blocks) Use of proper notation to name lines, segments, rays, & angles (Chapter 11) Polygons through paper folding (Pentagon, Octagon, Decagon, Sliding Octagon) Van Hiele’s level of geometric development (Chapter 11) Hierarchy of polygons and solids (Chapter 11) Polyhedrons (Tetralope & Impact Cube) Nets (11‐8, & surface area applications) Spatial perception (Activity 11‐9 & additional handouts and online materials) Classifying polygons by their angles and sides (Chap 11) Identify patterns in polygons and polyhedral and generalize the relationship (Chap 11) Explain the relationship between angles formed by parallel lines and a transversal (Chap 11) Construct the following: congruent segments, congruent angles, parallel lines, perpendicular lines, bisecting a segment and bisecting an angle (Activity 12‐2) Slope of a line (Chapter 12, Activity 12‐8) Similarity to be addressed in more detail than congruence so that students can find missing lengths in “shadow problems” (Chap 12) Nonstandard units of measurement (Activity Chap 13.1 and 13.3) Use of dot paper and geoboards for area formulas of rectangles, parallelograms, rhombi, (Activities 13.7‐9) Dimensional analysis know the conversions from memory of the metric system from kilo to milli, inches to feet, feet to yards, feet to miles (Chap 13) Develop the Pythagorean Theorem and its converse (Activity 13‐11) Relationships between volume and capacity 1000 cm3 = 1 dm3 = 1 L (Chap 13 with Stations) Calculate the volume and surface area of a solid (Activity 13‐14) Carry out the following transformations: translations, rotations, reflection, glide reflections, & dilations (Activity 14‐1) Identify and complete in two‐dimensions line, rotation, and point symmetry (Chap 14) MN Board of Teaching Standards addressed:
Standard
C. demonstrate knowledge of fundamental
concepts of mathematics
(4) concepts of shape and space:
(a) shapes and the ways in which shape and space
can be derived and described in terms of
dimension, direction, orientation, perspective, and
relationships among these properties;
(b) spatial sense and the ways in which shapes can
be visualized, combined, subdivided, and changed
to illustrate concepts, properties, and relationships;
(c) spatial reasoning and the use of geometric
models to represent, visualize, and solve problems;
(d) motion and the ways in which rotation,
reflection, and translation of shapes can illustrate
concepts, properties, and relationships;
(e) formal and informal argument, including the
processes if making assumptions; formulating,
testing, and reformulating conjectures; justifying
arguments based on geometric figures; and
evaluating the arguments of others;
(f) plane, solid, and coordinate geometry systems,
including relations between coordinate and
synthetic geometry and generalizing geometric
principles from a two-dimensional system to a
three-dimensional system;
(g) attributes of shapes and objects that can be
measured, including length, area, volume,
capacity, size of angles, weight, and mass;
(h) the structure of systems of measurement,
including the development and use of
measurement systems and the relationships among
different systems; and
(i) measuring, estimating, and using
measurements to describe and compare geometric
phenomena;
(6) concepts of randomness and uncertainty:
(c) predicting outcomes based on exploration of
probability through data collection, experiments,
and simulations; and
(d) predicting outcomes based on theoretical
probabilities and comparing mathematical
expectations with experimental results.
Instruction & Assessment:
Section 11.1 – Basic Notations &Sec 11.4 - Geometry in Three
Dimensions
The building of shape and space derived through points, lines, planes
to create an axiomatic system. In the study of three-dimensional
figures students will draw perspectives under different orientations
Sec 11.1 #1 – 3,11,13 Sec 11.4 #1,5,8,9,15
Section 11.2 –Polygons
Students will create a hierarchy among quadrilaterals relationships
describing the properties that distinguish each polygon.
#1, 5, 6, 8, 9, 10
Section 11.4- Geometry in Three Dimensions
Students will use models to determine the
cross section created when polyhedrons are cut by a plane.
Mathematical Connections #1, 7, 9
Sections 14.1-Transformations and Rotations & Sec 14.2- Reflections
and Glide Reflections
Student will complete transformations describe the properties each
change posses.
p. 946 #1-3, 7, 12, p. 953 # 9, p. 962 #1, 4, 8 p. 966 # 4, 12
12.4- Similar Triangles and Similar Figures
Students will justify arguments based on geometric figures that
involve similar triangles. They will also make conjectures about scale
factors and test those conjectures
p. 802 #1, 6, 7
Section 12.5- Cartesian Coordinate System
Students will graph coordinates in two and
three dimensional systems. They will enlist axioms to prove lines are
parallel and perpendicular.
#2, 6, 9, 10
Section 13.2 -Areas of polygons and circles & Sec 13.5- Volume and
Mass
Students will measure and calculate the area of two dimensional
figures and given
solids calculate the volume and mass.
p. 868 #2, 4, 7, 8, 21 & p. 923 #3, 16, 24,25
Section 13.1- Linear Measurement
Students will convert lengths among different units and explain the
relationships between the units of measurement.
#1, 5, 7, 10, 11 & Measurement Labs
Section 13.3-The Pythagorean Thm, Distance Formula, and Equation
of a Circle
Student will find the length of a segment given its endpoints through
estimation, measurement, and calculation. They will compare the
Pythagorean Theorem to the Distance Formula as they look at ways
to help students understand the relationship of these.
#1, 3, 7, 9, 10, 19
Section 9.3 Using Simulations in Probability
Students will conduct experiments to estimate the population given
sample along with using simulations to predict the likelihood of a an
outcome #8, 9
Section 9-2 Multistage Experiments with Tree Diagrams and
Geometric Probabilities
Students will calculate the theoretical probabilities and conduct
experiments compare the outcomes.
#1, 8, 11, 16