Effective: Late Fall 8-Week, 2018/2019

## MATH 165: *Geometric Reasoning For Elementary And Middle School Teachers

### Course Description

This course introduces some basic concepts of geometric and measurement that underlie these concepts in elementary and middle grades, with a focus on collaborative learning and technology.

Prerequisite: MATH 102 and MATH 150 (or higher)

Proctored Exams: Midterm and Final

### Textbooks

#### Required

• (2001). Navigating through Geometry in Grades 3-5.Reston, VA: NCTM.
• [ISBN-978-0-87353-512-0]
• (2012). Developing Essential Understanding of Gemetry: Grades 6-8.Reston, VA: NCTM.
• [ISBN-978-0-87353-691-2]

#### Math Manipulatives Kit

ISBN: 978-0-618-19093-5

This kit will be used in MATH 155 and MATH 165.

#### MBS Information

Textbooks for the course may be ordered from MBS Direct. You can order

### Course Overview

Geometry is an area of mathematics that permits us to describe and analyze our physical world. You will explore the big ideas of geometry that are currently taught in elementary and middle schools in the United States. You will complete activities that build conceptual understanding between and among these big ideas. Topics covered include shapes, location, transformations, spatial visualization, decomposition and rearrangement, imagery, geometric tools, classification and definitions, ratio and proportional thinking for dilations, trigonometry and tessellations.

### Technology Requirements

Participation in this course will require the basic technology for all online classes at Columbia College:
• A computer with reliable Internet access
• A web browser
• Microsoft Office or another word processor such as Open Office

You can find more details about standard technical requirements for our courses on our site.

You can find more details about standard technical requirements for our courses on our site.

### Course Objectives

• To learn about the axiomatic nature of geometry.
• To read, write, and critique basic geometric proofs.
• To explore concepts of Euclidean geometry.
• To use technology as an integral part of the process of formulation, solution and communication of geometric ideas.

### Measurable Learning Outcomes

• Solve mathematical problems using geometric thinking.
• Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships.
• Specify locations and describe spatial relationships using coordinate geometry and other representational systems.
• Apply transformations and use symmetry to analyze mathematical situations.
• Use visualization, spatial reasoning, and geometric modeling to solve problems.
• Recognize two- and three-dimensional geometric shapes and describe their characteristics.
• Know simple geometrical concepts and facts and their applications: point, line, plane, parallel, perpendicular, sum of the angles of a triangle is 180 degrees, the Pythagorean Theorem.
• Perform elementary geometric constructions with ruler and compass, and with dynamic geometry software (GeoGebra).
• Compute perimeters, areas, and volumes of elementary geometric objects: rectangle, circle, triangle, cone, pyramid, cylinder, and sphere.
• Demonstrate understanding of the concept of measurement units in both the standard and metric systems, be able to convert measurements within systems (e.g. yards to inches) and from one system to another (e.g. miles to kilometers).
• Measure lengths, angles, area (including surface area), and volumes in standard and metric units.
• Understand congruence and similarity and apply them to solve problems.
• Apply transformations to geometric figures and determine if such transformations are isometries.

A 720-800 90-100%
B 640-719 80-89%
C 560-639 70-79%
D 480-559 60-69%
F 0-479 0-59%

Assignment Category Points Percent
Discussions 210 26%
Dropbox Assignments 200 25%
Quizzes 90 11%
Exams 300 38%
Total 800 100%

### Schedule of Due Dates

#### Week 1

Assignment Points Due
Discussions 1-3 45 Wednesday/Saturday
Dropbox 1 25 Friday
Quiz 1 15 Sunday

#### Week 2

Assignment Points Due
Discussions 4-5 30 Wednesday/Saturday
Dropbox 2 25 Friday
Quiz 2 15 Sunday
Proctor Information N/A

#### Week 3

Assignment Points Due
Discussions 6-7 30 Wednesday/Saturday
Dropbox 3 25 Friday
Quiz 3 15 Sunday

#### Week 4

Assignment Points Due
Discussion 8 15 Wednesday/Saturday
Dropbox 4 25 Friday
Midterm Exam 150 Sunday

#### Week 5

Assignment Points Due
Discussions 9-10 30 Wednesday/Saturday
Dropbox 5 25 Friday
Quiz 4 15 Sunday

#### Week 6

Assignment Points Due
Discussions 11-12 30 Wednesday/Saturday
Dropbox 6 25 Friday
Quiz 5 15 Sunday

#### Week 7

Assignment Points Due
Discussion 13 15 Wednesday/Saturday
Dropbox 7 25 Friday
Quiz 6 15 Sunday

#### Week 8

Assignment Points Due
Discussion 14 15 Wednesday/Saturday
Dropbox 8 25 Friday
Final Exam 150 Saturday
Total Points: 800

### Assignment Overview

You should complete all assigned weekly readings and activities prior to participating in discussions, submitting assignments, or taking quizzes so the concepts covered can inform your posts and work. Some activities are from the weekly readings and some are located in the Content area of the course.

#### Discussions

Weekly discussion posts are objective academic exercises. Discussion questions are structured around the readings and activities for each week, but you may be expected to incorporate information from secondary sources into your answers on occasion. Your postings should be original, relevant observations of the assigned topic(s). You are expected to read your classmates’ postings and respond to them. Simply rephrasing the textbook or another student’s post is not acceptable. All responses should be original and relevant to the assigned topic. While discussion postings are informal, they should be intelligible and effectively communicate your idea(s). Please pay attention to use of capitalization and avoid misspellings, incomplete sentences, and other violations of grammatical rules.

To receive full credit, you must post a minimum of three times throughout the week, and on at least two separate days. Once you have posted your initial response, read your classmates’ posts and respond to a minimum of two posts. Your responses to your classmates do not have to be as thorough as your initial posts, but they must be substantive, thought provoking, and contribute to the topic and conversation in a meaningful way. Your initial post must be submitted by 11:59 pm CT on Wednesday of each week. Responses are due 11:59 pm CT on Saturday of each week.

#### Dropbox Assignments

The dropbox activities are extensions of the weekly readings, activities and discussions. The dropbox assignments give you an opportunity to apply what we learn together as a class on an individual basis. You will complete these activities and scan (or take pictures of them) and put them in the dropbox for the week. For specifics on the dropbox assignments for each week please see the Content area of the course. Dropbox activities must be submitted by 11:59 pm CT on Friday of each week.

#### Quizzes

In Weeks 1-3 and 5-7, you will take a short quiz over the material covered in the weekly readings. Quizzes will consist of 5 questions. These questions will be a mixture of multiple choice and true/false and will be based on both the readings and the activities for the week. You will have five attempts, but quizzes will close on 11:59 pm CT on Sunday of each week.

#### Exams

Your midterm and final exams are computer-based, proctored tests found in the Quizzes area of the course. Both exams are closed book and are comprised of short answer, multiple choice and true/false. The Midterm will cover the topics covered in Weeks 1-4 and the Final will cover the topics covered in Weeks 5-8.  You will have 2 hours to complete each exam. Both exams, worth 150 points, will be available beginning Monday and you must take the exam before 11:59 pm CT on the day it is due. See the Content area of the course for more information on proctoring.

### Course Outline

Click on each week to view details about the activities scheduled for that week.

Navigating Through Geometry: Introduction and Chapter 1

Complete the following activities:

2. Build What I’ve Created
3. 2-D Shape Sort
3. Triangle Family Trees
4. 3-Dimensional Shape Sort

1. Searching for the Perfect Solids
Discussions 1-3

Discussion 1: Build What I’ve Created Reflection.  What did you learn from this activity? What was important? What words or phrases helped you re-create the design? What words or phrased confused you? Why? Can you think of better ways to explain the directions for making the design?

Note: This discussion requires that you must post your initial response before you will be able to see posts from other students.

Discussion 2: 2-D Shape Short Reflection. By doing this shape sort, what did you find to be the importance of mathematical terms, properties, and definitions? What did you learn?

Note: This discussion requires that you must post your initial response before you will be able to see posts from other students.

Discussion 3: 3-D Shape Hunt. Locate four different 3-D shapes in real-life. Fully describe your objects using accurate mathematical terminology based on your readings and activities. Make sure to include their mathematical names. Include a picture of each object.

Dropbox 1
1. Classify 2-D Shapes
3. Side Lengths of Triangle
4. Euler’s Formula
5. Create Triangles and Quads in GeoGebra
Quiz 1

A 5-question quiz will be given that is a mixture of multiple choice and true/false questions related to your readings and activities for the week. You have five attempts on the quiz.  The quiz closes at 11:59 pm CT on Sunday this week.

Navigating Through Geometry: Chapter 2

Complete the following activities:

1. Xs and Os
2. Connecting the Dots
3. Introduction to Turtle Math (MS Logo)
Discussions 4-5

Discussion 4: Xs and Os Reflection. What are some strategies that will help you win this game? Is there a pattern? If there is, explain this pattern. Is it better to try to get your marks in a row or to try to block the other team? How will you play the game differently next time?

Discussion 5: Connecting the Dots Reflection. Discuss your design process for connecting the dots. What difficulties did you have if any?  What did you find enjoyable about the assignment, if anything?  What do you think your future students might think of an activity like this?

Q and A Discussion: Turtle Math (MS Logo). As you work with MS Logo please post any questions you have to this discussion.

Dropbox 2
1. Create your own connect the dots instructions and solution
Quiz 2

A 5-question quiz will be given that is a mixture of multiple choice and true/false questions related to your readings and activities for the week. You have five attempts on the quiz.  The quiz closes at 11:59 pm CT on Sunday this week.

Proctor Information
Submit your proctor form to the appropriate Dropbox folder by the end of the week. Remember to “Save” the form before placing it in Dropbox. See the Content area for more information.

Navigating Through Geometry: Chapter 3

Complete the following activities:

1. Patchwork Symmetry
2. Translation (Slide/Glide), Reflection (Flip), Rotation (Turn), Dilation (stretch or shrink) with pattern blocks
3. Translation (Slide/Glide), Reflection (Flip), Rotation (Turn), Dilation on Cartesian plane
Discussions 6-7

Discussion 6: Symmetrical Reflection. In the activities for this week you created and looked for symmetrical designs, was it harder to create or find symmetry? Why do you think this was the case? Which types of symmetry were harder for you to find or create?

Discussion 7: Pattern Reflection. Were the pattern block manipulatives helpful to you? Why or why not? Do you think manipulatives would be a benefit to your future students?

Q and A Discussion: Translation on Cartesian plane. Please use this discussion for any questions you may have on translations on the Cartesian plane.

Dropbox 3
1. Making an album of symmetry search (pattern blocks self-created designs, quilt blocks, tiles, logos) (shared album possibilities – Google photo, other options)
2. Questions over Transformations and Dilations
Quiz 3

A 5-question quiz will be given that is a mixture of multiple choice and true/false questions related to your readings and activities for the week. You have five attempts on the quiz.  The quiz closes at 11:59 pm CT on Sunday this week.

• Navigating Through Geometry: Chapter 4
• Article: Spatial Visualization [Located in the Content area of the course]

Complete the following activities

1. It’s All in the Packaging
1. Hexominoes and those that make boxes
2. It’s the View that Counts
1. Base Drawings
2. Right, left, front and back views
3. Isometric Drawings
4. Optional: Isometric Applet
Discussion 8

Discussion 8: Spatial Visualization Reflection. Describe your own experiences with spatial visualization. How have past experiences helped or hindered? How many of the hexominoes did you need to cut out to determine if they made boxes? Be honest. Describe your experience and strategy for converting 3-D items into 2-D drawings.

Dropbox 4
1. Draw all pentominoes and determine which ones make open boxes (i.e. no tops) (see instructions for activity 1)
2. Questions over base, view, and isometric drawings
Midterm Exam

Your midterm is computer-based, proctored exam located in the Quizzes area of the course. The exam is closed book and are comprised of short answer, multiple choice and true/false and cover the material from weeks 1-4. You will have 2 hours to complete each exam. When you are ready to take the midterm, your proctor will have the password to access the exam. The midterm, worth 150 points, will be available Monday morning and you must submit the exam before 11:59 pm CT on Sunday.

• Essential Understanding: Pages 1-24
• Grandfather Tang [Located in the Content area of the course]

Complete the following activities

1. Tangrams and Tangram Puzzles
1. Construct and design with tangrams pieces
2. Design with web or phone based Tangram app.
2. GeoGebra Shearing Activity for Area of a Triangle
3. Discovering Area Formulas on the Geoboards
4. Decomposing Shapes to Determine Areas
Discussions 9-10

Discussion 9: Tangram Refection. What might be the benefit of creating your own tangram pieces or using ready-made tangrams? What are the purposes or benefits of completing puzzles manually or online? Each have merit.  Why would you use one over the other?

Discussion 10: Surface-area Scavenger Hunt.  Find 2 different objects and take a photo of each. Calculate the surface area of the objects. Include your method of measurement in the image. Include the picture of each object.

Dropbox 5
1. What fraction of the whole area does each piece of a tangram set represent?
2. GeoGebra Shearing Activity for Area of a Parallelogram
Quiz 4

A 5-question quiz will be given that is a mixture of multiple choice and true/false questions related to your readings and activities for the week. You have five attempts on the quiz.  The quiz closes at 11:59 pm CT on Sunday this week.

Essential Understanding: Pages 25-38

Complete the following activities

1. Polygon Angle Measures
2. Properties of Diagonals of Special Quadrilaterals
3. Centers of Triangles
Discussions 11-12

Discussion 11: Formulas and Principles Reflection. Why do we use discovery or memorization of mathematical formulas and principles? Are there short-term and long-term benefits to either approach? What works best for you as a teacher or as a student?

Discussion 12: Mathematics Reflection. Some would say there is beauty of mathematics. What are some of the interesting/cool things you’ve discovered about triangles and quadrilaterals? Please explain. What other shapes, properties, etc. have you found appealing? Provide examples and explain.

Dropbox 6
1. Create Triangle Centers in GeoGebra and Corresponding Circles, where applicable.
2. Worksheet on angle measure and sum and properties of diagonals
Quiz 5

A 5-question quiz will be given that is a mixture of multiple choice and true/false questions related to your readings and activities for the week. You have five attempts on the quiz.  The quiz closes at 11:59 pm CT on Sunday this week.

Course Evaluation
Please evaluate the course. You will have an opportunity to evaluate the course near the end of the session. A link sent to your CougarMail will allow you to access the evaluation. Please note that these evaluations are provided so that I can improve the course, find out what students perceive to be its strengths and weaknesses, and in general assess the success of the course. Please do take the time to fill this out.

Essential Understanding: Pages 39-54

Complete the following activities

1. Basic Constructions with Paper
2. Basic Constructions with Compass and Straightedge
Discussion 13

Discussion 13: Basic Constructions Reflection. Compare and contrast the basic construction methods. What are benefits of these methods to yourself and your future students?

Dropbox 7

Construct several items using a combination of the basic constructions

Quiz 6

A 5-question quiz will be given that is a mixture of multiple choice and true/false questions related to your readings and activities for the week. You have five attempts on the quiz.  The quiz closes at 11:59 pm CT on Sunday this week.

Essential Understanding: Pages 55-67, 82-94

Complete the following activities

1. Polygon Tessellations
1. Polygons that Tessellate by themselves
2. Polygons that Tessellate in combination with other polygons
2. Escher-like Tessellations
1. Manual Heesch Types
2. Online Heesch Types
Discussion 14

Discussion 14: Basic Constructions Reflection. What are the benefits and purpose of doing tessellations manually vs with an application? Each have merit. Why would you use one over the other for learning or for teaching?

Dropbox 8
1. Self-created tessellation
2. Tessellation created with program.
Final Exam

Your final is computer-based, proctored exam located in the Quizzes area of the course. The exam is closed book and comprised of short answer, multiple choice and true/false questions and will be similar to those on quizzes 4-6 and cover the material from Weeks 5-8. You will have 2 hours to complete the exam. When you are ready to take the final, your proctor will have the password to access the exam. The final, worth 150 points, will be available Monday morning and you must submit the exam before 11:59 pm CT on Saturday.

### Course Policies

#### Student Conduct

All Columbia College students, whether enrolled in a land-based or online course, are responsible for behaving in a manner consistent with Columbia College's Student Conduct Code and Acceptable Use Policy. Students violating these policies will be referred to the office of Student Affairs and/or the office of Academic Affairs for possible disciplinary action. The Student Code of Conduct and the Computer Use Policy for students can be found in the Columbia College Student Handbook. The Handbook is available online; you can also obtain a copy by calling the Student Affairs office (Campus Life) at 573-875-7400. The teacher maintains the right to manage a positive learning environment, and all students must adhere to the conventions of online etiquette.

#### Plagiarism

Your grade will be based in large part on the originality of your ideas and your written presentation of these ideas. Presenting the words, ideas, or expression of another in any form as your own is plagiarism. Students who fail to properly give credit for information contained in their written work (papers, journals, exams, etc.) are violating the intellectual property rights of the original author. For proper citation of the original authors, you should reference the appropriate publication manual for your degree program or course (APA, MLA, etc.). Violations are taken seriously in higher education and may result in a failing grade on the assignment, a grade of "F" for the course, or dismissal from the College.

Collaboration conducted between students without prior permission from the instructor is considered plagiarism and will be treated as such. Spouses and roommates taking the same course should be particularly careful.

All required papers may be submitted for textual similarity review to Turnitin.com for the detection of plagiarism. All submitted papers may be included in the Turnitin.com reference database for the purpose of detecting plagiarism. This service is subject to the Terms and Conditions of Use posted on the Turnitin.com site.

#### Non-Discrimination

There will be no discrimination on the basis of sex, race, color, national origin, sexual orientation, religion, ideology, political affiliation, veteran status, age, physical handicap, or marital status.

#### Student Accessibility Resources

Students with documented disabilities who may need academic services for this course are required to register with the office of Student Accessibility Resources. Until the student has been cleared through this office, accommodations do not have to be granted. If you are a student who has a documented disability, it is important for you to read the entire syllabus as soon as possible. The structure or the content of the course may make an accommodation not feasible. Student Accessibility Resources is located in Student Affairs in AHSC 215 and can be reached by phone at (573) 875-7626 or email at sar@ccis.edu.

#### Online Participation

You are expected to read the assigned texts and participate in the discussions and other course activities each week. Assignments should be posted by the due dates stated on the grading schedule in your syllabus. If an emergency arises that prevents you from participating in class, please let your instructor know as soon as possible.

#### Attendance Policy

Attendance for a week will be counted as having submitted any assigned activity for which points are earned. Attendance for the week is based upon the date work is submitted. A class week is defined as the period of time between Monday and Sunday (except for week 8, when the work and the course will end on Saturday at midnight.) The course and system deadlines are based on the Central Time Zone.

#### Cougar Email

All students are provided a CougarMail account when they enroll in classes at Columbia College. You are responsible for monitoring email from that account for important messages from the College and from your instructor. You may forward your Cougar email account to another account; however, the College cannot be held responsible for breaches in security or service interruptions with other email providers.

Students should use email for private messages to the instructor and other students. The class discussions are for public messages so the class members can each see what others have to say about any given topic and respond.

#### Late Assignment Policy

An online class requires regular participation and a commitment to your instructor and your classmates to regularly engage in the reading, discussion and writing assignments. Although most of the online communication for this course is asynchronous, you must be able to commit to the schedule of work for the class for the next eight weeks. You must keep up with the schedule of reading and writing to successfully complete the class.

No late discussion posts will be accepted.

Late exams are not accepted without prior approval. Approval is only given under significant extenuating circumstances and must be requested before the due date.

No late weekly quizzes will be accepted.

Late dropbox assignments are accepted, but with a deduction of 5% for each day they are late.

#### Course Evaluation

You will have an opportunity to evaluate the course near the end of the session. A link will be sent to your CougarMail that will allow you to access the evaluation. Be assured that the evaluations are anonymous and that your instructor will not be able to see them until after final grades are submitted.

#### Proctor Policy

Students taking courses that require proctored exams must submit their completed proctor request forms to their instructors by the end of the second week of the session. Proctors located at Columbia College campuses are automatically approved. The use of ProctorU services is also automatically approved. The instructor of each course will consider any other choice of proctor for approval or denial. Additional proctor choices the instructor will consider include: public librarians, high school or college instructors, high school or college counseling services, commanding officers, education service officers, and other proctoring services. Personal friends, family members, athletic coaches and direct supervisors are not acceptable.

#### Orientation for New Students

This course is offered online, using course management software provided by Desire2Learn and Columbia College. The course user guide provides details about taking an online course at Columbia College. You may also want to visit the course demonstration to view a sample course before this one opens.

#### Technical Support

If you have problems accessing the course or posting your assignments, contact your instructor, the Columbia College Helpdesk, or the D2L Helpdesk for assistance. Contact information is also available within the online course environment.

#### Online Tutoring

Smarthinking is a free online tutoring service available to all Columbia College students. Smarthinking provides real-time online tutoring and homework help for Math, English, and Writing. Smarthinking also provides access to live tutorials in writing and math, as well as a full range of study resources, including writing manuals, sample problems, and study skills manuals. You can access the service from wherever you have a connection to the Internet. I encourage you to take advantage of this free service provided by the college.