LetGoOfMyLogo.pdf

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UVA-SCPS Office of Mathematics Outreach with support from VADOE Mathematics and Science Partnership Grant Program NCLB Title II Part B 21st Century Teaching and Learning: Project-based Unit

Snapshot of Unit Content and Student Expectations

Title of Unit: Let Go of My Logo! Unit Designers:

Meredith Zirkle, Frederick County Public Schools

Deanna Compton, Frederick County Public Schools Context of the Project: Organizations are always updating their logos. Some go from elaborate to

simple while others go from basic to three-dimensional. In this project, students research various logos from past and present. Using this information, the students creatively design a new logo.

Number of Class Hours:

15-18 hours Unit

Design: Project-based Unit Other Subject

Areas/Disciplines Addressed in the Unit:

Career and Technical Education (CTE) (i.e. Basic Technical Drawing; Design, Multimedia and Web Technology; Graphic Communications; Business; Carpentry; Sports; Entertainment; Introduction to Engineering; and Marketing, Architectural Design and CADD) Art Foundations; Leadership Development; English/Composition; World History; Economics

Driving Question: Why do you need to fix something if it is working? Do you need to keep up with the times? Or, is it important to make a change every once in a while?

Mathematics Content Addressed:

Transformations; Scale Drawings; Symmetry; Polygon Characteristics; Circle Attributes; Linear Equations; Proportions; Tessellations; Constructions

Mathematical Process Goals Addressed

_x_Problem Solving _x_Communication _x_Reasoning _x_Connections _x_Representations

Assumption of Prior Knowledge:

How to Solve Proportions Basic Geometry Vocabulary Angle Relationships

How to Use Construction Tools Graphing Linear Equations Courses for Which the

Unit is Appropriate

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UVA-SCPS Office of Mathematics Outreach with support from VADOE Mathematics and Science Partnership Grant Program NCLB Title II Part B College and Career

Readiness/21st Century Skills

BIE Page 35-37

T for skills to be taught and expected to use during the unit,

E for skills student are expected to know and be able to use during this unit A for skills that will be assessed during this unit

_E_Collaboration _A_Research _A_Communication (Oral and/or Written) _T,E,A_Technology _E,A_Critical Thinking/Decision Making

__Other: (Describe)

Major Student Products and/or Performances:

Group: Logo design Logo Development Letter to Company

Presentation Audience:

x Class

x School (teachers within other classes) Individual:

Individual roles and remediation activities Mathematicians Journals

Expert

x Community

x Other: Organization to which letters are written

Engage the students interest and inquiry:

Students review the following websites:

http://www.1stwebdesigner.com/inspiration/successful-failed-logo-transformation/

This website features different logos that were considered for design and may have or may not have been successful. http://curiousphotos.blogspot.com/2009/01/transformation-of-corporate-logos.html

This website features different logos that were changed over the years. http://www.sportslogos.net/teams/list_by_league/7

This website features NFL logo.

Evaluation: Formative Assessments (During the Unit)

Interview Practice Presentations

Mathematicians Journal x Notes

Preliminary

Plans/Outlines/Prototypes

x Checklists

Rough Drafts x Concept maps

Field Tests Other:

Summative Assessment (End of Project)

Written Products, with a rubric x Peer Evaluation, with a rubric

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UVA-SCPS Office of Mathematics Outreach with support from VADOE Mathematics and Science Partnership Grant Program NCLB Title II Part B rubric

Other Product(s) or

Performance(s), with a rubric

x Other:

Resources Needed:

On-site people,

facilities:

CTE teachers and shop areas; art and business teachers

Equipment/Technology:

Computers, Calculators, Compasses, Rulers, Geometer’s Sketchpad

Materials:

Graph paper, construction paper, chosen material for finished product, computer paper, art supplies

Community Resources:

Experts in graphic design; Marketing and advertising specialists

Reflection Methods:

Individual, Group,

and/or Whole Class

Mathematicians Journal

x Small/Focus Groups x

Whole Class Discussions

x Fishbowl Discussions

Survey

Other:

Material Adapted From: (Provide credit for any materials or activities adapted from other sources.) http://www.1stwebdesigner.com/inspiration/successful-failed-logo-transformation/

http://curiousphotos.blogspot.com/2009/01/transformation-of-corporate-logos.html http://www.sportslogos.net/teams/list_by_league/7

http://www.purplemath.com http://illuminations.nctm.org

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UVA-SCPS Office of Mathematics Outreach with support from VADOE Mathematics and Science Partnership Grant Program NCLB Title II Part B

Quick Snapshot for the Sequence of Unit Activities

UNIT TITLE: Let Go of My Logo? MINUTES PER CLASS : 90 minutes

D a y 1 D a y 2 D a y 3 D a y 4 D a y 5

P R O J E C T W E E K O N E

Notes

Review of material and concepts that will be covered:

1. Transformations 2. Constructions 3. Parallel and

Perpendicular

Launch project and review any additional information needed. Discuss mathematics involved.

Students begin to research a logo they want to create for a specific organization that is mutually decided upon. Students are given remedial work as deemed appropriate.

Students design a logo for their organization using two specific math skills. Students present this to their fellow classmates.

Finish up presentations and discuss the final project. Students begin work on the final project.

D a y 6 D a y 7 D a y 8 D a y 9 D a y 1 0

P R O J E C T W E E K T W O

Notes: A workshop day could involve having a guest speaker to come in and discuss this material or substitute the website activity for a guest speaker.

Workshop Day Workshop Day/Conferences with teacher to discuss progress.

Work on design within CTE classes.

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Overview of Student Knowledge and Skills

What do students need to know and be able to do to complete the unit successfully?

Project: Let Go of My Logo!

Analyze each major task and the final project for the unit for the knowledge and skills necessary to produce a high-quality product.

How and when will students assess their own necessary prior knowledge and skills?

How will they remediate their own gaps or weaknesses in expected prior knowledge and skills?

KNOWLEDGE AND SKILLS NEEDED Assumed already learned

Students will self-assess

Will be learned and assessed during the unit 1. Transformations X

2. Coordinate Geometry X

3. Color Coordination X

4. Constructions X

5. Proportional Reasoning X

6. Writing a professional letter X

7. A CTE Skill X

8. Geometric Vocabulary X

What project tools will student’s use to monitor their progress through the unit and especially the project?

 Student developed Know/need to know lists

 Student developed Daily goal sheet

 Student Mathematician’s Journals

 Student developed Briefs/Memos

 Student developed Task lists

 Student developed Planning Calendar

 Teacher developed Rubrics

Other:

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Unit Title: Let Go of My Logo!

Driving Question: Why do you need to fix something if it is working? Do you need to keep up with the times? Or, is it important to make a change every once in a while?

Project Description: Organizations are always updating their logos. Some go from elaborate to simple while others go from basic to three-dimensional. In this project, students research various logos from past and present. Using this information, the students creatively design a new logo.

ENGAGE

How will student’s interested be piqued so they want to engage in the inquiry in this project-based unit?

Number of hours _20 min___

Students review the following websites:

http://www.1stwebdesigner.com/inspiration/successful-failed-logo-transformation/

This website has different logos that were considered for design and may have or may not have been successful.

http://curiousphotos.blogspot.com/2009/01/transformation-of-corporate-logos.html

This website features different logos that were changed over the years.

http://www.sportslogos.net/teams/list_by_league/7 This website features NFL logos.

A. Directions for Instructor

1. The teacher pulls up the websites and students get into groups of 2-3 to review the content on the websites. The students will review each of the examples and discuss as a group to see how logos have changed or disappeared over the years.

2. The teacher questions:

1. Why do you think the logos have changed? 2. Is that a good thing or a bad thing?

3. What do you think makes these good logos (i.e. memorable, important, catchy, etc.)

4. Which organizations do you like the best? Why? 5. Which organizations do you like the least? Why? 3. Teachers may choose to have students make a

presentation in regards to the above information; however, the students can simply have a formal or informal discussion with the teacher.

B. Students form a response in their mathematician journals.

Mathematician Journal Prompts Why do you think that some organizations have never really “changed” their logos? List some that have not.

EXPLORE Activity 1: Mathematician

21st Century Teaching and Learning Inquiry Learning Project-based Learning Unit

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Teacher provides guidance for the explorations to prepare students with the

knowledge and skills to engage in the project-based unit. Students will self-assess on the prior knowledge and skills assumed for the unit

Number of hours_2__

Complete the activity sheets that are attached with HO #1, pages 1-8.

The students need to review how to do these items prior to beginning this project. These activities were taken from:

http://illuminations.nctm.org. The students can practice looking at rotational symmetry and line symmetry before utilizing the computer to practice the symmetry.

Activity 2:

Transformations and Frieze Patterns – Students go to:

http://illuminations.nctm.org/ActivityDetail.aspx?ID=168 Students complete the various activities that are on the website.

Activity 3: Cyclic Figures – Students go to:

http://illuminations.nctm.org/ActivityDetail.aspx?ID=167 Students complete the various activities that are on the website.

Activity 4: Dihedral Figures: Students go to:

http://illuminations.nctm.org/ActivityDetail.aspx?ID=169 Students complete the various activities that are on the website. Students complete HO #2 with examples copied from each of the activities 2-4. This provides an opportunity for students to be creative and for teacher monitoring. Teachers can see where students’ thought processes are at this point.

Note to instructor: Students need to use the copy and paste feature in order to complete this activity. Students may use the print screen option.

Activity 5: Constructions:

Students go to: http://www.mathopenref.com

Students watch the video clips on the different constructions that are required by state. Students should complete each of the different constructions on a piece of graph paper. The graphs can be turned in to the teacher as a grade for this activity. The students can create a picture out of the different constructions, or they can

Journal Prompts What trends have you noticed in logo changes? Good or bad?

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use the constructions individually. Activity 6:

Parallel vs. Perpendicular: Use the website:

http://www.youtube.com/watch?v=aq_XL6FrmGs

Show the video linked above. Discuss with the students the similarities and differences between parallel and perpendicular lines. Students complete HO#3 related to parallel and

perpendicular slopes. Note: Teachers might want to show the websites again to discuss the differences of parallel and perpendicular lines in the different logos.

EXPLAIN

Teacher introduces the project and prepares

students to work independently in small groups

Number of Hours_1__

A. Introduce the Project:

Notes to Teacher: Students have had the chance to view logos and been able to practice learning information about the different logos. Students should now have some ideas about what is needed in a logo for an organization. The students should be able to begin researching at this phase.

Instructions for students:

1. Students research organization logos by looking through magazines, internet websites, pictures, etc. Students choose an organization.

(Note: School divisions that are looking to build a new school could choose to look at creating the logo for the new school in the school division). 2. Students prepare the logo using a minimum of two

of the math skills presented to develop their logo. More is acceptable, less is not. The students develop the logo on graph paper to begin with and get approval from teacher.

3. Students prepare their logo to meet with a CTE teacher who assists in the creation of the student’s logo.

4. Students present the logo to their fellow classmates. Students also have the option of writing a letter to the organization for whom they created the logo.

B. Final Product:

1. Logo on graph paper

2. Presentation of logo to teacher 3. Logo created with the CTE teacher

4. Presentation of logo to a group of people or in a letter format to the organization.

Mathematician Journal Prompts Which logo did you choose and why?

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Note to teacher: Be sure to cover all math skills presented earlier in order to be able to have the students prepared for the activity.

ELABORATE

The student groups are working independently with teacher consultations. Number of Hours___10__

A. Teacher monitors web usage.

B. Teacher initials student checklist. Teacher reviews sketches and monitors for remediation.

C. Students self-monitor using HO #4 and #5 I.

Mathematician Journal Prompts For the journal prompts, students should be filling in a timeline of where they are and where they want to be throughout this project.

EVALUATE Working groups submit products or make

presentations

Number of Hours__3_

Teacher, student, and audience use HO #5

Teacher may determine the due dates based on each student’s chosen logo and CTE connection.

Note: The rubric (HO #5) encompasses the entire project as it was designed to be a project rubric instead of multiple rubrics used at different intervals.

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HO #1, page 1

NAME:

Recognizing Reflection Symmetry — Notes



Two-dimensional figures have reflection symmetry if you can draw a line(s) through the figure so that one portion of the figure is the mirror image of another. Shown below are some decorative figures that contain reflection symmetry with the line(s) of symmetry shown.

Example: For the following figures, draw all possible lines of symmetry:

• Frieze patterns can also contain reflection symmetry, but these can only be horizontal and/or vertical.

Note:For horizontal symmetry, there is only one possible line that can be drawn.

Note: For vertical symmetry, there are often many different lines that can be drawn

.

Example: For the following frieze pattern, draw at least two lines of symmetry:

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HO #1, page 2

Recognizing Rotation Symmetry — Notes

•

Two-dimensional figures have rotation symmetry if you can rotate the figure around its center a certain angle (number of degrees) so that after the rotation it appears exactly the same as before the rotation. Shown below are some decorative figures that contain rotation symmetry with the angles of rotation shown.

How were the angles of rotation determined?

Example: Draw and determine the angles of rotation for the following figures:

How can you determine how many rotations there are? What formula helps you find the angles of rotation?



Frieze patterns can also have rotation symmetry, but the only rotation symmetry possible is 180°.

Look at the following figures right side up, and then upside down. Do they look the same?

Adapted from NCTM Illuminations,

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HO #1, page 3

Recognizing Symmetry — Practice

NAME:

1. For each capital letter in the alphabet, determine whether it has vertical reflection (label with v), horizontal reflection (label with h), and/or 180° rotation symmetry (label with r).

2. For each of the following figures, determine how many reflection and/or rotation symmetries the figure has. If the figure has reflection symmetry, draw in the lines of reflection. If the figure has rotation symmetry, draw and determine the angles of rotation.

a)

b)

c)

d)

Adapted from NCTM Illuminations,

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HO #1, page 4

3. For each of the following strip patterns, determine which ones have vertical reflection (label with v), horizontal reflection (label with h), and/or 180° rotation symmetry (label with r). For the figures that have reflection symmetry, draw at least one line of reflection.

a)

b)

c)

S

4. For each of the following, create a figure from the initial pattern with the specified number of symmetries:

a)

5 rotation symmetries b) 6 reflection symmetries

5. Go to http://home.windstream.net/jreeder43 and use the JavaSketchpad applets to create two cyclic figures, two dihedral figures, and two frieze patterns. Cut and paste each figure into one page of a word processing document, print it, and bring it with you to class on the assigned date. Be creative!

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HO #2

Symmetry Practice With Computer Applications http://illuminations.nctm.org/ActivityDetail.aspx?ID=168

An example of a Cyclical Figure:

Explain the reflection and rotational symmetries:

An example of a Dihedral Figure:

An example of a Frieze Pattern:

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HO #2b Symmetry Practice With Computer Applications

Answer KEY!

An example of a Cyclical Figure:

An example of a Dihedral Figure:

An example of a Frieze Pattern:

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HO#3:

Parallel and Perpendicular Lines Worksheet

Answer the following questions:

What are parallel lines?

Draw a set of parallel lines.

What are perpendicular lines?

Draw a set of perpendicular lines.

What is the difference between parallel and perpendicular lines?

How do their slopes compare to each other?

Give 3 real-life logos that feature parallel lines.

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HO#3b Parallel and Perpendicular Lines Worksheet Answer KEY!

Answer the following questions: What are parallel lines?

*Two lines that never intersect and are equidistant apart from each other at any given point. Furthermore, the two lines must lie in the same plane.

Draw a set of parallel lines.

What are perpendicular lines?

*Two lines that intersect each other at right angles. Must be in the same plane. Draw a set of perpendicular lines.

What is the difference between parallel and perpendicular lines?

*Parallel lines never intersect each other and perpendicular lines intersect at right angles.

How do their slopes compare to each other?

*Parallel slopes are the same and perpendicular slopes are negative reciprocals of each other.

Give 3 real-life logos that feature parallel lines.

*Answers will vary

Give 3 real-life logos that feature perpendicular lines.

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HO #4, page 1 Due Date: ____________

Project Checklist and Requirements:

CONGRATULATIONS!!! You have been hired by Mathonomics to create a logo for an organization. The bad part is that they forgot the name of the company! So, you have to figure out which logo it is that they forgot! To do so, follow this checklist and be sure to get your teacher, the manager, to initial every place that is needed. Otherwise, you might get fired (or lose a few points here and there!)

_____ Research an organization’s logo – Research a company that you would like to try to change the logo. Perhaps, you no longer like the logo or you think that it needs some pizzazz. Work with your team to find that organization’s logo. You may use a sports team, clothing company, restaurant, media, school, or other teacher approved organization.

_____Website used: ___________________________________________________ _____Organization chosen: _____________________________________________

Teacher approval (initials): ________

_____Rough sketch: __________________________________________________ Grade and teacher initials: ______________ ___________

_______Blueprint with details – You will draw an in-depth picture of the logo with specific

measurements. The blueprint must be neat, organized, and colored. The mathematics must be included. This is part of the final rubric (under Diagrams and Sketches). You will need to make sure that you include the Blueprint with your final submissions. You need to show the Blueprint to your teacher prior to moving on to the next step.

Teacher approval (initials): ________

_______List of Mathematics skills that are used – You will need to tell which of the mathematics skills that have been reviewed that you used for your project. You must choose at least two skills; however, you may use more than two skills. Using less than two skills is not an option. You will list those two skills here and get your teacher to initial off on them. You need to explain where you used the skill in the logo on this sheet as well.

Math Skill I: ______________________________________________ Where it is used:

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HO #4, page 2

Math Skill II: _____________________________________________ Where it is used:

Teacher initials: _________

Additional Math Skills: _____________________________________ Where they are used:

Teacher initials: _________

________Additional remediation needed? ______________Teacher initials: ________

________CTE Match-up – What do you want to do with your logo? Do you want to digitalize it or do you want to try and burn it into wood? What else can you do with your logo? Think of different places in the school in which you would be able to expand your logo onto something more materialized.

_______Supplies Needed:

_______Due Date: __________________________________

_______CTE Match-up approved: _____________________

Teacher initials: ______________

________Presentation – You will be presenting your Blueprint of your logo and your CTE expanded logo to your classmates. Through doing this, you will need to present it as a PowerPoint, poster, or a letter. We can send your letters to the organizations if you wish to write a letter.

_______Format chosen: _________________________________ _______Teacher initials: ____________

_______Final Grade: ____________

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HO #5

Math - Problem Solving : Let Go of my Logo - Rubric Student Name_________________________ Logo Name

_____________________________

CATEGORY 4 3 2 1

Diagrams and Sketches

Diagrams and/or sketches are clear and greatly add to the creator\'s

understanding of the procedure(s).

Diagrams and/or sketches are clear and easy to understand.

Diagrams and/or sketches are

somewhat difficult to understand.

Diagrams and/or sketches are difficult to understand or are not used.

Strategy/ Procedures

Typically, uses an efficient and effective strategy to create the logo.

Typically, uses an effective strategy to create the logo.

Sometimes uses an effective strategy to create the logo, but does not do it consistently.

Rarely uses an effective strategy to create the logo.

Neatness and Organization

The work is presented in a neat, clear, organized fashion that is easy to read.

The work is presented in a neat and organized fashion that is usually easy to read.

The work is presented in an organized fashion but may be hard to read at times.

The work appears sloppy and unorganized. It is hard to know what information goes together.

Working with Others

Student was an engaged partner, listening to suggestions of others and working cooperatively throughout lesson.

Student was an engaged partner but had trouble listening to others and/or working cooperatively.

Student cooperated with others, but needed prompting to stay on-task.

Student did not work effectively with others.

Explanation/ Presentation (x2 – should count twice)

Explanation/

Presentation is detailed and clear.

Explanation/ Presentation is clear.

Explanation/

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Mathematical Concepts

Explanation shows

complete understanding of the mathematical concepts used to create the logo.

Explanation shows substantial

understanding of the mathematical concepts used to create the logo.

Explanation shows some understanding of the mathematical concepts needed to create the logo.

Explanation shows very limited

understanding of the underlying concepts needed to create the logo OR is not written.

Final Rubric Grade: _______/24 Teacher Comments: _______/24

_____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _________________________________________________________

Student Comments: ______/24

_____________________________________________________________________________________ _____________________________________________________________________________________ _____________________________________________________________________________________ _________________________________________________________

Audience Comments: ______/24