 Graphing in SlopeIntercept form is a large concept that will be utilized in all math classes after 8th grade. So, it is imperative for students to mastery the topic and be able to apply it.
The Big Idea (including global relevance)
Students are constantly exposed to media, graphic art, and propaganda that is trying to sway them to buy a product. Unbeknownst to most students, the golden ratio is an embedded concept that influences people to perceive something as visually appealing. Students should be aware of this natural occurrence (golden ratio) and how it is used in graphic arts and their everyday life.
The Essential Questions:
 What is the golden ratio?
 How is the golden ratio used in everyday life?
 How is the golden ratio used in design and the real world?
 How can you use the golden ratio and mathematical equations to define a company’s graphic art and why is this ability important?
Justification for Selection of Content:
 Misconceptions regarding this content are prevalent.
 Content is suited well for teaching via CBL and EDP pedagogies.
 The selected content follows the pacing guide for when this content is scheduled to be taught during the school year. (Unit 1 covers atomic structure because it is taught in October when I should be conducting my first unit.)
 Graphing in SlopeIntercept form is a large concept that will be utilized in all math classes after 8th grade. So, it is imperative for students to mastery the topic and be able to apply it.
The Hook:
Hook Option 1:
 Have a graphic designer come in and show students different graphic art work and the importance of designing something that will stick with its customers or draw people in.
Hook Option 2:
 Logos Challenge #1 (link) – Have students take the following quiz to show them how familiar they are with logos and how important they are to branding a company. Winners will correctly identify the most logos in 7 minutes.
 Logos Challenge #2 (link): Students will be given 15 everyday logos and asked to find the hidden meanings in them. This will show students how logos can have multiple meanings, utilize the golden ratio, and be more than just a picture. Winners will correctly identify the most hidden meanings in 7 minutes.
Misconceptions:
 Students often times mix up the slope and yintercept of a linear equation.
 Students often times mix up vertical and horizontal lines.
 Students think that math is not used in the real world, let alone to design something in a creative way.
Unit Lessons and Activities:
PreTest (4.0.0a.)
Lesson 1: Introduction (3 days)
 Activity 1: Logos (4.1.01.) – (55 mins) 2 days
 Hook – Logos Game (CBL PowerPoint (4.1.01b.))
 Big Idea, Societal Impact, Challenge (CBL PowerPoint (2.1.01b.) & EDP WS (4.1.01.c), & Challenge Guidelines & Rubric (4.1.01d.0))
 **Includes Define & Identify Parts of EDP WS/Process
 Activity 2: Golden Ratio (4.1.02.) – 1 day
 Golden Ratio Investigation (4.1.02e.)
 **Includes Gather Information, Identify Alternatives Part of EDP WS/Process
Lesson 2: Challenge (5 days)
 Activity 1: Sketch & Design (4.2.01.) – 3 days
 **Includes Select, Implement, Evaluate Solution, Communicate, and Refine Solution of EDP WS/Process
 Activity 2: Gallery Walk (4.2.02.) – 2 days
 Designer Evaluations (4.2.02f.)
 Maker Bot – 3D Guide (4.2.02g.)
 PostTest (4.2.02h.)
 **Includes Select, Implement, Evaluate Solution, Communicate, and Refine Solution of EDP WS/Process
Description of Challenge
Students will create a 2D graphic design as members of Argo Graph(it) Design (a local design firm). They will choose from a variety of companies that wish to contract their services for a new graphic art/logo. The company uses a software that takes linear functions and uses them to make graphic art via Desmos graphing site (link).
List of Constraints Applied
 Students must use at least 30 linear equations
 Students design must incorporate the golden ratio.
 Students must restrict the domain and range of the functions in Desmos.
Team Roles:
 Technology Manager: This team member is in charge of implementing their 2D design into Desmos.
 Creative Manager: The creative manager is in charge of leading creative discussions and major design choices and completing the EDP WS.
Company requirements:
 Task 1: Sketch  Create a rough graphic design on graph paper (must get approval by Ms. Argo)  HAND
 Task 2: Final Sketch  Create a detailed graphic design on graph paper that utilizes the golden ratio (must get approval by Ms. Argo)  HAND
 Task 3: Desmos  Create art on Desmos using different functions, changing domains, and window  COMPUTER
Anticipated Guiding Questions
 What is the golden ratio?
 Where is the golden ratio used?
 How is the golden ratio used in design?
 Why are meaningful graphic designs important?
 What is graphic design?
 What does a graphic designer do?
 What stages does a graphic designer go through when designing a logo?
 What makes a sketch a “good” sketch?
 How detailed do sketches need to be?
 What is a reference point for the sketch?
 What is the scale size for the sketch?
 Why is it important to make a sketch that is to scale and detailed?
 What is Desmos and how does it work?
How will students test or implement the solution? What is the evidence that the solution worked? Describe how the iterative process from the EDP applies to your Challenge.
Students will test their solution by taking their 2D sketch and trying to recreate it in Desmos using linear equations. If their sketch isn’t 100% accurate, they will need to use their knowledge of linear functions and transform their equations/lines to complete the sketch. They will also be testing that their solution has golden ratio proportions somewhere in the sketch. Students will be in charge of choosing how to illustrate that the golden ratio is present (through measuring, diagrams, etc). Students will choose how they want to demonstrate this. In addition, they will be then scaling their sketch from 2D to 3D.
How will students present or defend the solution? Describe if any formal training or resource guides will be provided to the students for best practices (e.g., poster, flyer, video, advertisement, etc.) used to present work.
Students will let their design speak for itself during a gallery walk of all of the students graphic art work. Local graphic designers and former University of Cincinnati DAAP designers will be in to judge the graphic art, creativity, and visual appeal. Students will engage in a Q&A with designers, make edits based on their feedback, and submit a final project. Then, the top 3 students will get to 3d print their graphic art as a key chain.
What academic content is being taught through this Challenge?
Students will be applying their knowledge of linear functions in the form y=mx+b. They will be graphing the functions, restricting their domain and ranges, as well as transforming the functions using their knowledge of rate of change (slope) and yintercept in relation to the origin.
Real world applications:
I think this unit applies to the real world in that graphic design and logos are everywhere in first world countries and have a major impact on consumerism, marketing, and purchases made. I didn’t place it all the way to the right of the spectrum because I felt like it wasn’t as applicable in third world countries, so it isn’t necessarily a 100% global concept. In addition, the golden ratio is present in nature, structural design, body proportions, etc.
What activities in this Unit apply to real world context?
The golden ratio is utilized in the world to increase visual appeal in many forms. It is used in the beauty industry to create symmetry through makeup (contouring), and plastic surgery. It is utilized in structural design to create a building that is pleasing to the eye (pyramids). It is used in everyday objects (credit cards, tv screen ratios, music).
Societal Impact:
I think this unit applies to the real world in that graphic design and logos are everywhere in first world countries and have a major impact on consumerism, marketing, and purchases made. In additional, the social implications of using the golden ratio for beauty is becoming increasingly controversial (plastic surgery, constructed beauty, etc).
What activities in this Unit apply to societal impact?
 The Hook – How does graphic art and marketing impact an individual?
 Activity #2: Golden Ratio investigation
 The Challenge
What careers will you introduce (and how) to the students that are related to the Challenge? (Examples: career research assignment, guest speakers, fieldtrips, Skype with a professional, etc.)
 Students will be introduced to the careers of graphic designers as one will be coming in to speak with them for the hook and coming back in to evaluate their final work.
 Structural Engineers (constructing buildings using golden ratio)
 Biomedical Engineers (plastic surgery and the golden ratio)
 Industrial Designers (creating 3D products using the golden raito)
 In addition to graphic designers), students will be introduced to 3D printing and computerengineers that utilize this software. You could also argue that virtually any engineering field, biomedical, mechanical, etc. will use 3D printing in the future.
Unit Academic Standards  ONLS
8.EE.5: Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distancetime graph to a distancetime equation to determine which of two moving objects has greater speed.
8.EE.6: Use similar triangles to explain why the slope m is the same between any two distinct points on a nonvertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.
8.F.1: Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output.1
8.F.3: Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s^2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line.
Results:
Reflection
Students definitely had a better idea and confidence when graphing/writing equations in slope intercept form. The technology manager’s especially improved more in this regard as they received more training in the software/mathematics. One change I would make is to include the desmos/math training for everyone in the research stages of the engineering process. In addition, I would give students an additional day and change the equations requirements to 20 as some students truly struggled with coming up with an intricate enough design.
Overall, students saw the power in knowing the math and how it applied to the real world!
Common Core State Standards  Mathematics (CCSS)

Standards for Mathematical Practice

Make sense of problems and persevere in solving them

Reason abstractly and quantitatively

Construct viable arguments and critique the reasoning of others

Model with mathematics

Use appropriate tools strategically

Attend to precision

Look for and make use of structure

Look for and express regularity in repeated reasoning
