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The Arizona STEM Acceleration Project

Logo Design

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Can Math Make Art?

Logo Design, Congruence, Similarity

An 8th Grade STEM lesson

Matthew Heaston

June 2024

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Notes for teachers

This lesson supports math curriculum by providing an opportunity to practice similarities and congruence.

Please be familiar with rotations, reflections, translations, and dilations.

Keep the logo designs simple.

This lesson is broken into two 55 minute classes.

This lesson assumes the content is prior knowledge that will be accessed.

Better results are expected when collaborating with your math department.

List of Materials

  • Simple drawing or logo as an example
  • paper and pencil
  • whiteboards
  • graphing software (optional)
  • Laptop/Chromebook
  • GoeGebra simulation - link
  • Rotation sim - link
  • Reflection sim - link

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Math Standards

AZ Math Standards

  • 8.G.A Understand congruence and similarity
    • 8.G.A.1 - Verify experimentally the properties of rotations, reflections, and translations.
    • 8.G.A.3 - Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.
    • 8.G.A.4 - Understand that a two-dimensional figure is similar to another if, and only if, one can be obtained from the other by a sequence of rotations, reflections, translations, and dilations

Technology Standards

AZ Tech Standards

6-8.1.b. Students identify and begin to develop online networks of experts and peers to customize their learning environments in accordance with school policy

6-8.2.b. Students demonstrate and advocate for positive, safe, legal, and ethical behavior when using technology and when interacting with others online

6-8.2.c. Students demonstrate and advocate for an understanding of intellectual property including copyright, permission, and fair use by including appropriate citation and attribution elements

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Objectives:

In this unit, students will be using their math knowledge to manipulate a logo they will create. Students will come up with a logo, use that logo to practice translations, dilations, rotations, reflections. Students will then use those congruence and similarity properties to create their own “Warhol-esque” art from their logo.

Students that have access to such programs can use Desmos or your favorite graphing program.

Students will create their logo, translate, rotate, dilate and reflect their logos.

Students will then use these practices to modify their logos.

Additionally, students can then create their art digitally to be produced into a sticker (Cricut) or finished however you see fit.

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Agenda

Day 1

Review rotations, reflections, translations, dilations.

Connect the terms with art/design.

Have students play with simulators and paint programs.

Provide assignment: Personal logo design using transformations.

Day 2

Logo creation

Rotate, Dilate, reflect and translate the logo to make art/designs

Label the art as examples of the four terms of congruence

Walking gallery, showcase, exhibit work

Connect to Cricut - future lesson

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Big Question: Can math make art?

Tessellations, Fractals, Fibonacci sequence… Some student responses may include these examples.

8th graders have learned about Dilation, Reflection, Rotation, Translation in math.

Could this be considered art?

Let students explore:

PLAYTIME - link to reflection painter

PLAYTIME - link to rotation painter

ASK: if they can identify any math properties in this paint program

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Hands-on Activity Instructions

  • This exercise can be done individually, but groups can be created for themes or specific examples (this group do Translations/This group do these colors)
  • Pick a favorite logo (Nike, Apple)
  • Students can print, trace, draw and make copies of a logo
    • Students then use these drawings to Rotate, Translate, Reflect, Dilate
    • Students will learn they need to flip images or reduce/enlarge images
    • Can be done digitally in many paint programs
    • Ask students to identify transformations in the images

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Hands-on Activity Instructions

  • Students can begin creating their own transformation examples
    • Teacher preference -
      • deliverables digital or printed/drawn
      • 1 per page, all 4 per page
    • Students who finish early
      • have them think of a business or concept, or spin a new take on an old logo
      • create versions of the logo by rotating, translating, dilating and reflecting their image to make the logo unique
      • allow room for creative interpretation
    • Students who struggle
      • Focus first on the examples and terminology
      • Try using familiar logos (sports, Marvel, etc.) and ask the student to identify what transformations are at work. Sometime more than one transformation is being used.
      • Use the images provided as needed finding lines of symmetry, points of rotation or evidence or dilation or rotation.

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Examples, Definitions, Models

  • More examples of Dilation

  • More examples of Reflection

  • More examples of Rotation

  • More examples of Translation

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Assessment

Students will be able to create or use a logo to successfully demonstrate the four types of geometric transformations: Rotation, Dilation, Reflection, Translation.

Students can create their work digitally or by hand, depending on resources and desired outcome.

Students can work individually to perform the task, and as a group to ensure all members work demonstrates the learning objectives. This can be done with peer review, walking galleries, etc.

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Differentiation

In small groups, we can use examples of the logos provided on slides 8 and 9. Students can be given whiteboards to respond to questions such as:

  • Do you see any lines of symmetry?
  • has the logo rotated or just moved?
  • has the logo flipped or changed size?

Remediation

Extension/Enrichment

Students may find they want to create their own logo, or work with a current logo and improve it.

Students can find patterns in logos regarding symmetry, methods of transformations and even color. Have students make note of those patterns and see if they can incorporate them into their logo.

Students can ask why the above patterns are found. For example, why are so many logos round? Is there a connection between the amount of symmetry and the appeal of the logo?