For the daily warm-up exercise, 5 questions will be on the board to spark interest in the topic:
- Do you have any tattoos? If so, how many?
- How many people do you know with tattoos?
- Why do you think people get tattoos?
- How does society view people who have tattoos?
- Do you know any songs about tattoos?
- How many tattoos do you think Ms. Edmondson has?
(If technology permits, a short video could be shown about the changing perception of tattoos; Or, if possible, the hook could include a tattoo artist as a guest speaker.)
The Challenge and Constraints
Description of Challenge (Either Product or Process is clearly explained below):
List the Constraints Applied
Students will: 1) Create a tattoo design,
2) Graph it on the coordinate plane and provide specific instructions for their apprentice to replicate the design, 3) Re-design the directions in order to perform a transformation on the tattoo, and 4) Create an Excel spreadsheet embedded with the transformation rules required to translate, reflect, rotate, or dilate any tattoo, given the coordinates.
--The tattoo design must use a minimum of 25, maximum of 50 coordinates.
--The design must be in at least 2 quadrants.
--The coordinates must be within the specified boundaries: -20<x<20 and
--The Excel spreadsheet must be embedded with formulas to perform the transformation, not just list the correct coordinates.
Anticipated Guiding Questions
- How can we connect tattoo design to geometry?
- How can I instruct an apprentice to accurately replicate a tattoo design?
- How do you write a rule to perform a given transformation (translation, reflection, rotation, dilation) on an ordered pair (x, y)?
Engineering Design Process (EDP)
The students’ test to determine if their design coordinates are accurate will be done by the apprentice’s ability to duplicate the design. If there are errors, they will have to edit the instructions. Similarly, if the transformation instructions listed in the Excel spreadsheet do not produce the specified transformation on the coordinate plane, the spreadsheet will need some revision.
How the EDP Process applies:
- Identify & Define/ Gather Information: Lesson 1—Students will research tattoos and gather information about the business and artistry of tattoo design.
- Identify Alternatives, Select Solutions: Lesson 1—Students will design an original tattoo to be graphed and transformed on the coordinate plane.
- Communicate, Implement, Evaluate, and Refine Solution: Lesson 2—Students will communicate their design to their “apprentice” by ordered pair instructions only. If the design is not replicated accurately, they must revise or refine the design instructions. The design must then be transformed in some manner, which will require a re-design of the original instructions.
- Communicate solution: Lesson 2—Students will share final designs along with transformations and discuss challenges encountered during the process. If the Excel coordinates do not match the apprentice’s coordinates for transformation, students must work together to adjust the embedded formulas accordingly, in order to produce the specified transformation.
The students will present their original, duplicated, and transformed tattoo designs as evidence that their instructions and spreadsheet were accurate.
What academic content is being taught through this Challenge?
Graphing on the coordinate plane, performing transformations on the coordinate plane, and writing transformation rules
Students may switch the order of the x and y-coordinates in the ordered pair. (Remind students that x comes before y, just like in the alphabet.
Students may plot points in the wrong quadrants.
Students may confuse which coordinate changes to the opposite sign when a reflection across one of the axes is performed.
Lesson 1: Design Your Tattoo (4 days)
- Activity 1: Design Your Tattoo (2 days) (Worksheet 4.01.01a)
- Activity 2: Graphing Your Tattoo (2 days) *CBL/EDP* (Worksheet 4.01.02b)
Lesson 2: Transformations (5 days)
- Activity 3: Transformations Practice (1 day) (Worksheet 4.02.03c)
- Activity 4: Transform Your Tattoo (2 days) *CBL/EDP* (Worksheet 4.02.04d)
- Activity 5: Using Excel to Transform Your Tattoo (2 days) *CBL/EDP* (Worksheet 4.02.05e)
Pre-Unit and Post-Unit Assessment Instrument
A pre-assessment will be administered prior to the unit. A post-assessment will be administered after the unit.
Successes—Many students designed tattoos that had real meaning to them, making the topic relevant to their life. Also, many students reflected that they understood transformations better after the unit than they did prior to. The engineering design process was definitely used in the implementation of the unit, as students had to continually communicate, edit, revise, and redesign throughout the challenge.
Shortcomings—The design of the unit relied upon partners completing different parts of the unit in a timely manner. However, many students did not, which resulted in their partner not being able to move forward in the process.
If I were to teach this unit again I would:
- Make sure to have designs on hand for students whose partners did not complete their portion of the activity by the deadline.
- Adapt the EXCEL portion of the unit to GOOGLE sheets, as my students did not have Excel on their laptops.
- As an alternative to the large group discussion, have students work in small groups and record answers on chart paper. This may increase participation.
- Allot more points for creativity and originality, as many students went above and beyond to create unique deigns.