Geometry UBD Stage 2: Evidence
Jackson Sevieux
Jackson Sevieux
Seasons Greetings Tim, Beau, and to the rest of the Math Cohort,
I hope you guys are enjoying your break, but I think it is high time that we start collaborating on completing the UbD stage 2 for the first semester of Geometry. I attempted to create the necessary work and to leave a record of the procedure so that I might easily share, replicate, and discuss the process. First, I find that the greatest challenge is to integrate all the standards seemlessly within one lesson, yet luckily multi-part lessons have the potential to do them justice. Second, brainstorming creative ways to introduce topics can be uncomfortable at times, but upon review of those ways, a bigger picture starts to form. Note: The information has yet to be loaded into the "L4L Math Cohort UbD Stage 2 Worksheet due to the fact that this only represents an intermediate step in the process, which must be subject to review. The section that explains the six facets of understanding must be further developed (let alone the dispositions).
Google doc link: https://docs.google.com/document/d/1CXNuGhRLj0f3HY4oHpPs6y7hWXz6X6AyRT62Jpud-aE/edit?usp=sharing
*Sample procedure for developing the GRASPS activity (see above link for GRASPS only)
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Geometry Module 1 – Geometric Transformations |
1. Making reference to the work from stage 1, use your own words to bundle groups of related standards. Overlay the bundles with the relevant math practice standards referencing those suggested in the work from stage 1. (Materials: Stage 1 Document, CCSS Toolbox Document)
A. G-CO.A.1, G-CO.A.4 - Make connections from undefined notions in geometry to more advanced definitions and concepts (ie transformations). (MP5, MP6)
B. G-CO.A.2, G-CO.A.3, G-CO.A.5 – Represent transformations using various methods (functions, geometry software, constructions). (MP4, MP5)
C. G-CO.A.4, G-CO.B.6- Understand features of the key types of transformations (rigid/non-rigid) and what they can be used to do (carry figures onto other figures, prove congruence). (MP5)
2. For all the major topics covered in the module (refer to work from stage 1), brainstorm/gather information and themes that are potentially interesting to students and/or that bridge into scientific topics. Be sure to note the relationship with the standards/topics if not apparent. Some areas to consider include the following:
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· Thinking skills |
· Images/video/media |
· Games/videogames |
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· Hobbies |
· Occupations |
· Projects |
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· Historical figure |
· Scenario |
· Technology |
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· Applications (real life) |
· Similarities |
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A. Euclid (historical figure), lawyers (occupation), building blocks (similarities), reasoning (thinking), Programming apprentice (occupation),
B. Programmer (occupation), graphic designer (occupation), architect (occupation), computer software (technology), tools (similarities)
C. Nature (applications), patterns (applications), designs (applications), animations (applications), programmer (occupation)
3. Develop and compose a series (or sequence) of themes, which attempt to cover all the standards, from among the most favorable topics brainstormed above. Try to draw relationships between information by utilizing recurring themes where possible.
Theme 1: You are a budding programmer on your first assignment tasked with collaborating with the video game designer (and other relevant parties) to help them to design various components of a videogame.
4. With explicit reference to the work from stage 1, construct a performance task scenario that addresses each of the bundles of standards. Try to utilize the 6 facets of understanding [Explain, Interpret, Apply (by doing what), point of view of, empathizing with, reflecting on] where possible.
Theme 1:
A. Because the software you are using to program the videogame is highly mathematical, you must clarify your understanding of the undefined notions of geometry and
a. Use them as building blocks to clearly program (define) the following basic notions: angles, perpendicular lines, and line segments in order to make future programming tasks easier.
b. Moreover, you must use these aforementioned basic notions as building blocks to program (define) rigid motions (transformations) to include: rotations, reflections, and translations.
B. You will use various methods to represent the videogame designers rigid motions to different parties involved in the design process.
a. Use functional notation to communicate with mathematical scientists.
b. Use geometry software to communicate with graphic designers.
c. Use straight edge and compass to communicate with architects.
C. Discuss with the video game designer the salient features of rigid and non-rigid transformations to inform this stage of the videogame design.
a. Discuss occurrence of transformations in nature (hint at congruence, similarity)
b. Discuss carrying figures onto themselves.
c. Define congruence in terms of the rigid transformations.
5. Reference the components of the performance task scenario with the associated G.R.A.S.P. areas. Show alignment to content and math practice standards where possible.
GOAL: Help videogame designer describe and create videogame designs and motion paths with computer software.
ROLE: Videogame programmer must facilitate communication with various members of the videogame development team.
AUDIENCE: Videogame development team (programmers, graphic designers, architects, mathematical scientists)
SITUATION: The videogame designer has the creative responsibility of making the game, but they are not always proficient in their programming ability. As the resident programmer, you will assist the videogame designer (and development team) with programming designs and motion paths. Additionally, you will use various geometric tools as you assist the rest of the development team with realizing the vision of the videogame designer.
PRODUCTS/PERFORMANCE: Create a technical document to standardize programming methods (vocabulary) and across members of the development team.
STANDARDS (Rubric categories): Technical document must use precise language and provide readers with clear explanations of terminology. Terminology must include undefined notions of geometry, basic notions, rigid/non-rigid transformations, & congruence in terms of rigid motion). Include sample models to describe functionality of said programming methods to creating videogame designs (ie mappings) and motion paths with the computer software. Make explicit reference to how you utilized the following math practice standards: MP4, MP5, MP6.
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Stage 1 |
Stage 2 |
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If the desired end result is for learners to… |
then you need evidence of the learners’ ability to… |
so the assessments need to require products/performances like… Performance Task (GRASPS): [Percentage of the grade: ____%] GOAL: ROLE: AUDIENCE: SITUATION: PRODUCTS/PERFORMANCE: STANDARDS (Rubric categories):
Next step, consider other evidences (diagnostic, formative and summative assessments):
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Established goals–
Transfer –
Understand that–
And thoughtfully consider the question(s) –
Know–
Be skilled at–
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Six Facets of Understanding/Dispositions |
Performing |
Inventing |
Thinking/Creating |
Relating/Inspiring |
Producing |
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Explain–
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Interpret–
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Apply, by–
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See from the points of view of–
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Empathize with–
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Reflect on–
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Geometry Module 2 – Angles and Lines |
1. Making reference to the work from stage 1, use your own words to bundle groups of related standards. Overlay the bundles with the relevant math practice standards referencing those suggested in the work from stage 1. (Materials: Stage 1 Document, CCSS Toolbox Document)
A. G-CO.A.1, G-CO.A.9 - Make connections from undefined notions in geometry to more advanced definitions and concepts (ie developing proofs surrounding angles and lines). (MP3, MP6)
B. G-CO.C.9 – Prove theorems about lines and angles (e.g. congruence of vertical angles, angles formed when a transversal crosses parallel lines, equidistance of points on a perpendicular bisector from the line segments endpoints) (MP3, MP7)
C. G-GPE.B.5 – Prove slope criteria for parallel and perpendicular lines and use them to solve problems (i.e. finding parallel or perpendicular equations passing through a point, etc). (MP3, MP7)
2. For all the major topics covered in the module (refer to work from stage 1), brainstorm/gather information and themes that are potentially interesting to students and/or that bridge into scientific topics. Be sure to note the relationship with the standards/topics if not apparent. Some areas to consider include the following:
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· Thinking skills |
· Images/video/media |
· Games/videogames |
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· Hobbies |
· Occupations |
· Projects |
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· Historical figure |
· Scenario |
· Technology |
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· Applications (real life) |
· Similarities |
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A. Urban design planner (occupation), reasoning (thinking), Programming apprentice (occupation), , architect (occupation)
B. Urban design planner (occupation), construction code inspector (occupation), billiards instructor (occupation), civil engineer (occupation),
C. Urban design planner (occupation), construction code inspector (occupation), billiards instructor (occupation), civil engineer (occupation), graphic designer (occupation), architect (occupation), computer software & programming (technology), Physics & Nature (applications), patterns and properties (applications), designs (applications), ballistics
3. Develop and compose a series (or sequence) of themes, which attempt to cover all the standards, from among the most favorable topics brainstormed above. Try to draw relationships between information by utilizing recurring themes where possible.
Theme 1: You are an urban designer tasked to work with a videogame developer to help make the communities in his videogames more realistic. In this particular scenario, you have designed the layout of streets (and houses) and are attempting to explain (and justify) the various properties surrounding the lines and angles formed by these many intersecting streets of your design.
4. With explicit reference to the work from stage 1, construct a performance task scenario that addresses each of the bundles of standards. Try to utilize the 6 facets of understanding [Explain, Interpret, Apply (by doing what), point of view of, empathizing with, reflecting on] where possible.
Theme 1:
A. As the resident urban planner on the videogame development team, you must also utilize the language contained within the technical document created by the programmer in the previous module (using undefined+basic geometrical notions to define and explain lines and angles). As you define new concepts, you must work with the technical writers to the update the previous technical document with additional terminology and concepts using aforementioned basic notions as building blocks that will serve to explain (define) the types of angles formed by intersecting lines.
a. Group 1 Terminology: transversals, vertical angles, parallel lines, perpendicular bisectors, equidistance.
b. Group 2 Terminology: slope, parallel slope, perpendicular slope, slope intercepts.
B. You will address questions surrounding various properties (theorems) regarding the lines and angles in your city layout (e.g. congruence of vertical angles, angles formed when a transversal crosses parallel lines, equidistance of points on a perpendicular bisector from the line segments endpoints) justifying (proving) properties as necessary.
C. You will address questions surrounding various properties (theorems) regarding the lines and angles in your city layout (i.e. slope criteria for parallel and perpendicular lines, finding parallel or perpendicular equations passing through a point, etc) justifying (proving) properties as necessary.
5. Reference the components of the performance task scenario with the associated G.R.A.S.P. areas. Show alignment to content and math practice standards where possible.
GOAL: Explain and justify various properties of the lines and angles in the design of the city layout to the graphic designer
ROLE: Urban planner must bring various members of the development team up to speed with the types of lines and angles used in his or her proposed city layout of the videogame.
AUDIENCE: Videogame development team (graphic designer, technical writers, programmers, graphic designers)
SITUATION: To add to the realism of the videogame world, the graphic designer of the videogame has enlisted the help of an urban planner to develop the look and feel of the city. Upon showing the designer your proposal, you must assist the graphic designer with understanding the associated terminology that you use to describe the relative position of angles and lines within your city layout. Additionally, you will examine and justify the various properties of these lines and angles. Moreover, you will work with the technical writer to update the language utilized in the prior technical document (module 1).
PRODUCTS/PERFORMANCE: (a) Appendix to the technical document in which vocabulary has been added to further standardize language and concepts surrounding lines and angles across members of the development team. (b) Report/Analysis of properties (theorems) surrounding lines and angles. Justification may take the form of paragraph proofs, flow-chart proofs, or two column proofs.
STANDARDS (Rubric categories): (a) The appendix to the technical document must use precise language and provide readers with clear explanations of terminology. Group 1 terminology must include: transversals, vertical angles, parallel lines, perpendicular bisectors, equidistance. Group 2 terminology must include: slope, parallel slope, perpendicular slope, slope intercepts. (b) The report/analysis of properties (theorems) surrounding lines and angles must include examples and justifications in the form of paragraph proofs, flow-chart proofs, or two column proofs. Make explicit reference to how you utilized the following math practice standards: MP3, MP6, MP7.
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(Template) Geometry Module XX – Topic Name |
1. Making reference to the work from stage 1, use your own words to bundle groups of related standards. Overlay the bundles with the relevant math practice standards referencing those suggested in the work from stage 1. (Materials: Stage 1 Document, CCSS Toolbox Document)
2. For all the major topics covered in the module (refer to work from stage 1), brainstorm/gather information and themes that are potentially interesting to students and/or that bridge into scientific topics. Be sure to note the relationship with the standards/topics if not apparent. Some areas to consider include the following:
|
· Thinking skills |
· Images/video/media |
· Games/videogames |
|
· Hobbies |
· Occupations |
· Projects |
|
· Historical figure |
· Scenario |
· Technology |
|
· Applications (real life) |
· Similarities |
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3. Develop and compose a series (or sequence) of themes, which attempt to cover all the standards, from among the most favorable topics brainstormed above. Try to draw relationships between information by utilizing recurring themes where possible.
Theme 1:
4. With explicit reference to the work from stage 1, construct a performance task scenario that addresses each of the bundles of standards. Try to utilize the 6 facets of understanding [Explain, Interpret, Apply (by doing what), point of view of, empathizing with, reflecting on] where possible.
Theme 1:
5. Reference the components of the performance task scenario with the associated G.R.A.S.P. areas. Show alignment to content and math practice standards where possible.
GOAL: Provide a statement of the task. Establish the goal, problem, challenge, or obstacle in the task.
ROLE: Define the role of the students in the task. State the job of the students for the task.
AUDIENCE: Identify the targent audience within the context of the scenario. Example audiences might include a client or committee.
SITUATION: Set the context of the scenario. Explain the situation.
PRODUCTS/PERFORMANCE: Clarify what the students will create and why they will create it.
STANDARDS (Rubric categories): Provide students with a clear picture of success. Identify specific standards for success. Issue rubrics to the students or develop them with the students.
