UBD

The National Council of Teachers of Mathematics recognizes the importance of geometry and spatial sense in its publication //Curriculum and Evaluation Standards for School Mathematics// (1989). > Spatial understandings are necessary for interpreting, understanding, and appreciating our inherently geometric world. Insights and intuitions about two- and three-dimensional shapes and their characteristics, the interrelationships of shapes, and the effects of changes to shapes are important aspects of spatial sense. Children who develop a strong sense of spatial relationships and who master the concepts and language of geometry are better prepared to learn number and measurement ideas, as well as other advanced mathematical topics. (p. 48) >  **Summary of Curricular Context**: Students will be studying geometry and how it relates to the world. Prior knowledge of 6 basic geometric shapes is required.
 * //Geometry and Architecture//**

** Standard/Objectives for Unit or Lesson:** (Illinois and, or ISTE NETS)

**__Illinois State Learning Standard:__** ** 9.A.2b ** Identify and describe how geometric figures are used in practical settings (e.g., construction, art, advertising).

**__Illinois State Learning Goals:__** Use geometric methods to analyze, categorize and draw conclusions about points, lines, planes and space.

**Unit Goal:** The goal of the unit is practical application and analyzation of geometric figures.

**// Stage 1 //** **//Enduring Understandings//** What are the overarching enduring understandings for the unit/lesson? (big ideas that transcend the unit)
 * 1) The world is built of shape and space, and geometry is its mathematics.
 * 2) Spatial sense and geometric relationships are a means to solve problems and make sense of a variety of phenomena.
 * 3) Geometric relationships provide a means to make sense of a variety of phenomena.
 * 4) Math can be used in everyday life
 * 5) The geometric shapes we see all over the world can tell us stories about the past

**//Essential Questions//** What are the essential questions you can ask to guide inquiry?
 * 1) How is geometry used in the real world?
 * 2) What would the world be like without geometry?

* Basic geography - location of some famous places in the world * Biographical knowledge of some famous/local architects. * Geometric terminology || * Use of Google Earth navigation tools * Use of Google Presentation tools to share knowledge * Use of Google Sketchup creation tools * Time management * Basic problem solving skills * Oral presentation skills * Writing skills * Use of Voice Thread (optional) * Use of digital video camera (optional) * NCTM Illumination site navigation ||
 * ** Knowledge ** || ** Skills ** ||
 * * Use of 2d and 3d geometric shapes in architecture

** Stage 2 ** **//Step 1: Performance Tasks//** __//** Goal **//__ Your task is to build a new town hall that will live in history forever and be studied by the schoolchildren of the future. Your previous experience studying the buildings of the world, past and present, and identifying the geometric shapes will help you.

//__**Role**__// You are being asked to design a building

__**//Audience//**__ Your first audience will be your parents on school visitation day. Ultimately, the Town board will review your designs.

__**//Situation//**__ The town council has heard about the extensive work you have done studying famous architects as well as your classroom work building with toothpicks and gumdrops, creating with Lego architecture, Frodo blocks, and Frank Lloyd Wright blocks. They say your presentations on the use of geometric shapes in famous places show great promise. The city planner has asked for you to design and build a new town hall. Your competition is the Mayor's choice, the designer of The Crooked House (Sopot, Poland). Construction of The Crooked House building started in in January 2003 and in December 2003 it was finished. House architecture is based on Jan Marcin Szancer (famous Polish artist and child books illustrator) and Per Dahlberg (Swedish painter living in Sopot) pictures and paintings. The town council is counting on you saving them.

__**//Product//**__ You will use the great tool called Google Sketchup to create a new Town Hall using all that you've learned in your study of geometry and design as well as your biographical research. You will defend the geometric choices you make for your town hall and compare them to the other places you studied. You may present your recommendations, including your sketch up and explanation, via Google Presentation, Voice Thread, or "live" video recording.

__ **//Standards//** __ You will be evaluated on the following criteria
 * Original design of a new town hall
 * Write a 1 page paper describing why you designed you building as you did, compare and contrast to the pieces you studied, and describe what the world would be like if geometry was neglected
 * Roll it all into a presentation

**__ // Step 2: A // //ssessments// __** Over the course of the unit, students have had a series of authentic assessments while building shapes with toothpicks and gumdrops and finding 3d geometric shapes in famous places.

__** //Step 3: Self reflection// **__ Students will write in a journal daily to reflect upon the tasks that they were responsible for that day. Some of the questions/prompts that will be asked to guide them are: **Day 1-**How can you use what you already know about geometric figures to help construct, and assemble your town hall? **Day 2**-Now that you have begun using Google Sketch what do you need to do with your schedule to make sure that you can accomplish everything? **Day 3**- You should begin thinking about defending the choices you have made. What are some of the geometric elements that will help the mayor distinguish your town hall as the right choice for the town.

__ **//Stage 3//** __ **//W//** The purpose of this culminating lesson is to use your knowledge of how geometry is used to build great buildings all over the world and what the world would be like if we didn't use a variety of geometric figures.

**//H//** Show a series of strange buildings of the world, including The Crooked House, The Basket Building, The Kettle house, and the Hole House. Explain the situation as described above.

**//E//** Guided Instructions: Day 1 Review prior experiences, view presentations, explain responsibilities, share rubrics, pen/pencil sketching of ideas/notes Day 2 Google Sketch Up Tutorial and begin design Day 3 Design work and Design Defense Day 4 work continues, begin presentations Day 5 work finishes, finalize presentations

**//R//** Students will be encouraged to ask questions during the presentations about the design choices and connections that were made Guided re-thinking about the Parthenon will help continue discussion. Google Earth and architectural biographies will be available as resources.

**//E//** **Self assessment questions in the middle of day 1-** What have you learned so far about the geometry of buildings? Why do you think the architects made some of these geometric choices? **Self Evaluation at the end of day 1-** Re-read the rubric and form a plan for day 2 **Adjustment encouragement day 3-** As you plan your town hall remember that you will need to defend the geometric choices you made. What changes are you thinking of making now that you have looked at other great geometric places? **Self assessment questions beginning of day 2-** How can we connect the geometry we've seen with or sketch for our new town hall? What important features do you want to include and why? Final Summative

**//T//** **Developmental needs** There are two students in the classroom that have cognitive delays and both are non-verbal. There is also a teacher’s assistant in the classroom. The two students will create a poster of a small town instead of using SketchUp. The two students will be provided with different cut out shapes varying in sizes. The assistant will ask the students to find a certain shape and then the assistant will help them glue it onto the poster board to build a building. The assistant will then give the student a choice of two shapes, a square and circle and will then have to find the shape. For example, “Find the blue square”. The student will find the correct shape and glue it on the board. When it is time to present, they will present their poster by using a prerecorded Step-by-step. The students will also complete a teacher made worksheet of what they have learned. **Differentiation** A student was added to the class mid unit. A pre-test was administered t and it was decided that they did not have as much background knowledge as a majority of the class. The student was able to work in small groups with the teacher as well as others to "catch up" on terms and was assigned a project partner that would help to guide but not do all the work. **Interests** There are two students in the class that have visited the Parthenon and would like to bring in the pictures that they have. Other students have suggested looking up specific buildings or locations that they know are geometrically interesting and use those for their project.

**//O//** Over the course of this three week unit, students have wrapped and unwrapped 3d geometric shapes and explored their faces, sides, vertices, and edges with gum drops and toothpicks. They have used the [|NCTM Illuminations] site to explore geometric solids and their properties They've built with unit, Frodo, and Frank Lloyd Wright blocks as well as Lego Architecture. They have researched architects and famous places. They now have a to do list for their culminating project.

__**Student To Do List (final project)**__
 * 1) Create original design of a Town Hall
 * 2) Identify geometric shapes found (include at least 3)
 * 3) Make connections between your design and famous places/architecture
 * 4) Write at least 1/2 page persuasive essay "selling" your design, including connections.
 * 5) Write at least 1/2 page persuasive essay to the Town Council to use geometric design, dramatically pointing out what the world would be without geometry.
 * 6) Create a presentation (have a partner video tape you, use Google Presentation, or use voice thread) to share your presentation with the Town Council.

__**Rubric**__

** 4 ** || ** Meets Expectations ** ** 3 ** || ** Approaching Expectations ** ** 2 ** || ** Expectations Not Met ** ** 1 ** ||
 * CATEGORY || ** Exceeds Expectations **
 * Planning || Project looks like student had a plan prior to drawing. || Project looks like there may have been a plan prior to drawing, with a few details added later. || Project looks like it was planned as it was drawn. Sizing and layout may have been an afterthought. || No effort to plan visible ||
 * Attention to Details || Student paid close attention to all details in the project. Lots of extras here that make the project seem very real. || Student paid attention to most of the details of the project. There are several examples of "extras." || Student had one or two examples of fine details. || Student had no examples. ||
 * Use of Materials || <span style="color: #000000; display: block; font-family: arial,verdana,tahoma; font-size: 9pt;">Student explored the program and its toolbars. Used items in the project that may not have been demonstrated in class. Went above and beyond expectations. || <span style="color: #000000; display: block; font-family: arial,verdana,tahoma; font-size: 9pt;">Student used the basics of the program well and explored somewhat on their own. || <span style="color: #000000; display: block; font-family: arial,verdana,tahoma; font-size: 9pt;">Student used the basics of the program. || Student could not attempt the program. ||
 * <span style="color: #000000; display: block; font-family: arial,verdana,tahoma; font-size: 11pt;">Program Knowledge || <span style="color: #000000; display: block; font-family: arial,verdana,tahoma; font-size: 9pt;">Student's project and their ability to navigate through the program shows an extensive understanding of Google SketchUp. || <span style="color: #000000; display: block; font-family: arial,verdana,tahoma; font-size: 9pt;">Student's project and their ability to navigate through the program shows an above average understanding of Google SketchUp. || <span style="color: #000000; display: block; font-family: arial,verdana,tahoma; font-size: 9pt;">Student's project and their ability to navigate through the program shows an acceptable understanding of Google SketchUp. || Student could not attempt the program. ||
 * <span style="color: #000000; display: block; font-family: arial,verdana,tahoma; font-size: 11pt;">Time || <span style="color: #000000; display: block; font-family: arial,verdana,tahoma; font-size: 9pt;">Student used their time extremely well. Student was focused with no talking to peers other than collaboration. || <span style="color: #000000; display: block; font-family: arial,verdana,tahoma; font-size: 9pt;">Student used their time well. There was some collaboration with peers. || <span style="color: #000000; display: block; font-family: arial,verdana,tahoma; font-size: 9pt;">Student could have used their time better. Student was redirected back to project more than once. || Student did not participate ||
 * <span style="font-family: arial,verdana,tahoma;">Creativity || Your Google SketchUp Design is complex and complete. There are many interesting features to explore. You have incorporated your own interests into this design in some way. || Your Google SketchUp Design is complex and complete. There are several interesting features to explore. || Your Google SketchUp Design is complex and partially complete. There are some interesting features to explore || Your Google SketchUp Design is neither complex nor even partially complete. ||
 * Identifies geometric shapes || All of meets, plus begins to identify other 3D shapes not studied in class. || Identifies and names all geometric 3D shapes in lessons. || Identifies and/or names geometric 3D shapes, but does not know all of them. || No effort made ||
 * Shapes || Your Google SketchUp Design contains a wide variety of shapes. The shapes are very appropriate for the objects that they represent. There are no misplaced or confusing shapes. || Your Google SketchUp Design contains a variety of shapes. The shapes are appropriate for the objects that they represent. There are one or two misplaced or confusing shapes. || Your Google SketchUp Design contains a few shapes which are repeated. The shapes are appropriate for the objects that they represent. There are three or more misplaced or confusing shapes. || No effort made. ||
 * Presentation || You can show your Google SketchUp Design to someone else and describe at least five features of your design. || You can show your Google SketchUp Design to someone else and describe at least four features of your design. || You can show your Google SketchUp Design to someone else and describe at least three features of your design. || Not able to open application. ||

s Maintains position throughout paper in a logical manner. s Consistently supports a position with relevant evidence. || s The writer's position is clear and identified in the paper. s Maintains position throughout paper. s Supports a position with relevant evidence. || s The writer's position is evident, but may lack clarity. s Does not maintain position consistently throughout paper. s Supports a position, but all evidence may not be relevant. || s The writer's position is not evident. s Evidence of writer's position is not included in paper. s Insufficient support or evidence. || s Excludes extraneous details and inappropriate information s The conclusion effectively reinforces the writer's original position. || s The structure presents main points and evidence in a logical sequence. s Excludes extraneous details and inappropriate information s The conclusion provides a sense of closure to the writing. || s The structure has some evidence of sequence, but may not be effective. s Excludes most extraneous details and inappropriate information, but may have minor digressions. s The conclusion is evident, but may not be effective. || s The structure is not evident. s Includes extraneous details and inappropriate information. s The conclusion is not evident. || s Word choice conveys the writer's position in specific, vivid way. s Uses an effective variety of sentence beginnings, structures, and lengths. || s Uses voice to engage the reader, but may not be consistent throughout the paper. s Word choice conveys the writer's position in a functional way. s Attempts to vary sentence beginnings, structures, and lengths. || s Writer's voice is bland at times, and may not engage the reader. s Word choice is limited and may fail to convey the writer's position. s Uses little variety in sentence beginnings, structures, and lengths. || s Writer's voice is not noticeable. s Word choice does not convey the writer's position. s Uses an assortment of incomplete and/or incorrect sentences. ||
 * = **Writing** ||= ** Exceeds Expectations **
 * 4 ** ||= ** Meets Expectations **
 * 3 ** ||= ** Approaching Expectations **
 * 2 ** ||= ** Expectations Not Met **
 * 1** ||
 * ** Ideas ** || s The writer's position is clear and is identified in the opening statement.
 * ** Organization ** || s The structure presents main points and evidence in a logical and effective sequence.
 * ** Style ** || s Uses a lively writing voice to engage the reader.
 * ** Conventions ** || s Contains correct sentences, usage, grammar, and spelling that make the writer’s ideas understandable. || s Some errors are present, but they do not interfere with meaning. || s Errors interrupt the flow of communication and may interfere with meaning. || s Errors prevent the reader from understanding the writer’s message. ||

Resources: [|Getting Started Guide Sketch Up] [|Sketch Up Video Tutorials] [|Sketch Up Building Design examples]