Ohio Standards Connections: 3. Geometry and Spatial Sense: Students identify, classify, compare and analyze characteristics, properties and relationships of one-, two- and three-dimensional geometric figures and objects. Students use spatial reasoning, properties of geometric objects, and transformations to analyze mathematical situations and solve problems. Benchmarks: B. Describe & apply the properties of similar and congruent figures; & justify conjectures involving similarity & congruence. D. Use coordinate geometry to represent & examine the properties of geometric figures. F. Represent & model transforma-tions in a coordinate plane and describe the results. Indicators: 9^th grade: 2. Apply proportions and right triangle trigonometric ratios to solve problems involving missing lengths and angle measures in similar figures. 10^th grade: 5. Con-struct congruent figures & similar figures using tools, such as compass, straightedge, and protractor or dynamic geometry software. 6. Identify the reflection & rotation symmetries of two- & three-dimensional figures. 7. Perform reflections & rotations using compass & straightedge constructions & dynamic geometry software. 8. Derive coordinate rules for translations, reflections & rotations of geometric figures in the coordinate plane. 9. Show & describe the results of combinations of translations, reflections & rotations (compositions); e.g., perform compositions & specify the result of a composition as the outcome of a single motion, when applicable. Arts-Visual Arts 2. Creative Expression & Communication—Students create artworks that demonstrate a sense of purpose & understanding of the relationship among form, materials, techniques, & subject matter. Benchmark A. Demonstrate mastery of materials, concepts, & personal concentration when creating original artworks. Indicator B. Create expressive networks that demonstrate a sense of purpose & understanding of the relationship among form, materials, techniques, & subject matter. English/Language Arts: 9. Research Standard: Students define & investigate self-selected or assigned issues, topics & problems. Benchmark: B. Evaluate the usefulness & credibility of data & sources. C. Organize information from various resources & select appropriate sources to support central ideas, concepts & themes. Technology: 5. Technology & Information Literacy: Students engage in information literacy strategies, use the Internet, technology tools & resources, & apply information-management skills to answer questions & expand knowledge. Benchmark B: Apply a research process model to conduct research & meet information needs. Library 5: Effective school library media programs provide information literacy skills instruction. Benchmark D: Utilizes a research model to locate, use, & evaluate information.

Lesson Summary: At the completion of this lesson, students will describe and apply the properties of similar and congruent figures and justify conjectures involving similarity and congruence. Students will also use coordinate geometry to represent and examine the properties of geometric figures. Students will represent and model transformations in a coordinate plane and describe the results. Estimated Duration: 5- 54 minute class periods Commentary: This lesson will allow students the opportunity to use a visual that they created to study the geometry benchmarks listed in the sidebar. Pre-Assessment: To begin, students and teacher will play “Simon Says” with an alien cut-out. The teacher will ask them to place the alien on a coordinate axis and then play the game asking students to rotate and translate the alien to different positions. An informal discussion will also take place to see if students recall the ideas of similarity and congruence. The teacher will draw a figure on the board and students will draw both congruent and similar figures in their notebooks. Scoring Guidelines: The scoring guidelines for the pre-assessment are teacher judgment and self-assessment. The teacher should ask students how many rotations and translations they correctly performed. The teacher will walk around and quickly check the drawings in the notebooks. Post-Assessment: Students will create two pictures from photos of John Nash using scalar geometry, following specific directions on their creations. Students must correctly complete the goals outlined on the direction sheet. Students will have the opportunity to revise their drawings until the concepts are mastered. Scoring Guidelines: Teacher will use attached rubric. Students will need to correctly label drawings, perform rotations and translations correctly, draw to correct scale and create a coordinate system for the drawings so others can label in the same way as the artist. Instructional Procedures: · Students search for a picture of John Nash that is desired- 4 copies should be made. Media specialist Librarian will assist students, using library computers and resources, to locate these pictures and in printing, or, copying them to get the initial picture to a workable size. · Teacher directed lesson explaining the concepts of congruence and similarity as well as rotations and translations. · Students will decide on the size of grid over picture and draw the grid over one copy of their photos- teacher needs to check grids for accuracy before beginning drawings. · Students will begin with congruent drawing- the student must use at least 3 rotations or translations- documenting their moves using a coordinate system correctly. Differentiated Instructional Support Describe how instruction can be differentiated according to learner needs, to help all learners either meet the intent of the specified indicator(s) or, if the indicator is already met, to advance beyond the specified indicator(s). Some students may only be required to perform the scalar drawing without the translations and rotations at this time. Students needing additional assistance will receive one-on-one help from the teacher. Since students in the class have low reading abilities (which hinder their ability to do well on story problems) the teacher wanted to utilize Gardner’s theory of multiple intelligences to complete some of the work. The bulk of the work dealt with right-brained, hands-on activities, such as typing on the computer keyboard, re-sizing pictures and re-drawing their pictures to scale using the overlying grid as a guideline. What we first took to be a distinct disadvantage, the inability to use a computer program to rotate and overlay the grid over a scanned picture turned out to be an advantage. The teacher believed that the hands-on practice of drawing and re-drawing the picture made this a more valuable means of achieving the task. It did, however, take more time than the computer program would have taken. Extension Students would have the opportunity, if done early, to go to our computer lab to playpractice using with the single copy of Photo sShop. Photo shop which allows a student to perform rotations on screen rather than by hand. Homework Options and Home Connections Most work on this project iswill be done in class. The kids students were assigned various homework assignments that dealt with rotations and translations from their books. Interdisciplinary Connections The study of John Nash can be connected to history and physics. This biographical unit was the beginning of studying these topics further and looking at his life as a historical figure. Unfortunately, information available was sketchy and repetitive. Information on his game theory was at a college level and inappropriate for this lesson and these students. Materials and Resources: For teachers Make a list of websites the students will use to find their pictures. A computer with printing capability must be available. The proximity of a copy machine that will enlarge pictures will save student time. If available, Photoshop or similar software can be used to do rotations and manipulate the size of the portrait on the computer screen. For students Paper, pencil, rulers, compasses and protractors. Key Vocabulary Scalar, rotation, translation, congruent, similar Technology Connections Students will utilize library The computers will be used to find locate pictures of John Nash. They will try school databases first and migrate to search engines, such as Google, only if the school resources cannot locate usable photographs. Photo shop can be used as a supplement. Free downloaded programs and Photoshop elements could not do the grids as required by the lesson. The cost of purchasing Photo shop for each library computers was not feasible as the program cost $249 cost per computer. Other avenues and grants were written to address this problem. Research Connections The librarian directed students to use www.infohio.org and to select the Britannica Encyclopedia icon. Students who preferred a different pose, a full-length pose, or a childhood photograph were further instructed to use Google. Since Google + Images is blocked by our filtering program, students needed to do a simple Google search and use images or pictures as the second keyword. Include research that supports the content or methods of instruction within the lesson. The librarian directed students to a specific search engine to eliminate the usage of Ask Jeeves and other natural language search engines that erode students’ ability to identify and refine search terms. Reference books were searched by the librarian but proved disappointing in that many did not contain pictures of John Nash. Students were able to utilize the pictures from the book, Beautiful Mind, if they so desired. General Tips Students should be given plenty of time to complete their drawings. Be ready to provide supplemental activities as some students will finish much more quickly than others. Attachments See attached for rubrics and a picture of the alien cutout. Also attached is the list of reference books searched for information on John Nash.