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EAST ALLEN COUNTY SCHOOLS Bundle 6 Geometry Algebra to Geometry Big Idea: Bridges Enduring Understandings Essential Questions The coordinate plane can be used to prove geometric theorems. The coordinate plane can be used to compute area and perimeter of geometric shapes. Equations of lines are used to prove that lines are parallel or perpendicular. Distance formulas can be used to find the ratios of divided segments. CC/Learning Targets G.GPE.4 G.GPE.5 How could the coordinate plane be used to prove geometric theorems of quadrilaterals algebraically? How can the coordinate plane be used to algebraically calculate the area and perimeter of geometric shapes? How could a segment be partitioned into a given ratio? Core Vocabulary Links to Technology G.GPE.6 G.GPE.7 Bundle Performance Task(s) Groups will design and plan a fictional city using the Bundle 6 Performance Task Worksheet. The groups will be divided into the following roles: architect, supplier, and councilman. The city needs to include a name and projected population, six parallel streets, two transversal streets, and one perpendicular street. The city must include the following buildings: a gas station and restaurant with alternate exterior angles, a house and school with alternate interior angles, a courthouse and bank with vertical angles, a hardware store and church with corresponding angles. Don’t forget to include a traffic light at two intersections. The groups will need to name and label each building and street. The project will be created on a poster board. The groups will need to use crayons, colored pencils, or markers to draw the city. Three-dimensional objects may be used as well. Geometry Bundle 6 Quarter 3 Feb.-Mar. Geometry Bundle 6 CC/Learning Targets Resource of Ideas G.GPE.4 (G.1.1b) (G.2.6a) (G.3.1h) (G.3.4a-b) (G.4.9a-c) (G.6.3a) (G.6.8b) (G.7.5b) G.GPE.5 (G.1.4a-c) (G.4.2g) (G.8.8a) Use coordinates to prove simple geometric theorems algebraically. For example, prove or disprove that a figure defined by four given points in the coordinate plane is a rectangle; prove or disprove that the point (1, √3) lies on the circle centered at the origin and containing the point (0, 2). -Triangle Midsegments -Properties of Quadrilaterals using coordinate plane -Quadrilateral properties Prove the slope criteria for parallel and perpendicular lines and uses them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). -Equation of parallel and perpendicular lines -Slope G.GPE.6 (G.1.1c-d) (G.4.5b) Find the point on a directed line segment between two given points that partitions the segment in a given ratio. G.GPE.7 (G.1.4a) (G.2.1a) (G.2.2a-c) (G.2.5a-d) (G.3.1b,g) (G.3.2a,b) (G.3.3a-c) (G.4.7a-d) Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula. Correlating CC/Learning Targets G.CO.1 G.CO.6 G.SRT.1. G.SRT.2 Evidence of Learning -Journal -Note Card/Flash Card -Graphing -Homework -Prentice Hall Mathematics Lessons 5.1, 6.1, 6.7, 7.6, 7.7, 10.7 -iBook Prentice Hall Geometry Lessons 1.7, 6.7 -Homework -Journal -Graphing -White Board -Quiz/Test -Prentice Hall Mathematics Lessons 5.2, 5.3 -iBook Prentice Hall Geometry Lessons 3.7, 3.8, 7.3, 7.4 -Prentice Hall Mathematics Lessons 8.4, 8.5 -Worksheet -Class Discussion -Area and Perimeter of polygons -Graphing -White Board -Quiz/Test -Prentice Hall Mathematics Lessons 1.6, 1.7, 6.3, 6.5, 7.1-7.5, 8.6 -iBook Prentice Hall Geometry Lessons 6.7, 10.1, 10.7 Teacher Notes All embedded apps included in this curriculum are free. Geometry G.CO.7 G.CO.8 G.CO.9 G.CO.10 G.CO.11 G.CO.12 G.CO.13 G.MG.1 G.MG.2 G.MG.3 Bundle 6 G.SRT.3 G.SRT.4 G.SRT.6 G.SRT.7 G.SRT.8 G.SRT.9 G.SRT.10 G.SRT.11 G.GMD1 G.GMD.3 G.C.2 Name: ____________________________ Date:___________________ CITY PROJECT You will work in a group. Each group should have the following roles filled by different students: City Planner (makes up the names of streets and buildings) ___________________ Architect (builds/draws the streets and buildings) Supplier (gathers/delegates supply list for the group) ___________________ ___________________ Councilman (checks design has all requirements/appearance) ___________________ You and your group are to design your own city and include the following: 1. City name and population at the top of the project 2. Six parallel streets (each street must be named) 3. Two transversal streets (each street must be named) 4. One perpendicular street (each street must be named) The following buildings must be placed as directed: 1. The gas station and restaurant must be alternate exterior angles 2. Your house and school must be alternate interior angles 3. Courthouse and bank must be vertical angles 4. Hardware store and church must be corresponding angles 5. Traffic light at two intersections (draw 3 circles on top of each other like a stop light) 6. Name and label each building 7. Use crayons or colored pencils to draw your city or use 3-dimensional objects. BE CREATIVE!!!!! 8. Build the final city on poster board 9. Turn in this sheet with your project CHECKLIST: ITEM Parallel streets (named) Transversal streets (named) Perpendicular street (named) Hospital (name/location) Department Store (name/location) Gas station (named/location) Restaurant (named/location) House (named/location) School (named/location) Courthouse (named/location) Bank (named/location) Hardware Store (named/location) Church (named/location) Traffic lights (named/location) General appearance POINTS POSSIBLE 6 2 1 3 3 3 3 3 3 3 3 3 3 2 9 POINTS RECIEVED