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Guide Author |
Jena Greig |
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District |
Pine City High School, District 578 |
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Date Created |
06/10/11 |
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Guide Description |
Using the Geometry and Measurement Standards, students will increase their knowledge of symmetry and transformations. Students need to be able to identify the main types of transformations including translation, rotation, reflection, and dilation. By using the photographs in this guide, as well as others, teachers can show real life examples of these transformations. As an extension project, students can learn to recognize point and line symmetry, and know the difference between the two. By looking at a circular window of a church, students can recognize point symmetry and decide how many rotations exist within that object (or how many folds it has). Students can also look at line symmetry and see the translations and reflections that exist within that particular section. This guide can be used as a reinforcement level of learning or can be modified to be used as an extension project for students while the teacher works to review with others in the class (differentiated learning). |
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Title of Main Academic Standard used in Guide |
Minnesota K-12 Academic Standards in Mathematics (2007) |
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Grade Level |
9-12 |
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Learning Level |
Reinforce |
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National Holiday/Special Occasion (optional) |
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Source Format Emphasized |
Photographs |
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Geographic Region Emphasized (optional) |
The collections that I used were all of the Minnesota Colleges and Universities, but it does not have to be restricted to just those collections. |
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Other Minnesota Reflections Guide(s) Related to this Guide (optional) |
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Standard Title |
Minnesota K-12 Academic Standards in Mathematics (2007) |
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Category |
Mathematics |
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Strand |
Geometry and Measurement |
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Sub-strand |
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Standard |
Solve real-world and mathematical geometric problems using algebraic methods. |
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Benchmark 1: standard number |
9.3.4.6 |
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Benchmark 1: text |
Use numeric, graphic and symbolic representations of transformations in two dimensions, such as reflections, translations, scale changes and rotations about the origin by multiples of 90˚, to solve problems involving figures on a coordinate grid. |
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Benchmark 2: standard number |
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Benchmark 2: text |
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Benchmark 3: standard number |
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Benchmark 3: text |
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Benchmark 4: standard number |
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Benchmark 4: text |
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Standard Title |
Minnesota K-12 Academic Standards in Mathematics (2007) |
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Category |
Mathematics |
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Strand |
Geometry and Measurement |
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Sub-strand |
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Standard |
Know and apply properties of geometric figures to solve real-world and mathematical problems and to logically justify results in geometry. |
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Benchmark 1: standard number |
9.3.3.6 |
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Benchmark 1: text |
Know and apply properties of congruent and similar figures to solve problems and logically justify results. |
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Benchmark 2: standard number |
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Benchmark 2: text |
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Benchmark 3: standard number |
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Benchmark 3: text |
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Benchmark 4: standard number |
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Benchmark 4: text |
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Reading: standard number |
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Challenges to finding resources on this standard |
Finding pictures that had the entire façade of the building or 2 full sides of the building was the biggest challenge. |
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Title |
Date created |
Description |
Format (photo, map, letter) |
"Cite the Item" link |
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1935 St. Scholastica Graduates (Many of these type of photos) |
1935 |
Students could use the doors, people formation to talk about the reflective properties |
Photo |
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Nurse Capping ceremony at St. Scholastica |
1955 |
Students could use the arches in the background to talk about the transformation within architecture and CAD drawing today. |
Photo |
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Our Lady Queen of Peace Chapel St. Scholastica |
1949 |
Students could use the arches of the building to talk about scale factors, translations, and how to map this building into a CAD program. |
Photo |
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ArchbishopIreland reviewing the Cadets |
1917 |
Students could describe and label the symmetry with the cadets in the photo. |
Photo |
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Coach Rogers, University of St. Thomas |
1907 |
Students can explore the symmetry within the human face: reflection, translation and the golden ratio. |
Photo |
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1892 Republican National Convention Guest's Ticket |
1892 |
Back side especially students can note the rotational and point symmetry |
Ticket |
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Edwards Hall, Macalester College |
1892 |
Students should note the symmetry of the windows and porch. |
Photo |
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Hamline Methodist Episcopal Church |
1900 |
Students should note the symmetry from the North and East side of the building. |
Photo |
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Detached Ward, State Hospital for the Insane, St. Peter, Minnesota |
1900-1920 |
Students should note the reflection symmetry of the façade' |
Photo |
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Collections to consider: Basilica of St. Mary's, Bethel University, Carlton College, College of St. Catherine, College of St. Scholastica, Concordia University, Gustavus Adolphus College, Hamline University, Hazelden Foundation Using churches and colleges were the easiest collections to find symmetry. |
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Teachers can use the pictures in the Minnesota Reflections to aid with their teaching of Symmetry and Transformations. The pictures here in this guide give great examples of point symmetry (rotational), examples include circular church stained glass windows. There are also great examples of translational symmetry, examples include repeated archways along the side of building. Relational symmetry is easy to show with houses, faces, churches, and buildings. The last type of symmetry would be a dilation, which can be shown through circles, archways, and different sized windows on the buildings. The teacher could assign each group a different picture and the students could present all of the different symmetries that they found in their photograph. |
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Links Learning http://www.linkslearning.org/Kids/1_Math/2_Illustrated_Lessons/4_Line_Symmetry/index.html |
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Intuitive Symmetry - Point, Line, Plane, Rotational http://regentsprep.org/Regents/math/geometry/GT1a/indexGT1a.htm |
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Symmetry Web quest |