1: Symmetry and Transformations

2: Guide Creation Information

Guide Author

Jena Greig

District

Pine City High School, District 578

Date Created

06/10/11

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).

3: Guide Characteristics

Title of Main Academic Standard used in Guide

Minnesota K-12 Academic Standards in Mathematics (2007)

Grade Level

9-12

Learning Level

Reinforce

National Holiday/Special Occasion (optional)

Source Format Emphasized

Photographs

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.

Other Minnesota Reflections Guide(s) Related to this Guide (optional)

4: Main Standard Emphasized in Guide

Standard Title

Minnesota K-12 Academic Standards in Mathematics (2007)

Category

Mathematics

Strand

Geometry and Measurement

Sub-strand

Standard

Solve real-world and mathematical geometric problems using algebraic methods.

Benchmark 1: standard number

9.3.4.6

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.

Benchmark 2: standard number

Benchmark 2: text

Benchmark 3: standard number

Benchmark 3: text

Benchmark 4: standard number

Benchmark 4: text

5: Another Standard Emphasized in Guide (optional)

Standard Title

Minnesota K-12 Academic Standards in Mathematics (2007)

Category

Mathematics

Strand

Geometry and Measurement

Sub-strand

Standard

Know and apply properties of geometric figures to solve real-world and mathematical problems and to logically justify results in geometry.

Benchmark 1: standard number

9.3.3.6

Benchmark 1: text

Know and apply properties of congruent and similar figures to solve problems and logically justify results.

Benchmark 2: standard number

Benchmark 2: text

Benchmark 3: standard number

Benchmark 3: text

Benchmark 4: standard number

Benchmark 4: text

6: Additional Standards and/or Skills (reading, math, media literacy, interdisciplinary)

Reading: standard number

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.

8: Minnesota Reflections Top Picks

Title

Date created

Description

Format (photo, map, letter)

"Cite the Item" link

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

http://reflections.mndigital.org/u?/p15160coll8,90

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

http://reflections.mndigital.org/u?/p15160coll8,74

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

http://reflections.mndigital.org/u?/p15160coll8,83

ArchbishopIreland reviewing the Cadets

1917

Students could describe and label the symmetry with the cadets in the photo.

Photo

http://reflections.mndigital.org/u?/thomas,107

Coach Rogers, University of St. Thomas

1907

Students can explore the symmetry within the human face: reflection, translation and the golden ratio.

Photo

http://reflections.mndigital.org/u?/thomas,172

1892 Republican National Convention Guest's Ticket

1892

Back side especially students can note the rotational and point symmetry

Ticket

http://reflections.mndigital.org/u?/macal,302

Edwards Hall, Macalester College

1892

Students should note the symmetry of the windows and porch.

Photo

http://reflections.mndigital.org/u?/macal,60

Hamline Methodist Episcopal Church

1900

Students should note the symmetry from the North and East side of the building.

Photo

http://reflections.mndigital.org/u?/hmu,206

Detached Ward, State Hospital for the Insane, St. Peter, Minnesota

1900-1920

Students should note the reflection symmetry of the façade'

Photo

http://reflections.mndigital.org/u?/gust,257

9: Specific Minnesota Reflections Collection(s) to Consider (optional)

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.

10: Helpful Tips (optional)

11: Ideas for Lesson Plans Using this Guide (optional)

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.

12: Other Online Collections that Help teach this Standard (optional)

Links Learning http://www.linkslearning.org/Kids/1_Math/2_Illustrated_Lessons/4_Line_Symmetry/index.html

Intuitive Symmetry -
Point, Line, Plane, Rotational http://regentsprep.org/Regents/math/geometry/GT1a/indexGT1a.htm

Symmetry Web quest

http://www.adrianbruce.com/Symmetry/