1: Circles and Arches within Architecture

2: Guide Creation Information

Guide Author

Jena Greig

District

Pine City High School, District 578

Date Created

06/08/11

Guide Description

Using the Geometry and Measurement Standards, students will increase their knowledge of the properties of circles. Introductory: Students will use rulers to measure the diameter to find the area or circumference of the circle in the picture.

Reinforce: Students will use the introductory level knowledge of circles along with using problem solving to reinforce pre-learned concepts of circles. If a spoke on a wheel breaks, at what length should I cut a new spoke? Students can also apply their knowledge of circles to partial arches within the picture. What is the degree and arc length of the wheel that you can see in the picture?

Mastery: Students will use the reinforcement level knowledge and apply scale factors by measuring the people in the picture, themselves, and the circle in the picture to create the real-life measurements. These measurements can be used to compare the measurements of similar figures today.

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)

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

  • Area and Volume by Jena Greig for the reinforcement level
  • Indirect Measurement Based on Architecture by Jena Greig for the Mastery Level

4: Standard Emphasized in Guide

Standard Title

Minnesota K-12 Academic Standards in Mathematics (2007)

Category

Mathematics 9-12

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

9.3.3.8

Benchmark 2: text

Know and apply properties of a circle to solve problems and logically justify results.

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 9-12

Strand

Geometry

Sub-strand

Geometry and Measurement

Standard

Calculate measurements of plane and solid geometric figures; know that physical measurements depend on the choice of a unit and that they are approximations.

Benchmark 1: standard number

9.3.1.1

Benchmark 1: text

Determine the surface area and volume of pyramids, cones and spheres. Use measuring devices or formulas as appropriate.

Benchmark 2: standard number

9.3.1.2

Benchmark 2: text

Compose and decompose two- and three-dimensional figures; use decomposition to determine the perimeter, area, surface area and volume of various figures.

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

Reading: standard text

Math: standard number

Math: standard text

Media Literacy: standard number

Media Literacy: standard text

Interdisciplinary Connection

Industrial Technology, Art

Minnesota Reflections Resources

7: Search Strategy

Things to Think About

  • What types of buildings use circles in their architecture?
  • What building elements use circles to embellish their building?
  • What vehicles use circles for movements?

Keywords

cars, trucks, automobile, wagon, tires, fire, church, water tower, windows

Other ideas (to assist with discovery)

Collections to consider:

Baptist General Conference History Center

Luther Seminary Archives

Norseland Lutheran Church

St. Benedict's Monastery

St. Scholastica Monastery

Topics to consider:

Agriculture, Animals, Religion, Transportation,

Challenges to finding resources on this standard

1. Sifting through so many buildings that are not churches when you search church directly.

2. Search Truck: Fire truck comes up so often even when there is no photograph of a fire "truck" in the photo.

8: Minnesota Reflections Top Picks

Title

Date created

Description

Format (photo, map, letter …)

"Cite the Item" link

Church in Winona

1880

Use the church window and arches.

Photo

http://reflections.mndigital.org/u?/wch,223

Old Winona High School

1985-1890

Use the arches in the window and of the photo.

Photo

http://reflections.mndigital.org/u?/wch,205

Geist Gazebo

1885

Use the Gazebo as a Circle and you can measure the arc length and sector area between posts

Photo

http://reflections.mndigital.org/u?/white,11

Howard Huntley

Use the wheels, steering wheel, lights, and her hat to measure.

Photo

http://reflections.mndigital.org/u?/wch,381

Blacksmith Shop

1888

Use the windmill, wagon and bike wheels to compare and contrast.

Photo

http://reflections.mndigital.org/u?/stearns,217

Dreveskraght Land Office, Morris, Minnesota

1910

Compare and Contrast the wheel of the car and wagon.

Photo

http://reflections.mndigital.org/u?/ste,1157

Winona Wagon Works

Use the wheel of the wagon.

Photo

http://reflections.mndigital.org/u?/wch,360

Fire Station

1895

Use the wheel of the wagon.

Photo

http://reflections.mndigital.org/u?/white,15

Hall's Store fire, Foley

1911

Use the wheel of the trucks, the hose, pant legs.

Photo

http://reflections.mndigital.org/u?/stearns,1632

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

10: Helpful Tips (optional)

People (look for fire or automobiles, fire), Animals (look for wagons), Arts and Architecture (look for cars, windows water towers, windmills), Religion (church, windows)

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

For lesson plans,geometry teachers could use the circles in these pictures to find the radius, circumference, diameter, area, and the volume of spheres, cylinders, and cones. For beginning level you can assign a radius and have the students find the circumference of the tire. To increase the level of difficulty, you can have them determine how many rotations it would take that particular tire to travel 1 mile, versus tires used today. You could find the surface area of the tire and compare it with tires today. There are also many partial circles in these pictures, students could measure the length of the arches in the pictures and use that to work backwards to find out about the circle as a whole.

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

http://www.customwagonwheels.com/wagon-wheels.html

http://www.innovativebalancing.com/Classicchart.htm

http://churchwindowrestoration.com/home