1: Indirect Measurement based on Architecture

2: Guide Creation Information

Guide Author	Jena Greig
District	Pine City Public School, District 578
Date Created	06/08/2011
Guide Description	Using the Geometry and Measurement Standards, students will use indirect measurement and proportions to find lengths, areas, and volumes that cannot be physically measured. Introductory: Students will use rulers to measure the height of a person create a proportion with their height to find the height of an object in the photograph. Reinforce: Students will use problem solving to show how they can apply one proportion to other objects in the photograph. (I.e. students could create slideshows showing how they used one proportion, in order to find the measurements of five other objects in the photo. Mastery: Students will use the reinforcement level of knowledge and apply scale factors by having students measure the people in the picture and themselves to create the Real-life "stories" of what is mathematically going on in the photo and compare the measurements to those within their own house, church, or grocery store.

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	Surface Area and Volume by Jena Greig remember that scale factor k can be applied to area as k² and to volume as k³

4: Standard Emphasized in Guide

Standard Title	Minnesota K-12 Academic Standards in Mathematics (2007)
Category	Grades 9-12
Strand	Geometry and Measurement
Sub-strand
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 formula
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

5: Another Standard Emphasized in Guide (optional)

Standard Title	Minnesota K-12 Academic Standards in Mathematics (2007)
Category	Grades 9-12
Strand	Geometry and Measurement
Sub-strand
Standard	Solve real-world and mathematical geometric problems using algebraic methods.
Benchmark 1: standard number	9.3.4.2
Benchmark 1: text	Apply the trigonometric ratios sine, cosine and tangent to solve problems, such as determining lengths and areas in right triangles and in figures that can be decomposed into right triangles. Know how to use calculators, tables or other technology to evaluate trigonometric ratios.
Benchmark 2: standard number	9.3.4.7
Benchmark 2: text	Use algebra to solve geometric problems unrelated to coordinate geometry, such as solving for an unknown length in a figure involving similar triangles, or using the Pythagorean Theorem to obtain a quadratic equation for a length in a geometric figure.
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	Art, Industrial Technology

Minnesota Reflections Resources

7: Search Strategy

Things to Think About	What pieces in each picture would be physically unable to be measured? What pieces in the background could be measured with indirect measurement?
Keywords	Angles, Lengths, Scale Factor, Trigonometry
Other ideas (to assist with discovery)	Teachers can have students measure the lengths in the pictures provided and apply a scale factor to create a model or "blue prints" of the building or do some type of renovation of the building.
Challenges to finding resources on this standard	Finding pictures that have direct or ¾ viewing so that angles can be measured, and straight lines so that lengths can be measured and scale factors applies.

8: Minnesota Reflections Top Picks

Title	Date created	Description	Format (photo, map, letter)	"Cite the Item" link
Fillebrown House, White Bear Lake	1970-1978	Use the window of the house to create a proportion, and find the height and length of the house and tree in the background	Photo	http://reflections.mndigital.org/u?/white,159
Ogden Hall Construction, Winona State	1908?	Construction site. You can use the beams to measure angles and prove similarity between the beams	Photo	http://reflections.mndigital.org/u?/winona,501
Old Main at Winona State	1900?	Using the building with scale factors you could assign a height to the building and the students could find 5 other measurements	Photo	http://reflections.mndigital.org/u?/winona,497
Winona High School Graduation	1886-1887	Using the average height of a person in that year you can find the height of the arch in the building,	Photo	http://reflections.mndigital.org/u?/wch,314
Oddfellows Building	1885	Using the scale factor of a person or of the horse, students can then find the heights of the building	Photo	http://reflections.mndigital.org/u?/wch,309
Unitarian Church	1895-1899	Using the angles and scale factors, you can prove which pieces are the church are similar or congruent.	Photo	http://reflections.mndigital.org/u?/wch,290
7^th Annual Report of the state board of health of Minnesota	1879	Students can use these heights for the people in the pictures	Text	http://reflections.mndigital.org/u?/mdh,607
Winona, MN, water tower	1895-1899	Using the height of the building and a scale factor to find the actual height of the water tower.	Photo	http://reflections.mndigital.org/u?/wch,273
Englelbert Greven Dry Goods and Mme E. Geise & Co	1875	Using the façade of the building to find measurements, using the double picture to prove congruence.	Photo	http://reflections.mndigital.org/u?/wch,260
Hawkes residence, Waseca	1902	Using the angles and lengths of the house to find a scale factor.	Photo	http://reflections.mndigital.org/u?/was,491

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

Winona County Historical Society

Any County Historical Society

10: Helpful Tips (optional)

Search by Topic: Education and Religion

Within these two topics there are a lot of pictures of buildings with people standing in them to create easy proportions.

Search Key Words: House, Architecture, Buildings especially in Art and Architecture

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

Teachers could have students measure the lengths in the photographs, and apply the actual dimensions of the house to create a possible floor plan.
Students could measure angles of the roofs and to find the area of the walls to help with renovation projects on the house.
Students could measure the pitch of the roof and the length of the house; using Pythagorean theorem they could find the height of the roof, while checking proportionality.
Knowing that angles stay constant in proportionality, they could measure the angle of the roof or a beam in the picture and find a missing side length of a triangle created in the picture.