1: Surface Area and Volume

2: Guide Creation Information

Guide Author	Jena Greig
District	Pine City High School, District 578
Date Created	06/08/2011
Guide Description	Using the Geometry and Measurement Standards, students will increase their knowledge of surface area and volume. Introductory: Students will use rulers to measure the lengths and widths of buildings in the picture to find the surface area and the volume. Reinforce: Students will use their introductory level of knowledge and problem solving skills to reinforce pre-learned concepts. How much would it cost to paint this building? How many shingles would you need and what would it cost to re-shingle this house? If we wanted to fence off an area that was four times as many square feet as the house, where could the fence go? Mastery: Students will use their reinforcement level of knowledge and apply scale factors in length, area, and volume. If we wanted to double the square footage of this house, what would that do to the volume and the length of each side of the house?

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)	· Indirect Measurement Based on Architecture by Jena Greig to find missing measurements · Circles and Arches within Architecture by Jena Greig to find the areas of the circles within the picture (especially on church windows) · Natural Disasters by Ann Woell

4: Main 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	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	9.3.1.4
Benchmark 3: text	Understand and apply the fact that the effect of a scale factor k on length, area and volume is to multiply each by k, k² and k³, respectively.
Benchmark 4: standard number	9.3.1.5
Benchmark 4: text	Make reasonable estimates and judgments about the accuracy of values resulting from calculations involving measurements.

5: Another Standard Emphasized in Guide (optional)

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	9.3.3.7
Benchmark 2: text	Use properties of polygons-including quadrilaterals and regular polygons-to define them, classify them, solve problems and logically justify results.
Benchmark 3: standard number	9.3.3.8
Benchmark 3: text	Know and apply properties of a circle to solve problems and logically justify results.
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, Engineering, Art

Minnesota Reflections Resources

7: Search Strategy

Things to Think About	What type of architecture could be renovated? What types of buildings need to be repainted or re-shingled? What type of area is needed for construction?
Keywords	Buildings: Houses, Schools, Churches, Façade' Ruins, Fire, Architecture
Other ideas (to assist with discovery)
Challenges to finding resources on this standard	Finding pictures of buildings that were orthogonal photos so that angles could be measured. Finding Fire and Ruins pictures that still had the shell of the buildings so that students could measure the base and height so that they could mathematically rebuild on that site.

8: Minnesota Reflections Top Picks

Title	Date created	Description	Format (photo, map, letter)	"Cite the Item" link
Odd Fellows Hall, Mankato, MN	1914	Building, Original	Photo	http://reflections.mndigital.org/u?/blue,1826
Odd Fellows Hall, Mankato, MN	1914	Building, Renovated	Photo	http://reflections.mndigital.org/u?/blue,1827
Elks New Lodge Mankato, MN	1911	Building, Original	Photo	http://reflections.mndigital.org/u?/blue,1828
Elks Lodge Mankato, MN	1911	Building, Renovated	Photo	http://reflections.mndigital.org/u?/blue,1829
Red Jacket, Mankato MN	1911	Bridge Construction	Photo	http://reflections.mndigital.org/u?/blue,1831
Spectators viewing burned out shell	1915	Building post fire, how could we renovate, cost?	Photo	http://reflections.mndigital.org/u?/blue,1867
Fire of 1918, Cloquet, MN	1918	How can we renovate after a fire?	Photo	http://reflections.mndigital.org/u?/carl,100
Noah's Arch Pavilion Madison, MN	1923	Pavilion	Photo	http://reflections.mndigital.org/u?/blue,1901
Log House, Blue Earth County	1923	Log House	Photo	http://reflections.mndigital.org/u?/blue,1914

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

Jackson County Historical Society

Lake of the Woods Historical Society

Minnesota Museum of Mining

Minnesota Street Car Museum

Murray County Historical Society

10: Helpful Tips (optional)

Search by Topic: Agriculture, Arts and Architecture, Education, Religion

Buildings are the most beneficial for this guide. Water towers and cylinders are also helpful, as is any solid prism or cylinder of any kind that students can use to find the surface area and volume.

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

For an introductory level, teachers can use these pictures to find the surface area of the façade or the entire structure of a building. To bring this into the level of reinforcement, students can find the surface area and the volume, and use that information to paint, re-surface, put a new roof on and calculate the cost of all of the renovations. To create a level of mastery, students could do all of the reinforcement level and also calculate the cost of doubling or tripling the dimensions of the building.

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

http://www.menards.com/main/building-materials/c-5640.htm (does not have to be Menards)