Ratios in Building Scale Models

This is the hands-on area of ratios! These activities are for students who like to get in there and get dirty—in other words, all middle schoolers. Here they can make models, maps, floor plans, and pyramids, or consider the length of the Statue of Liberty's nose. All the problems deal with the idea of scale, the application of a scale factor, and the central question: What changes when an object is enlarged or shrunk to scale?

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Floor Plan Your Classroom: Make an Architectural Plan in 3 Steps http://www.math-kitecture.com/floor.htm

This resource guides the learner step-by-step in creating a floor plan of a classroom. The directions include drawings of student work. The three parts of the activity are: sketching a map of the classroom, making a scale drawing from the sketch, and drafting a CAD (computer-aided design) floor plan from the drawing. MSP full record

Statue of Liberty: Is the Statue of Liberty's Nose Too Long? http://www.figurethis.org/challenges/c61/challenge.htm

The full question is: "The arm of the Statue of Liberty is 42 feet. How long is her nose?" To answer the question, students first find the ratio of their own arm length to nose length and then apply their findings to the statue's proportions. The solution sets out different approaches to the problem, including the mathematics involved in determining proportion. Extension problems deal with shrinking a T-shirt and the length-to-width ratios of cereal boxes. MSP full record

Scaling Away http://illuminations.nctm.org/LessonDetail.aspx?id=L584

For this one-period lesson, students bring to class either a cylinder or a rectangular prism, and their knowledge of how to find surface area and volume. They apply a scale factor to these dimensions and investigate how the scaled-up model has changed from the original. Activity sheets and overheads are included, as well as a complete step-by-step procedure and questions for class discussion.

Build a Solar System Activity http://www.exploratorium.edu/ronh/solar_system/index.html

This activity provides instructions for making a scale model of the solar system, including an interactive tool to calculate the distances between the planets. The student selects a measurement to represent the diameter of the Sun, and the other scaled measurements are automatically calculated. Students can experiment with various numbers for the Sun's diameter and see how the interplanetary distances adjust to the scale size. MSP full record

Mathematics of Cartography: Mathematics Topics http://math.rice.edu/~lanius/pres/map/mapmat.html

This web page looks at scale in relation to making maps. It discusses coordinate systems as well as the distortions created when projecting three -- dimensional space onto a two-dimensional paper. One activity here has students use an online site to create a map of their neighborhoods-to scale, of course! (MSP full record

Two Scale Models of the Earth-Moon System http://www.dnr.state.oh.us/geosurvey/edu/hands10.htm

Using information on the diameters of the Earth and the moon and the distances between the bodies, students construct scale models of the Earth-moon system. The page explains, but does not illustrate, how one of these models may be used to simulate solar and lunar eclipses. Although the activity seems designed as a hands-on investigation for older students, the idea could be adapted for middle school students. MSP full record

Size and Scale http://school.discovery.com/lessonplans/programs/sizeandscale/index.html

This is a challenging and thorough activity on the physics of size and scale. Again, the product is a scale model of the Earth-moon system, but the main objective is understanding the relative sizes of bodies in our solar system and the problem of making a scale model of the entire solar system. The site contains a complete lesson plan, including motivating questions for discussion and extension problems. MSP full record

Scaling the Pyramids http://www.pbs.org/wgbh/nova/pyramid/geometry/index.html

Students working on this activity will compare the Great Pyramid to such modern structures as the Statue of Liberty and the Eiffel Tower. The site contains all the information needed, including a template, to construct a scale model of the Great Pyramid. Heights of other tall structures are given. A beautifully illustrated site! MSP full record

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Copyright June 2006 — The Ohio State University. This material is based upon work supported by the National Science Foundation under Grant No. 0424671. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

This work is licensed under a Creative Commons License.