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Real World Math: Complex Area

 

Curator: William Stremple

 

Name & Link to Tech Tool or Tool homepage: http://www.realworldmath.org/measurement-lessons.html

 

Brief Description of Tech Tool: Complex Area provides students with three problems involving three crops fields. Students are asked to calculate the area of each field, convert it to acres, number of bushels, and finally the cost of each bushel according to specific values. After doing this with three fields, students are asked to compare the difference in two crops.

 

Technical & Cost considerations: This is a free tool. It requires Google Earth to be downloaded in order to work. There are no other special considerations (it worked just fine when all computers in my school were being used for benchmark testing).

 

Evaluation

Description of Learning Activity

 

Complex Area can be used in a variety of ways: to work through as a whole class, in groups, or even individually. Students will need a basic understanding of calculating area of simple shapes (rectangles/squares) and proportions. This tool forces students to think critically and search for answers. When I used these problems in class, I would not let them measure two sides of the corn field and forced them to use the other sides of the shape to figure out the missing lengths.

 

1. Learning Activity Types

 

  • Practice - Students are provided with a chance to practice calculating area and converting units using proportions.

  • Explore - Students are presented with several problems and asked to find various solutions.

  • Apply - The problems apply the mathematical skills and knowledge to real-world situations.

 

2. What mathematics is being learned?

 

NCTM Standards

  • NCTM-Geo-analyze - analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships;

  • NCTM-Geo-visualization - use visualization, spatial reasoning, and geometric modeling to solve problems.

 

VA SOL Strands

  • 8.11 - The student will solve practical area and perimeter problems involving composite plane figures.

 

Proficiency Strands

  • conceptual understanding - Students practice calculating area and perimeter of complex shapes.

  • procedural fluency - Accuracy will be important in calculation of area. This will affect the acres, bushels, and amount of money per bushel.

  • adaptive reasoning - Students use logic to create multiple strategies on how to calculate area and perimeter of complex shapes.

  • productive disposition - Students are faced with problems that require knowledge of realistic events.

 

3. How is the mathematics represented?

 

Complex Area represents the mathematics as a virtual manipulative. Google Earth provides an aerial view of the crop field and asks students to use the measurement tool to find the lengths of each side. Being able to manipulate the field, but not alter its dimensions is definitely a plus so students have different options of how to look at the shape, but it will remain constant. The technology makes it possible for students to view crop fields from hundreds of miles away.

 

4. What role does technology play?What advantages or disadvantages does the technology hold for this role? What unique contribution does the technology make in facilitating learning?

 

Advantages

Provides a bridge to other disciplinesAllows students to visualize geometric shapes in relation to real-world situationsIt might be beneficial to do some research on the actual costs of bushels of the crops.

Disadvantages

Anytime Google Earth is used by students it needs to be monitored closely.It may be difficult for some students to visualize how to separate the field into smaller simple shapes. (I provided students with a handout that had each shape drawn on it)

Unique Contribution

Students work at their own pace and the instructor is available to circulate the room and help where needed.

 

Affordances of Technology for Supporting Learning

Computing & Automating - Based on the predetermined shapes, students calculate area of the fields and use proportions to convert units.

Accessing Information - Students use Google Earth to access the problems and tools to solve the problems.

Communicating & Collaborating - Students work in pairs/groups to produce answers to the posed problems.

 

5. How does the technology fit or interact with the social context of learning?

 

This tech tool would best fit my students if it was used by pairs/groups sharing a computer. The collaboration would allow students to bounce ideas off each other and come up with unique strategies for finding area of complex shapes. The technology also forces students to assign roles for who does what in relation to the measurements and navigation of the tool.

 

6. What do teachers and learners need to know?

 

The teacher and learners need to have knowledge of how to navigate Google Earth. The tabs along the left side help navigate through each problem. Clicking on these tabs/arrows will open the 'folder' for each problem.

 

In addition, if you need to access the lesson plans for this lesson you will need the password: mango. This will allow you access to the standards and any handouts or extra sheets that accompany the lesson.

 

7.  How could this resource supplement/facilitate PBL?

This resource can be used to facilitate PBL because it presents students with problems they are asked to sovle.  These problems are related to real-life scenarios.

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