

Session 3: Finding Areas and Perimeters of Complex Shapes  
Objectives


Readings  
The following reading contains excerpts drawn from Issues in Mathematics Education: The Mathematical Education of Teachers, which discusses some current thinking about critical content, pedagogy, and policy related to the professional development of mathematics teachers. The reading focuses on geometry and measurement in elementary classrooms. This assessment and sampling of student work from the Investigations in Number, Data, and Space curriculum unit "Flips, Turns, and Area" illustrates a range of student work dealing with the areas of complex shapes. 

Activities  
1.  Do the "Going Around" activity with the pattern blocks virtual manipulatives to determine the perimeters of complex shapes.  
2. 
Do the "Exploring Area with Online Manipulatives" activity with the tangram virtual manipulatives to determine the areas of complex shapes. 

3.  View samples of student work from the "Exploring Area with Online Manipulatives" activity.  
4.  In
your Learning Log, respond to the following:


5.  Use the Digital Drop Box to send your Learning Log to your facilitator. (Your Learning Log should include entries from Sessions 2 and 3). If you did not already do so, please print out the Digital Drop Box instructions and read the "Uploading Files to the Digital Drop Box" section. Alternatively, you can email your Learning Log, as an attachment, to your facilitator.  
6.



7.

Watch the "A Common Misconception" video to observe one student's thinking as he tries to determine the area of the twosquareunit triangle. Notice how he confuses the idea of the fractional part of the whole with the concept of square units of area.  
8.

Watch the "Finding Areas of Complex Figures" video to see students using tangram pieces to help them determine the areas of complex figures. Note the multiple routes that students took to determine their answers.


Discussion  
Use the Discussion Board to address the following:  
1.

Reflect on your observations of the students from the three videos. What misconceptions did you observe and what questions could you ask to clarify their misunderstandings or deepen their thinking?  
2.

Read the responses in the Discussion Board and contribute to the conversation. If you like, you may review the expectations for contributing to the online discussion.  
Additional Activities (Optional)  
1.

"My Geoboard Shape" is an online activity designed to determine areas of complex shapes using a virtual geoboard.  
2.

"Tangram Areas I" and "Tangram Areas II" are handson activities using tangram pieces to determine the areas of shapes. These are the activities that the students participated in during the videos.  
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