Author: Jim Wilson
Company: Mathematics Education

ACTIVITY
(Teams of 3 I think would work best here)

Materials needed:  A set of 1" by 1" squares, paper, pencil, calculator, blank overhead transparencies, and overhead pens
Activity:  The task of your team today is to explore all the  different dimensions of rectangles that can be constructed using  specific numbers of your square manipulatives.  
Example:  You  can only make one type of rectangle (dimension 1 x 2) with  	two squares.   
How many can be made with three squares? four squares? etc.  I want you to investigate this situation with your team.  Please keep a record of the data your team collects.
Discussion Questions: ( to be given to the teams after they have investigated the problem for a while - I don't want my questions to guide their explorations)
1)	Tell me about any and all  interesting patterns that your team has found.
2)	Can you find and discuss any mathematical reasons why these patterns 	would be occurring?
3)  Can you think of ways to categorize different numbers of squares based on 	their ability to form one or more rectangles?
Please take out your journals at this point and do the following entry individually.
 Journal Entry:  Tell me what you and your team have been working on today.  Explain how your team approached the investigation.  What do you think that you personally contributed to this investigation?  Try to briefly summarize the conjectures your team made about this activity.  Bring me your journal when you have finished this entry and return to your team to continue the investigation.
Presentation:  I would like your team to  now develop a presentation of your  mathematical findings and/or conjectures to the class.  You will all need to have a part in your team's presentation.   Please give me your team's discussion questions at the end of your presentation.    
Assessment:  This activity will be assessed in four ways.  First , each student will be assessed on his or her involvement in the team's activity.   Second, the student's team will be assessed on their explorations based on the discussion questions that they work on and turn in.   Third, the student will be assessed on his or her individual perception of the activity, conceptual understanding,  and ability to communicate that perception in a written form (the meaning constructed so far) .    Fourth, each student will be assessed on the presentation.   In assessing the student in these four areas (cooperative skills, investigations, conceptual understanding, and communication),  I feel I will send the students the message that the entire process of learning is important, not just the final results.