Paul's Piglet Pandemonium Math Problem!

Third graders are working on a problem similar to "Janet's Chicken Problem."  In this problem students are, once again, building models.  Instead of using a one-foot paper strip to represent each foot of fencing, students are using a three-inch strip to represent each foot of fencing. Upon completion of this problem, students will compare piglet pen models to those discovered for "Janet's Chicken Problem."  One of the questions posed to students is:  

What happens to the area of a rectangle when the dimensions 

                                   change but the perimeter remains the same?  

Paul’s Piglet Pandemonium

Paul has a problem.  His pig Peggy has just delivered 8 little piglets.  Paul is going crazy.  The piglets are always underfoot when he goes out to feed Peggy.  He keeps tripping over them and then falls into the mud.  Paul has decided to build a special “piglet pen” just for the piglets so they can run around and roll in the mud all they want.  Paul has 24 feet of fencing to use to build the pen.  He is asking for your advice on the best dimensions for his piglet pen!

Criteria:     You must use all 24 feet of the fencing.

                  All of the piglet play spaces must be rectangular in shape.

   (Remember that a square is also a rectangle.)

1.      Use paper strips or linear pieces to determine all of the possible pens Paul can build that will have a perimeter of 24 feet. 

2.   Neatly sketch them onto your graph paper and then cut them out.

3.   Glue them onto your poster. 

4.   Label the perimeter (dimensions) and the area for each possible piglet pen.

5.   Use math equations to show your math work on your poster.  How did you determine the perimeter and the area?

Building a 1' X 9' model.

Building a 6' X 6' model.

Building a 5' X 7' model.

Sketching the models.

Organizing sketched models on a poster.

 Organizing sketched models on a poster.