Comparing "Janet's Chicken Rehabilitation Pen Problem" with "Peggy's Piglet Pandemonium Problem!"

Students completed work on Peggy's Piglet Pandemonium 
and then gathered around two posters to 

discuss similarities and differences.  

All possible chicken rehabilitation pens.

All possible piglet pens. 

Below is what the board looked liked when the students ended the discussion.  

There were many, many connections, ideas, thoughts, etc., but only a few are on 

the board.   Third graders did a great job explaining their thinking and reasoning. 

                   What students noticed:

"The rectangles start out tall and skinny and get wider and shorter."

"The greater the perimeter, the more possible 

rectangular pens you can make."

"The piglet's pen has more possible rectangles because 

it has 4 more feet of fencing."

“'Janet's Chicken Rehabilitation' problem ends with a pen 

that is 5’ X 5’ and there are 5 possible rectangular play spaces.  

'Peggy's Piglet’s Pandemonium' problem ends with a pen that 
is 6’ X 6’ and there are 6 possible rectangular play spaces.”

"The 1' X 9' and the 1' X 11' pens have the least amount of 

square feet and the square pens have the most square feet."

Students then wondered...

“Would using any number of feet for the perimeter 

always end with a square pen?”

Eliot's conjecture: "I think the number of feet of fencing 

would have to be a multiple of 4.

Students decided to test these hypotheses. 

They got busy, this time using linear pieces to

represent feet and then recording the results on

centimeter graph paper.

 Findings!

Teams	Perimeter in Feet	Did it end in a Square?	Dimensions of end rectangle (also greatest area)	Number of possible rectangles
Nora and John	12	Yes	3’ X 3’	3
*  Aidan's Play Space	20	Yes	5’ X 5’	5
Jack and Naomi	22	No	5’ X 6’	5
* Peggy's Pig Pandemonium	24	Yes	6’ X 6’	6
Eli and Eliot	28	Yes	7’ X 7’	7
Paige and Carter	30	No	7’ X 8’	7
Nora and John	36	Yes	9’ X 9’	9

     * These two had already been done by all students.

More student comments:

“The rectangle with the greatest area (for each perimeter) has at least one dimension that matches the number of possible rectangles.”

“The perimeter must be a multiple of 4 to have a rectangle that is a square.” (A square is a special type of rectangle.)

Third graders could go on and on with this math problem.  They did some great thinking and reasoning throughout these math sessions.