Wednesday, October 7, 2015

Expression Polygons

In the August 2015 issue of Mathematics Teacher the article Expression Polygons by Colin Foster caught my attention.  A quick google search lead me to a PDF of the article if you'd like to read it.

Just this morning my colleagues and I were talking about the struggle that students have when faced with an expression.  They are programmed to solve, so they insert an equal sign where ever they can.  Even Algebra II students.  I feel that this activity is a great way to help students understand the difference between expressions and equations.

In a nutshell, the students create 4 expressions and set each one equal to the others, so that there are a total of 6 equations:



Try it myself:

Before I try a new activity with students I like to try the activity for myself.  Here are the requirements I'd like to give the students:

  • Create 4 expressions where the 6 solutions will all be different integers.
  • Two of the expressions are of the form __x +- ___.
  • One of the expressions is of the form x +-____.
  • One of the expressions is a constant. 
It took me 6 minutes to come up with this, so I think it's a reasonable assignment for my students.  






For the Students:

I introduced the project to the students, put them into groups of 2 or 3 students, and gave them this link for a copy of the template.  Click here for template.  

I gave each student a copy of the rubric.  Click here for the rubric.

There was a lot of productive struggle going on in my classes.  One thing many groups were doing was not getting an integer answer, so they erased the entire equation rather than working backwards for a solution.  

Many times I hear the students say that the assignment was hard (not as a complaint though) and I was ready for them to give up and say that it was impossible.  But, this assignment must have had the right amount of flow to keep them going because not one group of students gave up.  

I also like all the bonus stuff we got to talk about other than solving equations.  First was vocabulary: expressions, equations, vertex, and polygon.  Students had many questions as to what an integer was since all the solutions had to be an integer.  And believe it or not, in high school the students wanted to know if there was a difference between 5 divided by 1 and 1 divided by 5.  

Action Shots:


















Results:

Here are some of the students' work ,worts and all.





I found this one interesting with all the same solution of 5.  












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