Solving systems concretely

We have learned to graph systems ... and we learned to build tables to solve them!  Before delving into substitution and elimination full force, we took a day to explore ... Lizards and Beetles, Motorcycles, Cars, and Wheels, Circles, Triangles, Squares ... with marshmallows, toothpicks, and Algebra Tiles!

Our exploration of puzzles ... systems of equations embedded ... concrete materials excites some students, frustrates others.  It is interesting to watch ninth graders reaction to puzzles.  It's clear that I have not presented enough of them throughout the year.  Their lack of confidence and hesitation were obvious.  And tiles, oh my!  I don't know if it is the way I present them ... or just the fact that we don't practice with them enough ... but students don't enjoy working with them!  One young lady ... a conscientious A student .... shook her head ... "I just don't get algebra tiles.  Can I please just do the math??"

Across the room the attention to math dissolves in guffaws and giggles as one boy swipes his marshmallow-y finger through a girl's hair.  She shrieks.  Sad to say, in those few minutes (maybe just seconds) of silliness, students recommended she cut the marshmallow out of her hair!  YIKES ... we had a quick lesson in melting sugar.  

I digress ... 

How are legs on beetles, wheels on cars, shapes, tiles relevant to students ... they are not.  But interestingly enough, students participated in solving the puzzles with enthusiasm albeit a lack of confidence.  And hopefully the illustration of concrete visuals with symbolic explanation will help lay the foundation for our next steps in solving with substitution and elimination.