Can You Prove It!!!!

Part of learning about a new concept is being able to explain to someone else what you know. 

The past few weeks in class, I have asked the kids to PROVE their thinking.  My goal is 2-fold.  The first part - the kids really have to understand a concept and use correct math vocabulary in order to explain it to someone else. 

The 2nd part - the students have to present their explanations, and then listen to others critique their ideas....they also have to critique other's ideas.  This is not easy....but out kids are learning.  Some of our ground rules are.....you won't always agree, but if you disagree, you must state your reasons?  Also, be prepared to answer the big "WHY" question from others.....you have to have EVIDENCE to support your thinking.......

I gave each group a shape that was divided in unusual ways......and asked the kids if their shape was divided into equal sections.  We reviewed that the sections might not "look" equal at first glance, but that equal means equal "space" in fractions.  Each group had to decided if their group was divided and then prove it to the class.

Here is one group developing their argument!!!

This group tried measuring each of the triangles first.....then they remembered that perimeter won't measure the space INSIDE each triangle.

They decided to cut out each triangle to make sure they took up equal space....they decided their shape was divided into equal parts....it didn't matter which way the triangles were facing.

 
Next group....

They also cut it apart to make sure their pieces were equal...they discovered, they were NOT!!!

This group used symmetry to figure it out......they colored in half and then looked to see if each side had the same shapes.....it worked!  There were many ways to figure this out, but this was one I hadn't thought about before hand and it was a great way!!!!

 Each group got to stand in front of the room and present their shape the class.  They also had to answer questions about their shape to defend their thinking. 
They all did great!!!

There was one group that had an extra hard shape.  This was tricky...so we ended up working on together as a class.  There is still some work to be done with this....but it was a good experience.