Prove it!

I have really been working with my Firsties groups to teach them how to "prove" their answer.  They need to prove it to themselves first through either manipulatives or a representation, and then be prepared to share their steps so that they can prove it to someone else.

Today's task was a pretty basic one, but I find that those are important for them to do as they grow their ability to explain to each other what they did and how they know.  Today I asked them to find the sum of 6 + 8.

The variety and levels of their strategies was, as always, quite interesting...

This little one counted out 6 green and 8 orange.  She needed to think about what to do with them, but she then realized she needed to put them together.  She then proceeded to count all to get to the sum of 14.

This guy counted out 6 and 8.  He organized them into a line and then counted all.  His counting was a bit easier because of the line and the differentiation between the 6 and 8, but he still counted all of the cubes to get 14.

A similar approach with the counters...this little guy organized his 6 yellow and his 8 red.  He began with the 6 at the top and then counted on the next 8 to get 14.

Here was one who grouped his 8 and 6. He then started with the 8 and counted on the next 6 to get 14.  He decided to build the plus sign while he was waiting for the others.

There was some organization in this guy's work.  He grouped his 8 and 6 and then counted on from 8 to get his 14.  While he was proving it to the group, one of the others,  who had used a much more mottled strategy, blurted out, "It's a ten frame!" We took the time to explore how it was like a ten frame, but not quite, so we moved two yellow to the end of the black blocks to make our ten.  They immediately saw the 10 +4 and called out, "14!"

Now it was my turn.  I started with a stack of 6 and a stack of 8.  This time, however, we broke two off of the 8 to identify that each of the stacks was now worth 6, and the students called out, "6 + 6 =12." They then knew they needed to add the two back to get the 14.

This little activity doesn't take us long, but it shows me so much about the students' thinking and levels.  They have all been taught in the classroom to "start big and add on."  However, when working independently, they don't all do that.  When we look at each other's strategies, we identify how it works for each person.  We identify what looks the same and what looks different.  I model and discuss the way to organize our blocks so that they are easier to total.  In the end, however, we have a discussion about the fact that there are many ways to get to the same place.  We all need to use what makes sense to us.  

I was glad to see when I was in one of these student's classrooms today leading a 3 act task that one of the students that I see regularly was organized in her representation of the problem.   We were able to share her representation with the class and discuss how the organization that she used helped to make finding the sum a little easier.  

They are 6 and working to make sense of it all.  😃