Math studio blog

" Please post a student conjecture or "near conjecture" before December 21. Or you can post a question you have about supporting students as they try to make conjectures. "





Ok, don't fall over in shock but I am actually having some fun with Number Corner and Odd and Even.  They are conjecturing like crazy- almost like a competition.  I still struggle with when it moves to a generalization and not all the students get it or remember it.

We started examining everyday if the days in school and days in the month are odd or even.  The first conjecture/ generalization that came out of it was we decided 10 is always even so we don't have to look at the 10 sticks in days in school to figure out if the number is odd or even.

Of course we had to establish that even numbers always have partners and odd numbers do not. (Generalization, right?)

At first everyone one would come up and use the magnet squares to prove if the number was odd or even by matching partners.  Then, Oh excitement!

One day M. and M. (no pun intended) built on each other and came up with the conjecture that every other number will be even.  We made a public record and it is proving to be true.  (Generalization?)

Then T. conjectured that if we count in 2's all those numbers are even.  Again we made a public record that we add to and it is true.  (Generalization?)

Then Z.  conjectured that 4 is always even.  I let that one ride for a couple of days to see what the students would add on to that.

T. conjectured that when a number ENDS in 5 it is always odd.

I let that one sit to see if Z would think of his conjecture a little differently.  He didn't so the next day I asked him about  the number 54 and if it was odd or even.  He was so stunned.  At first he said odd.  I mentioned his conjecture.  Major disequilibrium!


I gave some think time to see if he could work through it.  (Meanwhile the majority of the class was wiggling around like worms in a coffee can.)  I should have waited but I was losing my class.  So I asked if anyone could add to what I asked.

That's when T. said the number has to end in 4 to be even.  I walked the class through breaking 54 into the ten sticks, reminding them that we had already decided that 10's were always even so we didn't have to look at the 5.  I asked Z then if he agreed with what T said and he did.

The next conjecture came from M. again.
"If you add two odd numbers together the answer will always be an even number."

I don't know about you but I was really impressed with that!  We are checking it everyday to see if it is true.  (When do we have enough data to say it is a generalization?)  I'm waiting for someone now to conjecture about what happens if you add two even numbers together?  If you add an odd or even?

My white board is covered with our conjectures and public records we have created to use to keep track of our data.

Now when I ask them if a number is odd or even that are not just using the answer that it has a partner.  They use the if you count in two's record and every other number is even record too!

I find that I could go on and on in Number Corner on this conjecturing stuff!   Wait till I have time to write about what we are doing with numbers in a game we play everyday.  Introduced a bit of multiplication and telling how many are in our class and if it is odd or even!!!!!