What would you take on the Mayflower?

I love using the festive spirit of the holidays to learn.  The students are enthused and usually put forth a lot of effort into their projects.  In this activity, we studied about the Pilgrim's journey on the Mayflower.  Then, we wrote about the one item we would take on the Mayflower if we made the trip.  We were focusing on good Ideas and Organization in our writing.  I looked for a good beginning, ending, and original details.  Have a wonderful Thanksgiving!

Odd or Even?

One of the topics that we have been covering in math is the concept of odd and even numbers.  A very important component of teaching math is teaching for a high level of understanding.  Anything that I can take from an abstract idea to a concrete idea for my kids is fantastic.  If they can demonstrate the task for me using objects and explaining their thinking I know they have a good grasp.  Simple memorization of rules does not lead to a high level of understanding.  So, while it may have seemed simpler to simply tell them which numbers are odd, which numbers are even, and then how to apply that knowledge to larger numbers, it is much more effective to allow them to explore and discover the rule for themselves.  They will have a deeper level of understanding and meaning, which in turn will lead to better results.  Yes, it takes longer, but it has been so worth the time!

We started off with one digit numbers and explored how they could be put into partners.  They made a list of the one digit numbers and looked at which ones could be in even partners and which ones could not. 

Then, they progressed to putting two digit numbers in partners.  We discussed how it takes a really long time to get them all in partners so maybe they could do even teams.  They understood that if there were even teams that each person on a team would have one partner from the other team, so it would be the same as having a partner.  I got the idea of using linking cubes to represent the 2-digit numbers rather than B-10 blocks from another blogger I follow at www.mathcoachscorner.blogspot.com.  We began with numbers that had an even number of tens, such as 48.  Then the "tens" would divide evenly with two groups of ten on each team.  If the number was 47, they would have a "one" leftover in the middle with no team to go to.  Therefore, it was odd.  The next step was giving a number such as 58.  There is a "ten" leftover.  They quickly realized that the "ten" could be divided in half to put 5 on each team.  Then, it is an even number.  After several practice session they realized that it doesn't matter what is in the "tens" spot because you can always take the leftover "ten" and divide it in half evenly on each team. 

Eventually, we got to our rule.  Some may argue that it would have been easier to tell them all along to simply look at the number in the ones place and ignore the rest of the number...but, look at the learning and meaning making that would have been lost!  They now have a deeper understanding of WHY you only have to look in the ones column to determine if a larger number is even or odd.