Odd and Even: A Visual Exploration

Sometimes we need reminders about how important some things are.  I know our math should be visual, but sometimes, when you see someone teach something visually, it hits you upside the head!  How had I not seen that before?

I recently participated in a great webinar with @MonicaNeagoy entitled "Planting the Seeds of Algebra."  It was a very interesting and informative webinar.  If you would be interested in listening to her ideas on ways we can make our math come alive for our students and prepare them for increased math connections as they progress through math curriculum, you can access the webinar here.

Early in the webinar, she discussed an exploration she does with students where she discusses odd and even numbers.  She had the students create snap cubes models to match the story of double-decker buses and car trailers she was talking about.

6-A double decker bus with 3 windows on each level

3-A car trailer with the cab and two cars on back

After the models are created, students sequence them

And a pattern begins to emerge

Students then looked at the models, which were visually clear in the difference between odd and even numbers.  Students were then encouraged to continue their thinking about odd and even numbers by exploring the sums of these numbers, and hopefully finding and testing some common patterns in these additions.  Again, Ms. Neagoy goes into much more detail in her webinar, if you are interested.  (It is worth your time!)

EVEN + EVEN:  4 + 8 = 12

EVEN + ODD: 2 + 9 = 11

ODD + ODD:  5 + 11 = 16

Well--this discussion and model got me thinking about a similar exploration for older students.  Using the same odd/even models, what happens when you multiply by an even number an even number of times or an odd number an odd number times?  What can our students determine through this exploration?  How will it change as the numbers increase, or will it?  Can students determine and odd/even rule that accompanies the multiplication of whole numbers?  

EVEN x ODD:  4 x 3 = 12

EVEN x EVEN: 4 x 6 = 24

ODD x EVEN: 7 x 4 = 28

ODD x ODD: 7 x 7 = 49

What a worthwhile way to spend a class period!  The primary version of the odd/even exploration and the older student exploration may be subjects that you discuss in your classroom already, but do you make a point to do it in such a VISUAL way?  And are your students figuring this out on their own, or are you telling them the patterns that exist?  

The shifts in math instruction show us that students will learn and understand better if the math is visual and open.  Taking these basic ideas of instruction and creating a visual tool for our students to use to figure concepts out on their own are steps that we want to be taking as teachers

Let me know if you try this with your students and how it goes. I would also love to hear about other odd/even explorations that you have found for elementary school students!