Math moments!

What a difference 3 years make in my math mind! 

"Hey look, mom, no tears!"

I have been enjoying this class because I have a schema now!  Background!  Experience!  Success!  What a difference it makes!

Now I think of things in terms of what I am actively doing in my classroom and how successful it feels.  This year has really jelled something for me!  I feel much stronger in my teaching practice while still admitting to gaps in my math knowledge.

Today I noticed with the math problem, 12 divided by ¼, I immediately wanted to do the algorithm, but knew I needed to draw a picture first.  I have no background in drawing models really till I entered Math Studio.  I don’t get them, and I’m not sure how to draw them.  Yet they are essential to conceptual learning.  It is too valuable of a piece to deny children.

So I drew out my 12 boxes and divided them vertically to show the ¼.  Then I did not know what to do.

I moved on to the algorithm where I know you multiply the reciprocal with the denominator?  (Don’t ask me why, I just memorized the procedure.)  I did that and came up with 48, which just seemed WRONG to me!

Next I started sneaking peaks at Woody’s paper.  (WOW 6^th grade math teacher!!!!)  He divided his into squares, which really made more sense to me then what I had drawn.  I still didn’t know what to do with the ¼’s though.  Then Woody said something that changed my math life. 

“ Students don’t understand that sometimes when you divide you get a bigger number, like with fractions.”

Stop the press!  Hold your horses!  What??!!!  It clicked.  It’s going to be a bigger number like 48 because of the many pieces.  I still didn’t get though why we were dealing with all 4 pieces and not the ¼ piece.

Woody spoke again:

“I find that if I put the problem into an everyday situation my students get some understanding.”

He told me this story:

“I have 12 yards of ribbon.  ¼ of a yard makes a bow.  How many bows can I make?  48!”

That made sense to me!!!!!!

I was looking at the whole being one of the 12 instead of the whole being 12.

What really was my major “A Ha” moment was the story using money.  I understand fractions in money!!  (Why I have never connected and transferred that money knowledge to fractions I don’t know!)

“I have $12.00.  How many quarters would that be?”

48!

Real life stories are important in math!  In fact, the graphic organizer we used, (Can you call them graphic organizers in math?) had 4 different ways to represent 12 divided by ¼.

I need to make sure I make those connections for my students.  (I wonder if that is why Bridges spends a lot of time with students producing stories to match equations? Betcha it is!)

Quote I wrote down:

“  Productive struggle comes from solving problems within reach.”

With using 4 different ways to solve the problem it gives students multiple entryways to the problem.  If I can just figure out one of the ways I should be able to figure out the rest.

I wonder if I could come up with one for 1^st grade?

“Mathematician!”