Mathematically Thinking

So, as most of my readers know - I start student teaching in January. I have been placed in a 3rd grade class (YIPPEE! YEE-HAW! WOO-HOO! MY FAVE!!) and I'm starting to think about math and how important it is to teach kids strategies - NOT FORMULAS - for solving all different types of math problems. I absolutely LOVED my math class this semester and was fortunate enough to have a professor that taught us new strategies (ways I didn't even know!) for solving all types of math problems. I know that this is a monster of a post, but I promise I have a point.

I wanted to share some of the strategies and some of the math games that I learned about. I do not intend to teach my students regrouping and the "old school" algorithms for solving multiplication and division because I don't think those strategies teach students anything about the relationships of numbers or what it means to multiply or divide. {Now, obviously, I will teach regrouping during my student teaching if it's required of me, but when I get my own classroom, all bets are off!!}  I only WISH a teacher would have taught me even just ONE of the strategies that I learned this semester when I was little! I have always loved math, but I sometimes struggled with fractions and multiplication or division because I could never figure out WHY I was adding a zero or crossing out 1 to make 11 or doing whatever other silly algorithm told me I had to do; I just did it because that's what I was taught.

But noooww...I'm equipped with lots of strategies that will allow children to solve problems like 234 - 178 or 25 x 12 without pencil & paper in a matter of seconds.

Let me just use these two as examples. 234 - 178. Regrouping would tell me that I would have to line these up vertically, cross out the 4 to make 14 (which doesn't help children see the relationship of 234 and 178), then "borrow" from the 3, make that 2, which is actually going to be made 12 and then borrow again from the 2 next to that, making it a 1. WHAT?! No wonder kids hate math!!!!

I solved this in my head in a matter of seconds. All I did was round the 234 to 230, then rounded the 178 to 180. So I had 230 - 180. I know that 180 is 20 away from 200, and 230 is 30 away from 200. So I add the 20 and the 30 together to get 50. Then I just go back and take into account that I subtracted 4 from the original 234 (to get a "friendlier" number) and added 2 to the 178 to get 180. I need to add that 6 {4+2} back into my final answer to get my solution, which is 56.

The 25 x 12...let's see, to multiply that the old school way, I'd again line them up vertically, first multiply the 5 x 2 to get 10. I'd put the 0 below the 2 and then carry the one above the 2 and then multiply 2 x 2 to get 4, then add the one. Then I'd put a zero below the 0 that's already there (WHY!?????) and then multiply 5 x 1 to get 5, then multiply the 2 x 1 then add everything together. GEEZ. In the first step, this kid isn't even getting a hint as to what the answer might be. Not to mention if he screws up somewhere in the process and forgets the zero or forgets to add, his chance of getting the answer right is slim to none and even then, he won't recognize that he's wrong because he has NO CLUE that 25 x 12 means 25 sets of 12; he's too focused on this nonsense formula.

This problem can be SO EASY. Especially with the number 25. This number is most easily associated with a quarter. So if I have 12 quarters....how much do I have? $3.00. But let's say that this kid can't do that in his head that quickly. I bet he would know that 4 quarters equals a dollar. And if he knows that, I bet he also knows that there are 3 sets of 4 in the number 12...So he would know that he would have $3.00. Take out the monetary value and you have your answer; 300.

HELLOOOO!! EASY, RIGHT?! YES!! Of course I recognize that these types of problems and being able to solve them quickly will take lots of practice and classroom discussion and this type of thinking won't happen overnight. Which is why I love number talks. Oh how fun!! I think the best way to start these at the beginning of the year would be with something easy, then work to doubles, then talk about friendly numbers. Friendly numbers are anything that make it easy to add, subtract or multiply in your head. Like any number ending in 0. Or numbers that have the same number in the ones column (doubles).  There are a million ways to lead these discussion with your kids, but the most important thing is to give THEM the control. Encourage them to explain their thinking because 100% of the time, this will spark something in another kid, ad infinitum.

I love my professor and I love her book. If you like these strategies, that's just the tip of the iceberg. Check out her book - Number Talks by Dr. Sherry Parrish. It comes with a nifty DVD that shows some of the amazing thinking that can go on during these number talks.

And just so we're clear...NO she didn't give me extra credit for plugging her book; grades are already turned in, I promise. I just REALLY love her strategies for math. They're so obvious when you think about it. This new{ish} way of teaching is TRULY the way to go and I think every teacher should be exposed to this way of teaching and thinking about math. {But if I'm being honest, I am TOTALLY teacher's pet and I have no shame!}

I know this post is going on and on - but I want to share some math games that I learned as well. I redesigned them and I'm putting them on my TpT and TN shops. They're super simple and there really isn't much to them - just a game board and directions. But since this post is rambling on, I included the directions in the free downloads. Click here and here for my TpT site or here and here for my TN shop to download these 2 free math games. Here's a little sneak peak! I love my little math monsters. 

 

Do you teach regrouping or do you use number talks for sharing strategies within your class? Tell me what you do to teach math in your classroom.

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