Thursday, November 29, 2012

How do YOU divide?

Today is Thursday, so my post should be an iPad app suggestion, and I have a great one for you, but I had something cool come up in class today and decided to share it with you.  Stop by tomorrow for this week’s app suggestion.  Now, on to my eye opening math lesson.

Last week, on my kids math assessment, there was a problem that asked the kids to divide \$5 between 6 kids.  All of my kids got stuck on this problem, so I decided to take the opportunity to use this to review long division.

Now, bear in mind that my math program doesn’t actually teach long division, instead it teaches students to use multiplication to solve division problems.  However, many of my students have been taught to divide in previous years at other schools.  All of my students are new to this school and this math program, and as they are coming to me in 3rd or 4th grade, they already have a base built in their previous programs.  Unfortunately (or fortunately, depending on how you look at it), they don’t all come from the same previous programs.  Out of a class of 7 (Yes, I’m the luckiest teacher in the world and I only have 7 kids!), 2 have “American International School” backgrounds, 1 has a “British International School” background, 2 have “Moroccan  Private School” backgrounds and 2 have “Spanish Private School” backgrounds.  Because of all of this diversity, I always try to tell my kids that there are many ways to solve a problem and you should choose the way that makes the most sense to you.

Last night I assigned a few math division problems to help them review.  While we were reviewing them in class today, one of my students taught me a new way to divide.  Here’s what her paper looked like:

It totally blew my mind at first, and I actually had to go to my husband (who grew up in the Moroccan Private School system) to actually explain it to me.  Once he did, I was able to see the connections between the now 3 different ways we have used to solve a long division problem.  So, I decided to make a poster for my kids to help them see the similarities and to guide them through choosing the strategy that works best for them.  I’m going to make similar posters for the other operations, as I work out all the different ways to solve those problems too.  Right now, I only have division finished, but if you’d like a copy of the poster, feel free to grab a free copy from Google Docs.

Now, my curious mind is wondering – how do you divide?  Which of these methods is your preferred method?  Do you have another?  I’d love to hear about!  Please leave me a comment!

1. Hi Raki,

I thought there was only one way to divide. I was taught one way when I was in elementary school (just across the river from Buffalo--Welland Ontario), another way at teacher's college and still another way (European/metric way) when I was teaching French Immersion. Whatever way works.

2. When I taught fifth grade math, we taught four different ways and told the kids to use whatever works for them. They are hang seven, scaffolding, clustering, and the standard American algorithm. I will have to do a tutorial and share it with you, because three of them aren't anything like the ones you're doing! :)

Diane
Fifth in the Middle

1. Oh, Diane, I'd love to see the tutorial! If you have a blog post about it, I'll happily link it up here. Maybe we should do a linky party about all the ways to solve a division problem!

Heidi

2. I've had the best intentions of doing a tutorial this weekend, but then I saw this post today:
http://teachingtoinspirein5th.blogspot.com/2012/12/division-fun-and-tropical-christmas.html?showComment=1354475839151#c9080450642456975863

If you scroll down, she shows a method that we call Hang 7, but she calls partial quotients. It's an activity where the students have to find the mistake. Partway down, the 5 and 60 should flip-flop places. I really like this method because it uses powers of ten and students don't have to erase their too-little guesses. Eventually, they become better guessers and start with larger numbers. If you don't understand what they did, I can still work on my video :)

3. Heidi, great post! Question, do they solve division problems including decimals by multiplying, also? I teach grade 7 and they still struggle so much with division. It has stuck for some and for others it just hasn't. Diane, I'd love to know about those other methods!

Krystal
www.lessonsfromthemiddle.com

1. Hey Krystal,

With the way my math program presents this, you just seem to take out the decimal to do the math and then put it back in at the end. (It's my first year using the program, so I'm still figuring it out too!) I have talked to my kids about how to figure out where the decimal point goes, and we've mainly used this for dividing with money. (\$6 = 600 cents - or pence or Euro cents, but that's a whole other blog post!)

Heidi

4. I have taught 3rd or 4th graders the majority of my 20+ years of teaching. Most of my students are new to the country. When it comes to division I always seem to have a few parents that come in very confused by the "American" format of division the sideways L shape.... I hear about the arguments about the fact that what dad is showing a child is "not what the teacher said," when doing homework. I had one parent years ago try to explain this other format or something like it. I could never remember it. Thank you so much for sharing this with us - I am just moving into this topic so I am sure it will come in handy, very soon.

5. This is a great post Raki,
I remember watching a friend of mine (from a different school) do long division and saying to them "what on earth are you doing? that's not long division!" We had been friends for such a long time and for those few tense minutes we looked at each other as if we were meeting an alien from outer space. It's so funny (even when we struggle to understand something) the way the teacher does it has to be the right way! I teach my students that they just have to find a way that works for them. I like seeing your three methods and I'm totally going to share the poster with my colleagues at school. The method my friend used isn't shown on your poster either. He did explain it to me, but I don't think I could explain it to someone else... I stuck to the methods I had learned as they had become second nature to me.
I like the idea of a linky party for division methods (and ways of teaching it).

M
agreattitle.blogspot.com

6. Thank you! I just found this searching the web. My daughter is in a french immersion school that teaches the French National Curriculum (French teachers) and a lot of the parents (American) have been confused when trying to help the kids with their homework as they start long division. Your Google Docs document has been SOOO much help!

1. I'm so glad that it was helpful to you. It's been a big deal in my class this year, so I know how stressful it can be. I am working on similar posters for addition, subtraction and multiplication. Who knew how many ways there were to solve a problem, huh?

Pin It button on image hover