We've been doing division in class lately. Perhaps other school districts start teaching division before third grade, for almost all of our kids, they are learning and practicing division for the first time.
It makes me very happy when one of my kids can actually explain to me what a division problem means. Most of my kids probably could NOT explain it, but one of my girls did today, so I was pleased.
I asked why we could not do 3 divided by 15. She explained it perfectly, saying that we could not start with three things and put them into 15 equal groups because there weren't enough things to start with.
On the other side of logic, I wrote this word problem on the board today:
Erin wants to share her cookies with her 2 sisters. She has 18 cookies. How many cookies will each sister get?
I let my kids work with a partner and gave them a few minutes to come up with a picture, a number sentence, and an answer.
Every one of them told me the answer was 9 cookies. Wait, I take that back. Every one of them told me that 18 divided by 2 was the way to solve the problem. One girl said that 18 divided by 2 equaled 7.
When I told them (much to their shock) that 9 cookies was NOT the answer to the problem, and that I would give them a couple more minutes to go back and very carefully read the problem again, they all saw the trick and came up with the right answer.
I'm just not sure how to teach the skill of carefulness and scrutiny. Especially when I have a group of kids that don't really want to read the words but would rather just grab the numbers and perform a random operation on them...
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13 comments:
I still don't know how you do it. In any case, I've left you some love and lemonade at my site!
The trick, of course, is that the sibling with ALL THE COOKIES will not let her sisters know how many cookies there actually are. She will stuff all but four of them in her pockets, so the correct answer is 2 (except for Erin, who gets 14).
Have you never had younger siblings?
Amerloc, you bring up a GREAT point! I see now that I left a crucial word off of my blog entry that I DID include in the word problem for the kids today, and that word is "EVENLY." Erin wants to share her cookies EVENLY with her 2 sisters.
That's what really defines division after all, the equal groups!
Thanks!
Wow, does this bring back memories of when I taught 3rd grade. I feel your pain!
As far as the thinking part goes - I think some children just scrutinize things better from the start. I think it's hard to teach this.
Re: teaching scrutiny...
Do you teach your kids to dissect the questions? Meaning, do they circle what the question is asking and underline the important information?
I find this helps slow them down and they are (slightly) more likely to answer the questions correctly.
Angela, yes we go through this every day. Some of them get this, but some of them still think "How many" is a crucial part of the question, even though those words are in almost EVERY question...
My kids are all ESL, though even when my kids have been native English speakers, they all seem to want to just mash numbers together.
I teach high school computer science.
In high school they STILL ignore all the words and mash the numbers together.
Actually...... If we take those 3 items and "cut" each item into 5 equal pieces, we would then have 15 items to put into 15 groups. Each group gets 1/5 of a whole.
Keep your FOURTH grade math out of this, Ed!! I'm teaching THIRD grade math here!! hehe
I believe that third graders aren't developed enough to understand dcimals. Do you teach cursive to the hobbits? In teaching multiplication, did you teach memorization to where they know them by sight and if you ask it,they would answer it faster than you can say "No Recess for you today" like my third grade teacher did? The rumor my reading teacher said is that it has changed drastically in the last 5 yearsand it isn't taught like that anymore. I have a math joke: TEACHER: What is 7x6? STUDENT:42. TEACHER:What is 6x7? STUDENT: 24
My juniors still prefer to take two numbers and perform a random operation. And I hate to tell you, but you can divide 3 by 15 - it's called fractions. OK, I know you aren't doing it in 3rd grade, but I've have many students take 3/15 and put the 15 inside the division bracket when they try to change it to a decimal - one explained to me that the bigger number always goes there.
Yeah, Anony, I get the random operation syndrome as well (ROS), and I have told them that they will learn to do things like 3 divided by 5 later in school but that for right now, they need to have enough things to put into the groups equally.
My third grader loves these "trick questions." And the more I give her, the less often she's fooled by them. She LOOKS for the deception, the trick, the game; and it keeps her interest in math alive. Keep up the good fight!
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