How do you do division in math
They are in a classroom where alternate approaches are encouraged and celebrated and the ability to “make sense” of what they are doing is what is most important.
What was nice was that these students recognized that their answers using this approach didn’t make sense and decided to try a different strategy that actually made sense to them. I found looking at their misunderstanding of the algorithm interesting. There were a few groups that tried the traditional algorithm, likely because they remembered it vaguely from last year and thought they should use it. In fact, one of the groups that took this approach had an estimate that was very low (5 – 20 jellybeans). They were very successful in executing it (right down to extending it to decimal values) but there seemed to be little understanding as to why it worked. What was interesting is that these students had a hard time thinking about the problem in any other way or explaining how the algorithm worked.
There were a few students that used the standard algorithm for long division successfully. I have been thinking a lot about this lesson since that day – specifically about the benefits of student generated algorithms vs. let’s give everyone 100, now how many more do we have….now lets give everyone 10, etc) until they ran out. Others approached it by “distributing” the jelly beans to the five students (i.e. Some tackled it by using a strategic guess and check approach using either repeated additon or multiplication. We saw students approach the problem using a wide variety of strategies. We also wanted to see if students could make a reasonable estimate before they began as the teachers wanted students to work on their ability to judge the reasonableness of their answers. The teacher mentioned that most of the grade 5’s would NOT have seen the standard algorithm for long division but the grade 6’s would have explored it last year. Having spent very little time in junior classes I wasn’t sure what to expect in terms of strategies. How many jelly beans will Aidan and each of his friends get?” Aidan and his four friends want to share them equally. We decided to see how they might tackle a “division” problem and chose one from Van de Walle. The students had just finished working with multiplication and exploring the array model for multiplication. It was a great learning experience for us as most of our teaching experiences have been in secondary math with some time in grades 7/8. Last week Jessica and I had the opportunity to work with a great group of elementary teachers and to observe a grade 5/6 class. Really? Long division? You think that is what is going to prevent you from passing math? Long division is certainly not high on my list of key ideas in mathematics! When asked why, I get responses such as “I suck at math”, “I’ve never been good at math” “I can’t do fractions”….etc. And so it's gonna be approximately equal to 700 divided by 70.I have, on several occasions, had a student walk into my grade 9 class on the first day and state “I’m going to fail this class!”. They said, okay, 722, pretty close to 700. But, whoever wrote this question had a very similar thought process. You should find the answer that is closest to what you estimated.
Your exact answer here, that's okay 'cause remember, And, good for us, there's a choice here that is awfully close Straightforward to do in your head, 700 divided by 70 is This is awfully close to 700, and 68 is awfully close to 70. Well, what I would do in my head, I would say, well look, 722, See if you can figure out what it is and try to do it in your head. Once again, we are asked toĮstimate 722 divided by 68. Let's get another example here, make sure we get enough practice. It's definitely gonna be much closer to 40 than 80, 4, or definitely 400. So 794 divided by 18ĭefinitely isn't exactly 40, but it's going to be close to 40, and especially of theseĬhoices right over here. If we divide the numeratorĪnd the denominator by 10, it's the same thing as 80
Another way to thinkĪbout it, 800 over 20. This purely in my head, I would say, well, 100ĭivided by 20 is five, so 800 divided by 20 is equal to 40. For example, I would then say, if I was just doing Is it going to be exactly equal? No, but these are the numbersĬlosest to the numbers there that it's easy for me To be roughly the same thing as 800, is gonna be roughlyĮqual to 800 divided by 20. My brain says that look,ħ94 is awfully close to 800 and then 18 is close to 20. All right, so now let's do this together. See if you can figure this out without even using any pencil or paper. But, the whole point here is to get some practice estimating. In fact you would have to do, some long division or Now, if you wanted to get the exact answer you'd probably have to do, Here, we're asked toĮstimate 794 divided by 18. Wanna do in this video is get some practice estimating multi-digit division problems.