This week we focused more on division. We were given the following problem: A middle school will hold 609 students. Each class will have 29 students, how many classrooms will the school have?
I started with
290 Students 580 Students 29 Students
in 10 Classrooms X 2 in 20 Classrooms + 1 classroom = 21 Classrooms
Then I thought about the way I did this and realized this is very similar to a Ratio Table.
1 10 20 21
-------/-----------/-----------/------------
29 290 580 609
We then learned about PARTIAL QUOTIENTS
If you start with the problem 384/3 you think what can I multiply by 3 that will go into 384. If you do 100x3 you get 300. Subtract that from 384. Then see what will go into 84. If you multiply 3x10 you get 30 and subtract that from 84 and get 54. Then subtract another 30 and put 10 on the side because that is what you multiply 3 by. You are left over with 24 and 3 goes into 24 8 times so you put that on the side too .You then add all the side numbers up and get 128 and that is your answer.
AREA MODEL-DIVISION
You can decompose the number to make it friendlier to divide.
4816/4 -break up 4816 to make it easier to divide into 4
4000+800+16 /4 - You divide 4 into each number
1000+200+4=1,204
2642 / 3 -when the numbers aren't so friendly you have to see what 3 goes into that is close to 2642
2400+240+2 / 3 -Now divide 3 into each number
800+80 R2
=880 R 2
I really like the picture you used for the long division example. It is neat and easy to follow. Long division is something I struggled with all throughout elementary school, in fact I didn't fully understand it until we did it here this year. That picture with your description would have helped me understand it so much more when I was younger. Great blog and well organized concepts!
ReplyDeleteI like how you related your classroom problem method to the ratio table. Recognizing methods and the relationships they have is really important and I think it could really help kids to understand how division works. I also like how you used a photo of your own area model and how detailed you were in explaining steps to all the different methods.
ReplyDeleteI love the section on partial quotients and the example that you chose. Your explanation was very clear and it was very easy to follow your steps. I also found your area model to be very helpful. I like the way you showed how you broke up your rectangle, then showed your detailed work on the side. In your list of steps below your example, I loved how you explained that it's easier if you break it up into "friendly" numbers which is the key for any type of math. Great job!
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