Thursday, February 23, 2017

POTW #22 - Learning is Shown in Lots of Ways!

On the last POTW, I saw a lot of great learning going on both here on the blog and in-class. Rich math conversations were occurring and I really liked seeing Yoav use a protractor to help him visualize the work he was doing. It was also nice to see students using algebra do solve the problem, like John, Vivian and Seyone did. This week's POTW is GREAT patterning practice.

POTW #22 Gr. 7 Question


POTW #22 Gr.8 Question
 


POTW #21 Gr. 7 Answer
 

POTW #21 Gr. 8 Answer
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9 comments:

  1. AnonymousFebruary 28, 2017 at 10:06 AM

    The answer for the grade 7 potw is 504,101,605,706,1311,2017. I did this by first trying to find out what hundreds there would be. I tries 100 to get 500,100,600,700,1300,and 2000. Knowing this was correct I then had to adjust the ones, I started with 504,101,605,706,1311 and 2017 and that just happened to be correct.

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  2. AnonymousFebruary 28, 2017 at 3:27 PM

    Grade 7 POTW:

    I first decided to try and guess and check the answer for this question. I started off seeing if seeing if the second number would be around 100. I tried to use 100 because it was a good bench mark to start off with. So after following the pattern rule, I realized that it was correct. I ended up with 504, 100, 604, 704, 1308, 2012.
    After seeing that this was really close to the answer, I needed to just change the ones digit with something else to see if I was correct. So I started off with 101. After following the pattern rule, I discovered that this was the correct answer.
    Therefore, the answer is 504, 101, 605, 706, 1311, 2017.

    ReplyDelete
  3. AnonymousFebruary 28, 2017 at 3:37 PM

    The answer is 504, 101, 605, 706, 1311, 2017.

    I did my work in my math notebook

    ReplyDelete
  4. UnknownMarch 2, 2017 at 12:49 PM

    Grade 7 POTW

    In order to solve this problem, I decided to start with a benchmark, 100, being the 2nd leftmost number, and follow the pattern.

    Pattern:

    504, 100, 604, 704, 1308, 2012.

    Because 2012 is a bit less than 2017, I decided to now try the number 102.

    Pattern:

    504, 102, 606, 708, 1314, 2022.

    Because 2022 is a bit larger than 2017, I finally decided to try 101.

    Pattern:

    504, 101, 605, 706, 1311, 2017.

    Because this satisfies the pattern rule, the set of remaining four numbers are 101, 605, 706 and 1311.

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  5. AnonymousMarch 2, 2017 at 4:52 PM

    I will start by trying out benchmark numbers: 504,1000,1504,2502,4010,6512.
    Way too large. 504,500,1004,1504,2504,4010. Still way too large. Maybe it is closer to 100 with the basic benchmarks? 504,100,604,704,1308,2012. I think it needs to be raised slightly based on past results. 504,101,605,706,1311,2017. It worked!

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  6. AnonymousMarch 2, 2017 at 6:26 PM

    I'm not sure how to solve this POTW but this is what I have so far:
    If we were to use the formula they give above we would get:
    (n(n + 1))/2 = 2017
    which can be simplified to:
    n( n + 1) = 4034
    but now I don't know what to do...
    I COULD write all of it out.... but that would take an incredible amount of time.
    I would love for us to review just how to do this in class sometime though! I always see these kinds of questions on Caribou, but I never know how to solve them!

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  7. John H.March 2, 2017 at 7:00 PM

    So the 2017th digit is a 4. I know this because I looked at the pattern and found the pattern rule that every group of numbers up to 5 it increases the amount of numbers in that group and then it starts from 1 again after 5. Next after that I continued the pattern which resulted in the 2017th term digit to be a 4.

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  8. AnonymousMarch 3, 2017 at 8:21 AM

    Oops I forgot to do that one so I'm going to start working on it now!
    I will let x be the number right after 504.
    The next number would be 504+x, the next one being 504+x+x, the next one being 504+x+x+504+x, and the final one being given to you, which is 2017.

    The Algebraic equation I am going to used is 504+x+x+504+x+504+x+x=2017.
    Simplified, 1512+5x=2017.
    5x=505, so after isolation x=101.

    After checking, I can find that 101 is the correct answer.
    Therefore, the answer for the numbers are 504, 101, 605, 706, 1311, and 2017.
    -Alan

    ReplyDelete
  9. AnonymousMarch 3, 2017 at 8:30 AM

    Grade 7 POTW:
    Sorry for the late POTW.
    I first started with the bench mark of 100.
    504,100,604,704, 1308, 2012
    2012 isn't 2017 so I go one higher:
    504, 101, 605, 706, 1331, 2017
    So the numbers are 101, 605, 706, 1331.

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