Monday, September 7, 2015

Welcome Intermediates! It's POTW time!

Welcome back all returning Cranny Intermediates, and hello to all of you new Intermediates! (i.e. Grade 7s). As most of you know, this blog is a space where your teachers can share various things with you. We often reflect about field trips, post videos, share articles, but MOST OFTEN, we challenge you with the Math Problem of the Week Questions! (A.K.A. POTW).

Another great function of this blog is that it contains our wonderful Intermediate calendar (look to the right). Please use this as another way to track dates and deadlines, and also to keep your parents in-the-loop about your school.

The most important requirement of this blog is YOUR participation. This may come in the form of: 
- sharing your POTW answer
- posting your comments, questions, and replies to others
- seeking out the answers to POTWs (answers are posted a week after the question has been posted)
- reading and following new posts

With that being said, it is absolutely pivotal that you remind yourself about online netiquette. You must always consider the feelings of others when posting comments. Before you press 'submit' or 'send' or 'publish' please ask yourself two questions: "Would I say this to someone's face?" and "Is my comment helpful in any way?" If the answer to either of those questions is "No" then consider revising your comment.

Without further ado, below is your first POTW for the year! Please submit any and all responses regardless if you think someone else has the same answer. You can always show your work in different ways! And be sure to comment on other students' work, provide feedback, and ask clarifying questions. Always remember to be signed-in to your gapps account before submitting a response.

 (Thanks to the NRICH site and Byrony Black for the awesome inquiry problem)

56 comments:

  1. Let's all see if we can do this challenge.

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  2. Does anybody know exactly what triangle she is talking about? The smallest one in the very center or the meadium sized one?

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  3. Well, I`m still not exactly sure what triangle the question was reffering to, but I beleive the fraction of the smallest triangle is 1/512 and the fraction of the medium sized triangle is 1/128

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  4. Hi Anna, she points to the small shaded triangle. That's the one. Try to full screen the video or check the resolution. But I have to agree, it can be a little tricky to see.

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  5. My answer is: 1/128 is the fraction

    After making the origami i unraveled it stared at it for a while looking at the fold marks. I pin pointed the fold that created triangle, made some drawings and realized that one fourth of the paper has 32 of these triangles. Since 32x4=128, it means that this triangle is 1/128

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  6. how i solved it, I got 1/160, i dont know if this is right or not but i have no other way of solving.

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  7. I think that that shaded triangle is 1/128 of the original large square

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  8. I'm pretty sure that the small shaded triangle is 1/128 of the full sized original square

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  9. I found the answer out by folding the paper into a origami flower as shown and then by unfolding the entire paper and splitting the paper into smaller squares. I found small triangles on the sides, which I then figured out where 1/2 of a small square, so I counted two of the triangles as 1 square. I then cut out the small shaded piece, and found that 18 of these small triangles fit into a small square in the large square of paper. Knowing that there are 32 of these "small" squares, I multiplyed 32 x 18 to get 576. This mean that the small shaded triangle was 1/576 of the large square piece of paper. So overall, my answer is the small shaded triangle is 1/576 of the large piece of square paper.

    Great math question!

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  10. I agree with Anna. The smallest triangle is 1/512of the original square.

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  11. It's 1/512. I did this reopening the project after making it. I realized that there were 16 equal squares, so I decided to find the number of triangles in 1 square which was 32.
    So I did 32x16=512
    =1/512

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  12. I think the fraction of the smallest triangle out of the large square is 1/256. However, I wan't very sure which triangle to pick as it wasn't very clear in the video so I might be wrong

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  13. The small triangle is 1/512 of the full sheet of paper.

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  14. As far as I can tell, the triangle is 1/128 of the square, but it was very hard to tell what triangle was shaded (even in a higher resolution).

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  15. I also looked ahead at some of the other POTW's and the one with lines and slopes was really interesting, very similar to what I'm learning in my extracurricular math class. Do you happen to know whether or not there will be anything similar this year in math? I really enjoy trigonometry and linear functions in math.

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    1. That's actually "looking behind" because those are posted from last year. Linear functions and trig are most definitely NOT elementary curriculum. However, some contests and POTWs this year MAY have some aspects or questions like that. I do kind of doubt it though Jessica. But feel free to share questions or things you find interesting in math (either share in class or in google groups, or both!)

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    2. Well, that was something I was looking forward to. I guess I can live without it though. Do you happen to know what grade linears and trig get introduced? Just wondering.

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    3. Not exactly sure but early high school I presume. You should go back and try answering the previous POTWs if you're interested as well.

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  16. I think the answer is 1/512, but I'm not sure. I never did this before so I just divided and did other stuff in what I thought was a logical way.

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  17. Um the video won't show up on my screen what should I do?

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    Replies
    1. You need to try another internet browser. Some examples are Safari, Firefox, Chrome, Explorer.

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    2. my mom's laptop is a dell latitude E6400 i don't know if this affects my problem

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  18. To solve, I folded and made the flower and shaded the triangle (at least the triangle I thought she was talking about) and the unfolded and found out how many of those triangles were in the paper (through multiplication).
    But as far as I can tell, the shaded triangle may have been only half of the one which I thought it was, so the solution is either 1/128 or 1/512. Depends on which triangle is the shaded one.

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  19. Replies
    1. I agree. Especially if working on a mobile device, flash player is pretty often needed to play videos on a browser

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    2. Can't not allow to download stuff on my mom's laptop otherwise i won't be able to use it anymore

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  20. the triangle is 1 out of 512/128 (it is HARD to SEE!)but most likely 1/512 since it looks darker but i seriously can't tell

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    1. Damian, remember we talked in class about not using your last name here. Please alter your username.

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  21. I got 1/128 by folding the flower and then unfolding the paper and using the creases to figure out what fraction of the paper the triangle took up.

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  22. This isn't really related to the POTW, but it is math related. I'm doing a test at Kumon (extracurricular math class) tomorrow, and I'm worried about remembering a bunch of formulas (stuff for circumcenter, center of gravity, orthocenter, etc.). Anyone got tips on remembering those kind of formulas? Seyone, i know you passed the test a while ago, know anything that could help me out a bit?

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  23. I believe the smallest triangle counts for 1/256 of the piece of paper. I got this answer by recording what the fraction was for each triangle staring with the largest that counted for 1/8 recording what the rest counted for.

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  24. due to the picture of one side sent by Renee to me I counted 46 triangles in total FROM THE PARTS VISIBLE IN RENEE'S PICTURES
    I'm sure there is more than that but that is my minimum (1/46 minimum)

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    1. Vivian, have you considered looking for the video on YouTube? If it's there you might be able to watch it there rather than in this browser

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  25. The answer I got was 1/144.

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  26. I think small triangle is 1/512 i found out by looking at the paper after i folded it, after the 2nd fold you make 16 squares and in each of those 16 squares 32 small triangles fit inside, and since there are 16 squares you have to multiply 32 by 16 to get the total for the hole paper which was 512.

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  27. I think that the answer is 1/512 but i'm not sure

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  28. I'm not sure but my technique was to unfold the flower then figure out the answer. I saw that it a 4 by 4 grid of large squares. Inside those squares were four smaller triangles. For each triangle I figured out how many of those very small triangles could into that trinagle. I ended up with 9 in each triangle. Since there was 9 for all four triangles in one of those squares I I had to multiply 9 x 4 which equaled 36. After since there was four squares in the that collum, I had to multiply 36 by 4 which equalled 134. 134 very small triangle can fit in one out of four collums. That meant I had to also multiply that 134 by four once again which was 536. That means that one of those really small triangles is 1/536 of the square

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  29. Great work everyone on your first official POTW. Below is the answer. Remember there ARE MANY ways to solve problems in math. Did you use another way? Did some of your classmates use a different way than you? If you did not obtain 1/512 do you know why? How do you think you could alter your process in order to obtain the correct response of 1/512?
    The solution to the question is 1/512.
    The explanation is, after we created the flower we marked the triangle as we needed to find out what fraction this triangle was out of the original square.
    We unfolded the flower so we had the original square with the marked triangle in the bottom corner.
    We marked out 1/4 of the square, we then quartered this which gave us 1/16.
    We quartered again and got 1/64.
    Yet again we quartered giving us 1/256.
    The marked triangle was half of this so this time we halved and got 1/512.

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  30. One of the main reasons why I was wrong was that I compared the square ( 4 triangles ) to the total area of the "big" square. Second, instead of directly relating each downsize with the total area (e.g. 1/4, 1/16, 1/64...) , I did divide the length of the square unfolded by the length of the triangle, giving me 12.2 (forever). I rounded it down and then multiplied 12 x 12 to give me 144. altering the process would be to light of a description as I would have to change the very data of my calculation to get anywhere near it .

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