Look at the above solution. Is it the same as your response? If it is different explain how it is different? Do you think your answer is still correct even though it is different? Which answer do you think is better? Explain why. Post your response. (Remember to explain yourself clearly.)
David's Response -
Only answer a) is the same as my answer, b) and c) are not the same as mine.
On a) I had 2 adjacent squares and I only used 7 toothpicks. On b) I did not think of overlapping the squares to make 3 squares, Instead I just made two toothpicks double the size of the other three toothpicks like so, 2 lines are twice the size as so:
On c) I made three toothpicks double the size of the other 5 toothpicks to make 8 squares like so:
a) and c) are the same as my answers, but b) is not. I didn't think of overlapping two squares. I don't think my answer is correct because I said that b) is not possible because one toothpick doesn't make a square, just a single line. I also thought that if you tried to split one square in half it wouldn't make another square, just two rectangles. And a rectangle isn't a square, at least not on this Math POW, since most teachers I know don't give you a trick question until you are in that subject. We're doing geometry as in angles, not shapes. I think that the answer posted above is better, because I was rushed and I didn't think about it a lot, at least not as much as I was supposed to. -Sarah Jessica
ReplyDeleteThe solution is the exact same as my answer (a b and c), and I know that because the toothpicks were arranged in the exact same way, making our answers the same.
ReplyDeletea) Yes, my solution and solution above are the same.
ReplyDeleteb) My solution is not the same as the one above. To create three squares with eight toothpicks, I made one big square with one whole toothpick on each side. Then, I broke my remaining 4 toothpicks all in half. After that, made another square with a half toothpick on each side. I did the same with the other toothpicks. Yes, I do think that my answer is correct, even though it is different. This is because the question never specified that you COULDN'T break the toothpicks. I think that the solution above is better, since you don't need to break the toothpicks at all.
c) My solution and the above one are the same.
My answer is the same for a), I put that same one and 2 more for b), and I never thought of doing 9. I only put one with 4 squares and used 6. I never thought of 9! My a) is obviously correct, my b) is also correct because I added more to the answer. My c) is partially correct because I did add one with more then 3 squares, just that mine was with 4 and the solution was with 9, but it's more then 3 so it's correct. for a) neither is better or worse, for b) I think mine is better because I added the correct one AND more. on c) I think that the solution way is better because it has more squares. That one has 9 and mine has 4 so the solution one is better. -Xavier I.
ReplyDeleteMath P.O.W. : Don’t Be So Picky Answers
ReplyDeletea) Q: Can you make two squares using seven toothpicks?
A: Yes, you can. My answer was pretty much the same as the “textbook answer”. The only thing that was different was that the two squares (that were back to back) were on a vertical orientation on my work, and they were a horizontal orientation on the answer sheet.
b) Q: Can you use eight toothpicks to form exactly three squares?
My answer: No, you can not. My answer was wrong. The correct answer was that if you overlapped two squares (that were both made out of four toothpicks) at the corners, you would get three squares that were not of the same size (but it still counts).
c) Q: Can you use eight toothpicks to form more than three squares?
A: Yes, you can. My answer (which was a square made out of four toothpicks with four toothpicks crosshatched across the middle) was correct. It was also just the same as the answer on the answer sheet. -Sara
A) and C) was correct for me but B) I never thought of overlapping the two squares to make an extra square. For B) i did not find a way to make 3 squares only using 8 toothpicks so i wrote no. I do not think that my answer is correct. I think that the Answer above on this page is better then mine because I got B) wrong. I also think that I could of done better next time to take my time. -Ronan
ReplyDeleteAnswers A and C were exactly the same as the ones I did on my math POW. For B, though, it's a bit more complicated. For B I put down 2 answers I put down the same answer as the answer sheet, so I technically got the correct answer, but I also put down something before that I put down one large rectangle with two other toothpicks in the middle. I did the second answer (on the sheet stapled to the back) because I thought the other one may have been wrong because it made two rectangles, I kept it just in case it was right but, I also put the other answer!
ReplyDeleteIf you didn't guess who I am... seriously? Think HARDER!!!
Still don't know?
Fine.
~Amanda
these answers are not the same as my answers because I put no for a.),b.) and c.) then I put but if you crack them in half it is yes. my answers are different because I cracked them in half but this answer overlapped them and I honestly didn't think of that. Yes, I think my answer is still correct because I didn't use more toothpicks then allowed it's just that I approached it differently that's why I think it's correct. I think tat answer is better because that required more thinking.
ReplyDeletemy answers are different except from a, which is the same. I think my answer is still correct even if it isn't the same as the answer here. For the third question, I think the answer on the blog is better because I never thought of actually having 9 with 8 toothpicks.
ReplyDelete-Beth
My answer was the same for a), and also b), but not c). I put 2 squares together for a), and I overlapped 2 squares for b). What I did for c), was I accidentally used 6 toothpicks, and made 5 squares!
ReplyDeleteThe only answer that wasn't the same as mine was b), but my answer works just as well as the answer given. My answer to b) has random toothpicks sticking out, but it makes 3 squares. The answer given was a bit neater, but it never said that the toothpicks couldn't stick out. The other two I answered the same, though.
ReplyDelete~ Mackenzie :0
a) My solution is the same as the above on
ReplyDeleteb) My solution is not the same as above, I definitely did not think about it enough because I put no for b) when obviously I was very wrong, I did not even think to overlap my answer is definitely incorrect so I think that answer is much better.
c) My answer is definitely incorrect and the answer above is better as well different.
All of my answers were the same as the solution. I think that it was just a coincedence that they were the same because I didn't look at the solution when I thought of my answers I wasn't looking at the solution. So it was just a coincedence okay!................Stop judging me!
ReplyDelete~ Eileen
Don't judge me.........
I did a) the same but b) and c) I did different. I think that my answers are also possible. For b) I did the same thing. Like in a) but with the 8th toothpick I broke it in half and put it in the bottom left corner. Like this _| but upside down. They didn’t said that you can’t break them.
ReplyDeleteFor c) I made a square out of 4 toothpicks. Then I split them in ¼ and with the rest of the toothpicks I broke them in half and made them in a square. I made 6 squares using this method.
I think that their solution is better because they didn’t have to cut them in half. I didn’t think about that. - Andra
Oh by the way, I think my answers are still correct even if it is not the same as the solution above.
ReplyDeleteThis is my response to my response above!
ReplyDeleteI mean above in the post.
ReplyDeleteI am responding to David's response
ReplyDeleteI think that he responded VERY well and it is so cool that he got pictures on there to show what he meant, because I didn't even know what he meant until I looked at the picture. Also I agree with his solution. It is very explanitory and is very interesting. I wish that I had a response that good.
~Eileen :0
It looks like it can work and the picture makes sense, but it doesn't really make sense what he is explaining.........well not to me anyways!
ReplyDeleteI am responding to David's response. I think that he did a really good job in showing what he did instead of the "textbook" answers. He used a lot of rich detail to explain how his answers were different. I also like how he included pictures.
ReplyDeleteI am responding to David's response
ReplyDeleteJust saying I think that he shows what a good response is, he made his response detailed. I think that his answer is correct even know it is different then the solution it is still correct. I like the way he figured out the problem to.
My resp. to David's resp.:
ReplyDeleteI don't think that David's way of answering was correct (sorry David!) because you can't make the toothpicks larger, they only come in one size: toothpick size! Plus, if you lengthen the toothpick, it is not a toothpick any more, it's a stick! Also, how would you lengthen a toothpick? Tape two together?
If there was different lengths of toothpick, like small and large, it would work; but there isn't, witch is sad.
~Mackie Moo
Response to Davids response of the response for the Math POW!
ReplyDeleteI think that his idea was smart because when he doubled the size of the toothpicks, one covered 3 sides and the other one covered 2. I would have never thought to make one toothpick bigger than the other. In total, that was a REALLY smart idea! Good job David!
I think that David's response is great, because he did different things for b) and c)! He suggested that if the squares can be different sizes, the toothpicks can be different sizes, too. I never thought of his idea, I spent too much time focusing on one idea than looking a other ideas. I think David's response is a level 4 response.
ReplyDeleteresponse to David's responsly response responsersons
ReplyDeleteI think David's response was very detailed (and personally a bit confusing with the doubling), and very long. I liked the pictures and examples, because they kind of explained his thinking, but it still was kind of confusing. He could have been less confusing if he explained how he doubled the toothpicks (WAS IT MAGIC???).
David did a good job explaining though.
ReplyDelete(and I meant which, not witch)
~Mackie Moo
I think for David's response he put it together very good. Very well done with the pictures. But I am really comfused with the picture for c). But when you wrote it you forgot to say that if you think is corect. But I see that you posted it later. Try to remember that.
ReplyDeleteAll my answers were the same as the solution.
ReplyDelete