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TimestampYour answer.Comments.
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3/21/2017 22:36:28JSecret choice K - none of the above. J is the only one that makes sense to me. I'd like G if the arrows were pointed the other way
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3/21/2017 22:36:54JCould the numberline have been open, starting at 25 to the left and ending at 13 traveling to the right?
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3/21/2017 22:39:05J
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3/21/2017 22:42:12JBest represents my thinking of this change unknown problem because I see the 25 whole in the arrow pointing right....and 'traveling' back until I get to the 13 people who left with the arrow pointing left....which shows the answer in the arrow/line that is 12 units long....
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3/21/2017 22:46:45G, JJ is the obvious distance between 25 and 13. I think many Ss use adding up as a mental math strategy and would choose G. I liked how the prompt represents well the distance/difference model.
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3/21/2017 22:48:45G
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3/21/2017 22:56:38G
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3/21/2017 23:00:10G, J13 + x = 25 and 25 - x = 13 are both valid equations.
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3/21/2017 23:07:32G, JH is possible, but it doesn't show the 25.
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3/21/2017 23:40:59J
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3/21/2017 23:45:30J
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3/21/2017 23:59:56J
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3/22/2017 4:08:41J
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3/22/2017 4:20:44GFor me g or j would be acceptable but I chose g because it best represents a clear divide/segment on the number line to show the difference.
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3/22/2017 4:44:46J
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3/22/2017 5:52:34JThere ie more than 1 way to represent this situation. I wouldn't have picked any of these.
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3/22/2017 6:31:50J
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3/22/2017 6:38:30G, H, JI can see how a case could be made for all of the last three answer choices.
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3/22/2017 6:50:40GThis question was visually misleading to me. I know I should probably pick J but it really went against all my math instincts. It looked like I needed to count down to 13 and most people wouldn't use that as a strategy for that span of numbers.
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3/22/2017 7:19:12J
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3/22/2017 7:46:02J
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3/22/2017 7:56:14J
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3/22/2017 7:59:49GI think J works too. But to me, J makes it seem like two different groups and the problem context is only about one group of people. My only issue with G is the direction of the arrow. Is that really necessary? G makes it look like 13 people came and then 12 more people came.
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3/22/2017 8:10:01J
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3/22/2017 8:14:29G
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3/22/2017 8:41:48JI see g and j as the same answer. H may be an option but need more information. These three seem to all be one possible way to represent the problem
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3/22/2017 8:46:35JThe arrows in J follow the action sequence of the problem best.
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3/22/2017 8:58:12JI like that J shows the original 25 and then shows the others leaving with a separate arrow. The second arrow is pointing in the other direction, showing that the number in the library went down to 13. To find the number of people who left, we could count the distance covered by the second arrow.
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3/22/2017 8:58:47J
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3/22/2017 8:58:50J
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3/22/2017 9:14:08J
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3/22/2017 9:17:20J
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3/22/2017 9:24:38J
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3/22/2017 9:44:56G
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3/22/2017 10:17:27J
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3/22/2017 10:18:29J
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3/22/2017 10:21:05J
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3/22/2017 10:28:34G, J
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3/22/2017 11:05:05J
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3/22/2017 11:17:16JChose J because question is posed not as difference but as take away (Chanel unknown). Would love for number lines to more closely represent strategies Ss are using. I sent pucs
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3/22/2017 13:35:37J
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3/22/2017 13:56:33JFirst thought is that it took me a while to sift through the graphs and understand what the graphs represented. I feel like I'm so conditioned to see the horizontal axis representing time, it took me a few extra paces to see that represents the number. I also typically read top down, so I ordered the graphed vectors as first event on top, second event on bottom. I spent some time wondering why some vectors were next to each other while others had two layers.

I valued the time it took to decipher the graphs and make some meaning from them. Made me think way more than expected. I would expect students to need some guidance or prior knowledge on what makes a graph a good representation of a situation (or a helpful solving tool) - there's a potential to overload System 2.

I suppose if I were to draw this out using a number line & two vectors, I would make it vertical. That way I could have some sort of time dimension with the left most vectors being the first event.

I see value in G & J. H seems to have part of the information available. I chose J because it has the solution is present in the graph: the magnitude of the top vector.
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3/22/2017 14:34:39JI am thinking of 25 people being there and then some people leaving until 23 are left. You can count how far from 25 to 13 on number line J
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3/22/2017 14:51:37J
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3/22/2017 15:05:12GI would choose G because we know the part that remained in the library (13) and that the total was 25, so you could start at 13, move to 25 on the line and find the missing part (the difference between 13 and 25). J looks correct at first glance because you start at 25 (total), but the graphic feels confusing to me. The backward line shows counting back 12 (which is the unknown). I think it is the backward arrow that is throwing me off on that one. If it showed a mark at 13 and a mark at 25 and had a line to show the difference between them. I would be okay with that one, but that arrow makes me feel like you are starting at 25 and counting back 12.
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3/22/2017 15:28:08J
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3/22/2017 15:43:39JOne way would be J. How far back do I travel to get to 13 remaining. Travel back the 12. Also see G as an option. First arrow is 13 remaining. Second arrow up to 25 shows me the extra who left.
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3/22/2017 15:45:05J
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3/22/2017 16:07:14JI like how more than one number line could be argued. Should lead to rich discussion having students explain their choice.
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3/22/2017 16:35:38J
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3/22/2017 16:47:49J
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3/22/2017 16:54:19J
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3/22/2017 16:54:36G
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3/22/2017 17:37:49J
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3/22/2017 18:39:16G, J
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3/22/2017 18:41:58J
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3/22/2017 18:58:20G, J
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3/22/2017 19:13:29GI would say G if it represents starting at the 13 and seeing what can be added to make 25. Letter J seems to show this as well with the total amount of 25 and then finding the distance back to the 13 to show that difference. In both cases, I can see the 12 being arrived at for an answer. I think I prefer open numberlines which would more closely show the thinking behind the answer.
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3/22/2017 19:24:16J
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3/22/2017 19:47:45J
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3/22/2017 20:31:37J
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3/22/2017 21:27:27J
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