Pre-Work: January MTF by Emily Banks https://padlet.com/emilymbanks/bzr17k8b29iejkpe After reviewing the student solutions to the candy jar problem, what do you notice and what do you wonder about the different strategies students employed? en-us 2021-01-20 14:04:47 UTC 2021-01-28 18:00:28 UTC hello@padlet.com More than one way to solve vparis https://padlet.com/emilymbanks/bzr17k8b29iejkpe/wish/1124310434 Each group thought about equality in some way..
Group 1 saw it as adding equal amounts 
Group 2 saw it as multiplying by equal amounts (same scale factor)
Group 3 used a table to arrive at the answer
Group 4 clear understanding of using unit rate to find any amount
Group 5 has a clear understanding of composing and decomposing numbers
Group 6 used pictorial models to solve and showed clear understanding of the relationship between 5 and 13.]]> 2021-01-25 21:40:15 UTC https://padlet.com/emilymbanks/bzr17k8b29iejkpe/wish/1124310434 vparis https://padlet.com/emilymbanks/bzr17k8b29iejkpe/wish/1124321697 if Group 1 over generalized, "what you do to the bottom, you do to the top" or "what you do to one, you do too the other"

if Group 5 used additive or multiplicative to complete the table

If all groups have a clear understanding of proportionality and ratios ]]> 2021-01-25 21:44:54 UTC https://padlet.com/emilymbanks/bzr17k8b29iejkpe/wish/1124321697 I noticed that. . . Out of 6 groups, only one has obviously a misunderstanding of the meaning of "same ratio". It appears that this group has failed to grasp the physical representation of "there is something (quantitity) for every one of these (another quantity). Additionally, this group is struggling to visualize quantitatively the relationship between the JB and the JR, that no matter how many there are of each one, the relationship or pairing remains the same. https://padlet.com/emilymbanks/bzr17k8b29iejkpe/wish/1127030592 2021-01-26 14:56:35 UTC https://padlet.com/emilymbanks/bzr17k8b29iejkpe/wish/1127030592 I am wondering . . .at which stage of the lesson this is. Was this an opening problem to test the level of thinking that is presenr in the classroom? Or was this an independent group activity done after the teacher has taught the lesson, or was this the lesson where the students were directed to "discover" ways to solve the problem. Noted also, that Group 4's way is procedural, so I'm wondering if they have seen similar problems like this before. How did they know right away to divide something? https://padlet.com/emilymbanks/bzr17k8b29iejkpe/wish/1127124138 2021-01-26 15:12:15 UTC https://padlet.com/emilymbanks/bzr17k8b29iejkpe/wish/1127124138 group one did not understand the concept of ratios. The other groups worked the problem differently but they did have some knowledge of ratios and proportionality. eymoore https://padlet.com/emilymbanks/bzr17k8b29iejkpe/wish/1127577062 2021-01-26 16:25:24 UTC https://padlet.com/emilymbanks/bzr17k8b29iejkpe/wish/1127577062 if group one confused additive and multiplicative relationships. eymoore https://padlet.com/emilymbanks/bzr17k8b29iejkpe/wish/1127595383 2021-01-26 16:28:33 UTC https://padlet.com/emilymbanks/bzr17k8b29iejkpe/wish/1127595383 https://padlet.com/emilymbanks/bzr17k8b29iejkpe/wish/1129189567 The first group misunderstood the the concept while the other groups showed several methods of arriving at the solution.]]> 2021-01-26 21:55:47 UTC https://padlet.com/emilymbanks/bzr17k8b29iejkpe/wish/1129189567 What caused the first to become lost in the question. https://padlet.com/emilymbanks/bzr17k8b29iejkpe/wish/1129196544 2021-01-26 21:58:35 UTC https://padlet.com/emilymbanks/bzr17k8b29iejkpe/wish/1129196544 Every group accurately interpreted that the starting ratio was 5 to 13. Group one showed a misconception of what it means to be a ratio (a comparison by division) in that they added the same number to both amounts which would change the value of the ratio. Groups 1,4,5, and 6 explained their reasoning clearly. https://padlet.com/emilymbanks/bzr17k8b29iejkpe/wish/1131810867 2021-01-27 14:37:38 UTC https://padlet.com/emilymbanks/bzr17k8b29iejkpe/wish/1131810867 I am wondering what kinds of examples were modeled for the students before seeing this problem. https://padlet.com/emilymbanks/bzr17k8b29iejkpe/wish/1131827720 2021-01-27 14:40:35 UTC https://padlet.com/emilymbanks/bzr17k8b29iejkpe/wish/1131827720 https://padlet.com/emilymbanks/bzr17k8b29iejkpe/wish/1132123294 I noticed that that each group was able to pick out that the ratio was 5 jolly ranchers per every 13 jawbreakers. In group 1 they just added 95 to each, so there was a misconception present there. In group 2 they multiplied each starting value (5 and 13 by 20). Group 3 chose to make a table to show the ratios. Group 4 found the actual ratio of 1 JR to 2.6 JB and used multiplication and in group 5 they made a table as well to display their thinking. Group 6's strategy clearly explains their thinking without the use of a table.]]> 2021-01-27 15:30:04 UTC https://padlet.com/emilymbanks/bzr17k8b29iejkpe/wish/1132123294 I am wondering if there was an exemplar posted for the students to reference and how long have they been working on this SE. https://padlet.com/emilymbanks/bzr17k8b29iejkpe/wish/1132152992 2021-01-27 15:35:04 UTC https://padlet.com/emilymbanks/bzr17k8b29iejkpe/wish/1132152992 https://padlet.com/emilymbanks/bzr17k8b29iejkpe/wish/1133537276 That every group had their own method.  Even though group 1 was wrong every group had a justification for how they got their answer

]]> 2021-01-27 19:43:52 UTC https://padlet.com/emilymbanks/bzr17k8b29iejkpe/wish/1133537276 https://padlet.com/emilymbanks/bzr17k8b29iejkpe/wish/1133542156 Did the groups present their ways to each other so they could see the various ways and talk about what is right and wrong]]> 2021-01-27 19:44:53 UTC https://padlet.com/emilymbanks/bzr17k8b29iejkpe/wish/1133542156 https://padlet.com/emilymbanks/bzr17k8b29iejkpe/wish/1133797043 Group 1 does not have a understanding of ratios. There are different representations by each group in which 5 of the groups came up with the correct answer. ]]> 2021-01-27 20:51:25 UTC https://padlet.com/emilymbanks/bzr17k8b29iejkpe/wish/1133797043 https://padlet.com/emilymbanks/bzr17k8b29iejkpe/wish/1133807367 I am wondering what type of examples did the students receive during the guided practice of this lesson.]]> 2021-01-27 20:54:31 UTC https://padlet.com/emilymbanks/bzr17k8b29iejkpe/wish/1133807367 https://padlet.com/emilymbanks/bzr17k8b29iejkpe/wish/1136807083 I noticed that each group came to an answer using a different strategy and a different justification. All groups, except group 1 came to a correct solution. ]]> 2021-01-28 15:18:24 UTC https://padlet.com/emilymbanks/bzr17k8b29iejkpe/wish/1136807083 https://padlet.com/emilymbanks/bzr17k8b29iejkpe/wish/1136856098 I wonder where the misconception came into play for group 1, as they justified their work using an additive relationship. I wonder why group 6 thought to group the 100 JR in groups of 5.]]> 2021-01-28 15:26:50 UTC https://padlet.com/emilymbanks/bzr17k8b29iejkpe/wish/1136856098 I noticed that groups 2, 3 and 4 all demonstrated conceptual understanding of how to solve the problem, but groups 2 and 4 used the most efficient method. https://padlet.com/emilymbanks/bzr17k8b29iejkpe/wish/1137414973 2021-01-28 17:01:24 UTC https://padlet.com/emilymbanks/bzr17k8b29iejkpe/wish/1137414973 I wonder what ratio instruction has looked like up until this point what experience students have had with problems like this https://padlet.com/emilymbanks/bzr17k8b29iejkpe/wish/1137420514 2021-01-28 17:02:14 UTC https://padlet.com/emilymbanks/bzr17k8b29iejkpe/wish/1137420514 I wonder the students previous knowledge and the type of instructions each group receive, especially group 1 https://padlet.com/emilymbanks/bzr17k8b29iejkpe/wish/1137772287 2021-01-28 17:59:42 UTC https://padlet.com/emilymbanks/bzr17k8b29iejkpe/wish/1137772287