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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.

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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

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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.

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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.

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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?

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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?

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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.

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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.

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if group one confused additive and multiplicative relationships. 

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if group one confused additive and multiplicative relationships. 

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The first group misunderstood the the concept while the other groups showed several methods of arriving at the solution.

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What caused the first to become lost in the question.

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What caused the first to become lost in the question.

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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.

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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.

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I am wondering what kinds of examples were modeled for the students before seeing this problem.

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I am wondering what kinds of examples were modeled for the students before seeing this problem.

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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.

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I am wondering if there was an exemplar posted for the students to reference and how long have they been working on this SE.

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I am wondering if there was an exemplar posted for the students to reference and how long have they been working on this SE.

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That every group had their own method.  Even though group 1 was wrong every group had a justification for how they got their answer

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Did the groups present their ways to each other so they could see the various ways and talk about what is right and wrong

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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.

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I am wondering what type of examples did the students receive during the guided practice of this lesson.

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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.

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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.

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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. 

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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. 

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I wonder what ratio instruction has looked like up until this point what experience students have had with problems like this

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I wonder what ratio instruction has looked like up until this point what experience students have had with problems like this

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I wonder the students previous knowledge and the type of instructions each group receive, especially group 1

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I wonder the students previous knowledge and the type of instructions each group receive, especially group 1