**A Math Forum Project**

Student Work

## 12201: Ticket Tables

Richard needs to sell 16 tickets to a large group. Knowing that the cost of one ticket is $5.50, Richard calculates the cost of 16 tickets like this:Explain how Richard solved the problem using his ratio table.

## Teacher's post to a discussion

I have started with the paper version of PoW. Since my 7th graders were working with ratio tables, I decided to use PoW 12201. I had my students do a couple of revisions and then a final copy. I thought it would be helpful to get feedback from the Math Forum so that I could see the type of comments that mentors give and how the students' responses are evaluated.

I submitted one of the responses and the response from the mentor, Suzanne, was extremely helpful. My plan is to share this response with my students and discuss the comments and the grading. Suzanne directed me to a page which gave an explanation of the grading levels. I have printed this page for my students to keep in their folders.

I found the PoW to be extremely helpful as it supported the work we were doing. Also I was able to deal with certain issues which I saw as I reviewed their understanding of the problem.

## Imani, age 12

The final cost for 16 tickets was $88.00.

First Richard multiplied the cost of one ticket times 10 and got $55 a a result, then he multiplied the tickets cost for one times 2 and doubled that and the cost was $22 for 4 tickets. Next Richard added the cost for 2 tickets to the cost for 4 tickets, that got $33 for 6 and added that to $55.50 for 10 and ened up with $88.00 as a final cost for 16 tickets.

## Mentor's response

Hi, Imani. You have a great start on your solution. I like how you've explained both how many tickets Richard was thinking about in his chart and also how much that many tickets would cost.

At one point you write that Richard added to $55.50 but I don't see that number anywhere in the chart. I wonder if it might be helpful to explain how you used the "cost of one ticket." How does that work when you do it in your head?

Talk to you again soon.

SuzanneSummary: Problem Solving Interpretation: Practitioner Strategy: Practitioner Accuracy: Apprentice Communication Completeness: Practitioner Clarity: Apprentice Reflection: Novice## Teacher's post to a discussion after her student received a response

Today I shared with my 7th grade group the response to one of their classmate's submission. I referenced this in my last discussion dated 9/24. The response was mixed. Even though I had told them about it actually reading it seem to interest them.

In the response, the mentor, Suzanne, had a wondering about how the student had multiplied 5.50 by 10 because she came out with $55.50. We discussed this in the class by first giving the student the opportunity to explain what she was thinking. I then had other students chime in on their ideas about doing this problem mentally. I was surprised at the variety of "ideas." WE HAD A LOT TO TALK ABOUT.

As a teacher, this was a learning experience for me about looking at students' work. I would have dismissed the $55.50 as a mistake, which I did, when I looked at it. I was quite taken aback at how unsure and little they knew about the working of powers of ten. This provided us with a quick learning moment. This topic was actually a suggested area of review in the first week of the core curriculum and we did not get to it. I think we will continue to glimpse at it each day this week.

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