Fellow P.S. 130 bloggers! We’ve been working on writing about our problem solving and our thinking about the process. We’ll soon be posting our work on the school blog to hopefully receive some feedback on how we did. We decided to attach the problem we worked on and the rubric we used to evaluate how we did in case you’d like to look at them when commenting on our work. So when you have a chance, please read over one or more of our posts and let the mathematicians know what they did well and what could be improved or was unclearly explained. We’ll appreciate your comments to help us become better math communicators.

Looking forward to hearing from you all out there!

4-501 Mathematicians

a-fishy-dilemma.doc

mathrubric1.pdf

Amar-My theory about what the answer should be for a fishy dilemma is 0-36. First, I did a diagram and used numbers. Next, I tried to use a chart with tallies. After, I realised that I can do either addition and multiplication. Finally, my answer was all the numbers, 0-36. My theory was right.

Michael-My theory of the answer was 0-36. First, I read the store for the problem. A t first ,i thought it was easy but it was not. Second, I tried to understand that no one could cach more than 3 fish. Next, I got the answers 4 and 3 and i got 12.Then i said 12 times 3 is 36 so thats how I got my answer.

Sujana-My theory was that the answer is about 25. First, I did 3 boats and 4 people in each boat. Next I tried to give everybody 3 fishes and it worked. After I realized that how about if some people got 0, 1, 2 or 3 fishes. Finally I knew that the answer had to be numbers 0- 36 becausethe hightest number of fish people can get is 36, and the lowest is 0.

Felicidad-My theory about the answer for the fishy dilemma was that it would be below 50. First, I did some multiplying a chart the chart was coulmns in a row. Next, I tried putting explanations in so it made more sense and it did make more sense because you knew what the numbers ment. After, I realized because I did all the the number work and used a chart like Dr.Math so I didn’t have to change anything. Finally, my answer was zero through thirty-six because of all the multiplication combinations.

Aldin-My theory about the answer for fishy delemma was the answer would be 32. First, I found out that there was 12 people. Next,I tried to do adding to get my answer. But it did not work. After,I relized I need to use times tables.Finally,my answer was from 0to 36.

Claudia-My theory about what the answer shoud be around 20. First, I started drawing a picture. I drew 3 circles for a boat.I drew 4 little circlws in each boat. Iattached 3 lines to the little circel.I got 36.Next,I started thinking about the maxximun and minimun.The maxximun was,36.The minimun was 0. After I realized, that what if some people did not catch fish. Finely, my answer was 0 – 36. My theory was not correct.

Kayla-My theroy about the anser is 30. First,I did try to sketch out the little fishes and 3 boats with 4 people in each boat, butI did not give out the fishes to each person because if I give out the fishes it will not be the same amout so that each person can get the same thing. Next with my partners is to do like a table and that me and my partners did is make groups(group 1 and group 2 and group 3 which means boats). After, I relized that I can put fishes for each group and I put 3 in each group. And then each person got 3 groups for each boat and I started to count by 3’s 3 times and got the number 12. Finally, my anser was 12*3=36 because there woatsere 3 groups of fishes each boat and I counted by 12’s 3 times. I got the number 12 and the numeber 3 from the boats.

Sumaiya-My theory was this problem is going to be easy but it was hard First, I drew 3 boats and 4 people in each boat. Second, I tried multipacation. I multiply 4 times 3 it equals to 12 and then I multiply 12*3=36 . Third, I realized that the answer must be 0-36 and I drew tally marks in the chart. Finally, I found my answer using these steps.

Sammy-My theory about the answer is 3-06 First, I drew 4 boats then 3 in each boats each person caught 3 fish. Next, I tried to count it all up and I got 36. Next, I count all of it thats how I got 36 After I realized I should use a little bit more muiltplication. Finally, my answer is 36 and the minmium is 0.

Enrique-My theory was first to draw about three boats and in each boat I drew four persons in each boat. Second,I tried to add but it didnt work. Then I used multipacation I kept on doing it then I estimated I said 29. but when I imagind that each person got a fish and then what drew was what I imagind.Then I counted twelve 3 times and I told the teacher if it was 36 and it was.

You are very careful readers and think about what the problem means.

You all found different ways to solve the problem.

Amar, I like how you tried different ways in order to understand the problem. Drawing a diagram and using tallies on a chart are good ways to help you figure out if you need to add, subtract, multiply, or divide. Notice how spending time understanding the problem helped you them compute the answer.

Michael, you read carefully, good job. Notice how you found the amount for one boat and then multiplied by the number of boats. That is a good way to do it. You are very organized.

Sujana, you did a good job of thinking about what the question wants you to find. You first estimated an amount. This helped you to think more carefully about the wording in the problem. You realized that they could be other numbers of fish. This is good thinking outside the box.

Thank you for sharing your solutions. I am learning about how you solve problems.

Great stuff 4-501!

I made a Lesson Plans & Rubrics category so as you and others post these resources they’ll be easy to find in the future.

Keep up the good work!

Rhys

Moeez and Tandid’s comments

Amar- You have a good theory and you explained how you got your answer but you need to expand your explanation by what numbers you used for the problem.

Enrique- We think the way you did your steps were perfect but you were a little vague in some ways with your theory. For example, what made you say your estimation is 29?

Aldin- The way you found your answer was decent, but you need to explain where you got the numbers you used. For instance, how did you get the number 12?

Kayla-I really like the way you wrote about your multiplication in more than one way. You clearly understand multiplication when you can say 12*3=36 and then restate that as 12’s 3 times. That shows a deep understanding of what is happening in multiplication. GOOD JOB

Next you said your answer was 36. What is the 36 representing? Is there only one answer to this problem?

What would have happened if each person was able to catch as many as 4 fish?

Amar- I think I would really like to see your chart and your diagram and then you might be able to convince me that you indeed have a correct solution. What would happen if there were more boats or more people on the boats? What if each person was able to catch more fish or less fish? Once a mathematician solves a problem, he or she tries to solve more cases and come up with more generalizations. I would challenge you to try some of these extensions. Keep me updated on your work.

Claudia- I am very impressed with your precise mathematical language. You correctly used the terms maximum and minimum and I am glad to see you questioning your own thinking as you worked on this problem. Mathematicians do this all the time!

Sumaiya- Like Kayla you showed multiplication with more than one representation. How did you incorporate the tool of a tally chart to represent your work and bring you to a solution? It seems like you were the only one in your class who thought about it this way. I love originality and mathematicians are always looking for novel ways to express their thinking. Please show me your work one day.

Michael-Just like a real mathematician you thought at first the problem was easy and then changed your thinking when you realized it was more involved. You said your answers were 4 and 3 and 12. What were these the answers to? Try to be very precise and clear about what each of your numbers mean. This will help other mathematicians understand your work and see the validity in yoru numbers. Congratulations on reaching a correct solution and sticking with it until you reached that solution.

Sujana- I agree with your solution. I feel like you are missing a step in your explanation. What did you do after you thought about trying 0 fish, 1 fish and 2 fish for each person?

Felicidad- I would like to see your chart. I wish there was a way you could have included the chart here. What might you tell us specifically about the numbers in your chart that would prove that your solution is indeed correct? I noticed you wrote about multiplication combinations. This is very high level mathematics and combinations are difficult for many mathematicians that’s why I’d really like to see your chart.

Aldin- You surely are doing the work of a real mathematician. You, like the mathematician tried one way and realized that adding didn’t work and then tried multiplication. Congratulations!

Sammy- You also tried a few ways to get to your solution. I like the way you used the word minimum in your response. What does your answer 36 and a minimum of 0 mean? what are the numbers representing? Try to remember to answer the question being asked directly and explain how you got to your answer. The mathematician inside of you began with one answer and then very smartly change the answer as your understanding of the problem changed.

Enrique- I hope you realize that now you truly are a mathematician. You changed the way you thought about the problem, you revised your answer and you discussed with Ms. Silberman to be sure your thinking was on the right track. These are the same things mathematicians do as they solve problems.

One General Comment to the Math Community in Ms. Silberman’s Class:

Remember to always give labels to your numbers. For example, talk about the 3 boats; 4 people; 36 fish.

Try to extend your work by posing further questions like the ones I wrote in my comments to Amar.

Your writing needs to explain the work you’ve done on the charts diagrams or tallies. In other words explain in words your proofs. Now that we are good at reflecting on our work, we need to be able to construct beautiful proofs.

I look forward to seeing more of your work.

Ms. Fera,

I was reading through your post on the Math problem and i read what you wrote to Felicidad and there is a way we can put her chart on this Network? Really all you have to do is take a picture of it and upload it from the camera and then upload it to the page. I can show you a sample of how i did this if you would like.

Mr. Stegman