Final One is a Snail Ten is a Crab Problem, a set on Flickr.We've been working on a problem from the book One is a A Snail Ten is a Crab (great book for numbers and decomposing them).
The problem was:
If you can only use snails and dogs to make 25 feet, how many different ways can you do this?
The answer is 6 combinations but we took it a step further and organized our thinking to see if we could find patterns. This helps them know if they have all the combinations to the problem.
Organizing of data is also a skill students need to have in all subject areas. If their data or results are organized it becomes easier to read, know if you've gotten all the right information or finished the problem.
There was a tremendous amount of number and problem solving in this task.
1. They had to understand the problem, work with 25 blocks, realize that there is more than one answer, know if they were finished and work with another person.
2. They needed to understand what organizing their work meant. We'd done a lot of work with organizing our writing but it didn't always transfer over into math.
3. They were then expected to find a pattern. When I asked them what a pattern was, I got ababababab, etc. The standard answer. To be able to find an increasing or decreasing pattern in all of this data was a challenge. They could see the dogs increase by one dog but they were not thinking that it increased by 4 feet. I'm not sure they really get that part of it but for right now the task was about organizing their answers to see if they can find a pattern and know if they got all the combinations.
4. Organizing of the blocks was challenge, some were stuck on "How many they needed", or only making one combination (speaking of this word, it was difficult for them to figure out what this meant. The more I talked about it the more they figured it out).
5. They had to listen to one another and take suggestions.
6. I took pictures the whole way through so they could see what others were doing. We compared pictures and talked a lot about how do we read the data and where they were in the process (if you go to the flickr site you will find the beginning photo's).
7. The manipulating of the materials and following instructions was hard for some of them, but they worked through it to come to an answer.
8. They were constantly counting or doing some kind of adding to figure out if each combination made 25 feet. Practical and world math.
Problem solving is so worth the time and effort. There was no paper and pencil work, other than writing on their white boards. I have data to help influence my instruction of more number work and other problem solving.
We've got a long way to go, but I know it will get easier the more we do. If you have any questions please let us know and we'd be happy to answer them.