Thursday, April 11, 2013
Sampling - Mystery Bag!
This week we continued our math topic of data collection and probability, extending it slightly to include "sampling". Sampling is getting data from part of a group and use it to give information about the whole group. We read a story about a birthday party game where children could take a sample of candies from a huge jar to make a good guess about the total number of each color in the jar (without having to count each and every candy).
On Monday, I showed the children a bag and gave them hints about what was inside. There were 12 blocks in the bag, and some of the blocks were yellow and some were green. I asked them what could be in the bag. Someone raised their hand and said there could be 6 yellow and 6 green. I wrote this on the board. Then I asked for other suggestions. Another child said there could be 7 yellow and 5 green, and yet another chimed in and said that there could be 8 yellow and 4 green. We noticed a pattern! After we got to 11 yellow and 1 green, someone offered 12 yellow and 0 green - but we decided that didn't belong on the board because one of the first clues was that there were both yellow and green. Someone then said we "could go backward" and thus we started listing 11 green and 1 yellow, and so on.
Then we did a sample - taking the bag around, each child took a block without looking, told me the color, and then put the block back in the bag. We did this 12 times and looked at the result. Then we repeated the process 1 more time, so in all we did 24 draws. After looking at all the data we collected, we made guesses about how many blocks of each color were in the bag. Several guess correctly, that there were 7 yellow and 5 green.
On Tuesday and Wednesday we did the same thing - but this time there were 3 or 4 colors. We also extended our sample, drawing more and more times. The children are now all able to articulate that the larger the sample taken, the probability of a more accurate guess increases.
Today, the children completed their own samples. In groups, they did a sampling with 4 different bags with 4 different combinations of colors. This took a lot of team work, as roles were assigned, they had to decide which direction the bags would travel, etc. After the initial charts were completed, each child transferred the information into a graph. Then I read notes like, "this bag has an equal number of red, green, blue and yellow blocks" and children had to guess what bag that described. Not all were clear cut! Only one group made the right guess for all three bags ... but all were able to make good guesses that matched the data they had collected. Analyzing data is a very important math skill, and these young mathematicians are getting very good at it!