## Thursday, January 6, 2011

### New Math Topic

 Maddy draws a block while Arvid makes tally marks.

 The group chart

 This group elected Ariana to do all the marking. She didn't mind.

 Oliver and Owen look at the group data chart so they could complete their graphs.

 Sophie does such neat work on her graph.

Starting this past Monday, the children who come to me for math class are learning about a brand new concept. We are collecting data and analyzing the results, doing probability experiments and learning about sampling.

Sampling is a technique that is used in statistics to gather information about a lot of people or things without testing each one. For instance, scientists pull a small container of water from the ocean to test to see if the beach is safe for swimming. Businesses use this all the time - in fact, a parent who was observing in math class one day remarked that we were doing what a college marketing class might do!

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. Nilay said there could be 7 yellow and 5 green, and Maddy 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 2 more times, so in all we did 36 draws. After looking at all the data we collected, we made guesses about how many blocks of each color were in the bag. Maddy nailed it, and correctly guessed 8 yellow and 4 green.

On Tuesday, we did the same thing - but this time there were 3 colors!

On Wednesday and 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!

This is just an example (rather long winded, I apologize) of the type of whole group lessons I like to do.