## Friday, May 11, 2018

### Math Project - Sampling

This week, my math group embarked on a project that involved sampling. Sampling is a technique that is used in statistics to gather information about a lot of people or things without testing each one. In our scenario, we started on Monday by receiving a mysterious letter from Ms. Oatie Oats, the president of Cheerios. Somehow, she had heard of our math group, and the amazing work they have been doing collecting data, and probability work using dice and other tools. She needed our help.

This is the letter she sent us:

Dear Students of Carpenter’s Math Class,

I’ve heard that you are an amazing group of math students. I’ve also heard that you’ve been doing a lot of work learning about probability using one die. I was wondering if you could help me figure out something using a method called SAMPLING.

Many companies are putting toys in their products to try to get customers to buy more. Our company thinks this might be a good way to get families to buy more boxes of Cheerios. They will buy six different toys and put one in each box of Cheerios. That way, kids will want their parents to keep buying Cheerios until they have all six different toys.

I need you to figure out if this is a good plan. It will cost more to put toys in Cheerios, right? So I want to be sure that families will really buy more boxes of Cheerios to get the toys. Please answer these two questions:

·      What toy should Cheerios put in the boxes to make kids want to buy more?
·      How many boxes will a family buy (on average) to be sure they collect all 6 toys?

Sincerely,
Ms. Oatie Oats
President, Cheerios

So, what could we do? We figured we needed to use the tools we had used before - namely, some data charts and a die. Each child did four rounds of testing. Tossing a 6-sided die, we made tally marks on a chart to indicate a toy - if we rolled a 3, we got toy #3, for example. We kept tossing the die until we got every toy, and as soon as we got the last toy, we stopped and counted all of the tallies to see how many boxes we had to "buy" to get all 6 toys.

Since each child did four rounds of testing, and there are 11 children in math class, that means we had 44 "families" worth of data. Some families were lucky. They had to buy only 6 boxes of Cheerios to get all six toys (the child rolled a 1, 2, 3, 4, 5, 6 on their die, without rolling a single digit twice). Others were NOT so lucky - they had to buy many more boxes of cereal. One family had to buy 31 boxes before they got all 6 toys!

We played with this data all week. We found the average (or the mean) buy adding the numbers all up and dividing them by 44. That was a good lesson in itself - what does it mean to find the average? We decided it might be a good time to break out some calculators. Families ended up buying, on average, 12.6 boxes of cereal if they wanted to get all 6 toys.

We also spend some time find the median, the mode, and the range - just in case some students felt those were important statistics to add to their research.

Finally, on Friday, it was time to write back to Ms. Oats to tell her what we found. We talked about what part of our letter was fact-based, and what part was opinion based. We could include information about what our research showed us, and include some statistics. And then we could also give her our opinion on what toy we think would make a fun choice that kids would really love.

This was a fun and engaging project. And, yes, Pokemon booster packs with perhaps baby turtles would make for fine toys in Cheerios. Are you listening, Ms. Oatie Oats?