In my math 157 class, we turned this common problem among cereal eaters into a lesson activity. In our activity, our cereal box had six different toys to collect. I made a prediction that I would need to buy 36 boxes of cereal to collect all six. I figured that since 36 is the square root of 6, it made sense. Instead of going to the store and actually buying cereal boxes with prizes, we conducted a simulation using our graphing calculators. {Simulations are used in probability to model what could really happen in a given situation. There are other ways to run a simulation besides a random number generator. You can use cards, dice, coins, and spinners}
There is a program on graphing calculators that generates random numbers; it is really convenient. Here is a site that has directions. The directions are entitled, "Generating Random Integers on the Home Screen". (It should be the first set of directions of the page).
For the range in our simulation, we used 1 as the minimum and 6 for the max. The random number that displays on the calculator corresponds to the toy number (1 means toy 1). We recorded tallies in a table, that looks like this...
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There is a program on graphing calculators that generates random numbers; it is really convenient. Here is a site that has directions. The directions are entitled, "Generating Random Integers on the Home Screen". (It should be the first set of directions of the page).
If you don't have a graphing calculator, there is also a website that has a random number generator. Go to this website, scroll down the page until you see the Random Number Generator. Click the link Random Number Generator.
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We repeated this process until we had at least one tally mark in each box. Once we did have one tally mark, the simulation ended.
The data table above is actually the simulation that I performed. In my simulation, I had to buy 16 boxes of cereal to collect all of my six toys (not too shabby compared to my prediction before). Even though I didn't have to buy 36 boxes of cereal and I only had to get 16, is it worth it to collect all six toys? If each box of cereal costs $3.99, it would cost me $63.84 to have six cereal box toys. In my opinion, I could get something that has much more value than a collection of cereal box toys for the same price. I think I will stick with my chances, and hope that my luck wins me a cereal box prize.
Disclaimer: If this simulation was performed again, don't expect the same results! This is a random number generator simulation, so everything is random.
Source - This simulation was adapted by Roxanne Klassen from Simulation Station: Martha Frank, Central Michigan University and Explorations Activity 10 Collect All Ten to Win, 1998 Texas Instruments Incorporated.
The data table above is actually the simulation that I performed. In my simulation, I had to buy 16 boxes of cereal to collect all of my six toys (not too shabby compared to my prediction before). Even though I didn't have to buy 36 boxes of cereal and I only had to get 16, is it worth it to collect all six toys? If each box of cereal costs $3.99, it would cost me $63.84 to have six cereal box toys. In my opinion, I could get something that has much more value than a collection of cereal box toys for the same price. I think I will stick with my chances, and hope that my luck wins me a cereal box prize.
Disclaimer: If this simulation was performed again, don't expect the same results! This is a random number generator simulation, so everything is random.
Source - This simulation was adapted by Roxanne Klassen from Simulation Station: Martha Frank, Central Michigan University and Explorations Activity 10 Collect All Ten to Win, 1998 Texas Instruments Incorporated.
As a kid I always got caught up in getting all the prizes offered in a certian cereal box. Of course when I was a kid it seemed they offered better prizes...lol. I never really grasped the concept that it could take a lot of boxes of cereal if I was to get lets just say 6 different prizes. I just always figured 6 boxes of cereal would equel 6 different prizes. This is a good activity to remember when my kids want all the cereal prizes.
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