Thinking MEANingfully

Last Friday the SWEET TOOTH Candy Company ran into a quality control problem. It seems that someone forgot to switch on the counting machine that insures exactly the same number of pieces of their delicious chewy candy is placed in each bag before the bags are shipped to stores. All of the bags of candy produced on last Friday had different amounts of candy. The company manager decided to call in a group of second-graders from a nearby elementary school to help solve the problem. She gave each student a bag of candy and asked him or her to complete the following activity:

. Estimate the number of pieces of candy in your bag. Then count and record the number of pieces in your bag.

. Beginning with the persons sitting next to you, swap pieces of candy with someone who has a different number of pieces than you, so that each of you has the same number of pieces of candy. If you cant divide them equally, the person who began with more pieces keeps the extra one.

. Develop a format to record this transaction.

. Find a new person to swap candies with. Continue visiting your classmates, swapping pieces of candy, and recording your transactions until you can no longer find someone to swap with.

Now consider the following questions:

. Did this process enable you to solve the problem for the SWEET TOOTH Company?

How many pieces of candy should be put in each bag?

. What happened to the number of pieces of candy in your bag as you completed the exchanging processes?

. How did you record the transactions?

. Did the total number of pieces of candy involved change?

. Does this activity remind you of any commonly computed statistic in the elementary school?

Here is the data about the starting amount of candy in each bag. Compute the average amount of candy in each bag. W working in group of 2 or 3, use counting chips and the data on the starting amounts to construct a bar graph showing the starting amounts of candy in each bag. Place your pencil across the bars on your graph at the position you have calculated for the average. What visual conclusions can you draw concerning the starting amounts and the average?

A.5		F.10		K.15
B.7		G.9		L.6
C.6		H.11		M.5
D.7		I.18		N.13
E.12		J.7		O.4
P.9

Suppose you purchace a bag of 6 chocolate chip cookies from TASTY BAKERY, located next to sweet tooth Candy Company. The manager at the TASTY BAKERY claims that his chocolate chip cookies have an average of 12 chocolate chips in each cookie. What could be the exact number of chips in each of the 6 cookies to produce a mean of 12? Can you find more than one possible answer?