Well I've been a bit late on this assignment, for a couple of reasons: I don't have a class to work with; and, I've been in Florida, at the beach and on the golf course, and 80 degree weather tends to make one more into those activities than a hard concentration on a math project. However, I'm back and have given considerable thought to a project I'd love to do with kids (if I only had a class). I enjoyed Leinwand's examples of real world math and communications, and they caused me to think about the essential matter of student engagement and group discussion around a common interest/set of problems to solve.
I raise bees as a hobby and every year teachers in different schools have asked if I would come and demonstrate to the kids how bees live, work and make honey. It's generally related to a science lesson(s) on insects; but I'm thinking that there is considerable mathematics which can involve student study, research, graphing, learning basic statistical measures like mean, median and mode, cost calculations,marketing and profit. If one wanted to integrate some science and/or social studies as well, there are topics such as pollination, disease, genetically modified seeds, charity organizations like the Heifer Project and their relationship to stemming world hunger, etc. So, my project will have several learning targets: Develop an understanding of the differences between mean, median and mode through activities of weights and measures, comparative shopping, and timing of honey crystallization; learn the process of spinning honey; use estimations to facilitate reasoning; calculate cost, profit and loss.
As an opener, I'd display a few bees (dead, of course) and a large container of honey and ask what's the relationship between them, and assuming they'll comment that bees make honey, I'd ask how anything that small can make so much to fill a hive box that weighs up to 100 pounds (and, they'll do that up to three times in a summer!) For some kids, you could ask what's the ratio between 3 lbs. of bees (the standard one purchases for one hive) and a 100 lbs. of honey. I would continue by having the class weigh an empty super (the name of a hive box where honey is stored), and then weigh a full one and ask them to calculate the difference. This gives them a sense of the volume of honey made in one super They'll also use this difference later to calculate the potential amount, in lbs. and ounces, they could pour in containers and sell in their school. And related to this will be an activity where the teacher asks them to shop with their parent (for observational purposes) and compare the prices of different sizes of honey jars, different producers' pricing and perhaps even the differences between stores and a local farmers market. All of these data are brought to school and teams of students will chart them for comparative purposes, as well as to calculate the mean, median and mode in pricing in the different venues, and for different sizes. They can have a discussion about how much they think they might charge if they sell their honey (because the next activity is to spin) in their school, and why they'd charge that amount. So on to spinning - first we'll have a couple students weigh the empty spinner - we'd set up the equipment to spin 10 frames, having weighed each one first (so they can again calculate the average weight per frame) and commence spinning the honey. The teacher can also ask for opinions (and have the kids chart them) as to how much total honey (in lbs.) they estimate they'll draw. When the draw is completed, they can again weigh the spinner and compare their earlier answers to the amount they estimated. The next step is to fill containers (we'll use 12 or 16 oz. containers); as they are doing that, have them calculate how many 12 or 16 oz. containers will be filled by that much honey if they use the old axiom, " a pint's a pound the world around". They can then calculate how much money will be gained if they sell every jar. After they have a figure, they can be asked, if we subtract the cost of the containers, how much will we have then? and lastly, they can have a problem question that speaks to the real value of total cost against total income, such as, if we calculate the cost of three pounds of bees, what will our profit be then? or, how much would we have to sell them for if we include the cost of the bees and the containers? This, of course, says nothing of their labor for spinning, filling jars and marketing. There are many additional components to this kind of endeavor with the kids; one is only limited by imagination and desire to take them to a real world set of experiences using their math.
Should any of my colleagues in this mathematical adventure we're all in, have an interest in constructing this unit with me, I'd be more than happy to collaborate and come to school to discuss it.
