I guess God really did create the integers

Several years ago, I was reassured once again that I had married the right person when The (much smaller then but equally) Spoiled One asked him,

“What does the name of your book mean, God created the integers?”

He explained that while one can have 1 rabbit

or 2 rabbits

You can have zero rabbits.

All of those are concrete things that exist in nature. You cannot, however, have one-half of a rabbit or one-seventeenth of a rabbit.

Well, theoretically, you could, if you killed it and chopped it into four pieces, as The Spoiled One gruesomely pointed out. Her father, who watches too much Monty Python countered that then it would not be the rabbit as God made it but, in fact, an ex-rabbit.

All of which brings me to Fish Lake, the game we are working on currently, which involves fractions. It really has not been that difficult to come up with believable examples of how early Native Americans might have used fractions –

“Leave for camp when the lack is three-quarters in the shadow.”

“We used two rabbits to make enough stew for two people. If you are out hunting alone and just making stew for yourself, you would make half as much, so you’d only need one rabbit.”

As our Dakota cultural consultant, Dr. Erich Longie pointed out, of course the Dakota people used math. The traveled over a very wide area and would meet up in the same locations, it was hardly by accident – well, you’ll have to see the next two games.

The part I am having a hard time with, though, is coming up with realistic uses of percentages and decimals. I can see where a chief might have 100 warriors and need to put them into four groups, say, to attack from four different directions. So, 25/100 = 1/4  and maybe then each group would get 1/4 of the food, 1/4 of the war ponies and so on.

I really can’t think of any situations, though, where the chief would sit down and say,

“Okay, 75% of the warriors have a horse, that is the equivalent of 3/4.  Thinking of it another way, if I had ten warriors, 7.5 of them would have a horse.”

We have four cultural components – two are Dakota (Sioux) and two are Ojibwe (Chippewa) and they have given us a lot of great examples using math for travel, measurement, building tipis and wigwams, calculating odds when deciding to try to steal a buffalo pony and more. However, I’m still puzzling over how to include realistic problems to meet common core standards on decimals and percentage equivalence with fractions.

God may not have only created the integers, but I am pretty dead certain that it is accountants and engineers who created the decimals.

Any creative suggestions would be much appreciated.

local_offerevent_note July 28, 2013

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4 thoughts on “I guess God really did create the integers”

• Mahana says:

How about dividing something measured continuously (water, grain..) between something measured discretely (people, animals)? E.g family A has 6 people and family B has 3 people, therefore family A has 6 out of 9 people = 6/9 = 2/3. If we want to divide a container of water between the families, what percentage should fairly be given to each family?

• What about things related to distance or time, or some kind of “percentage completion”? I guess this is related to travel & measurement, and this one place people see percentages today (waiting for a program, e.g. a game, to load).

e.g. — We need to travel 5 km to get to the meeting place, and we’ve traveled 4 km. Are we 70%, 80% or 90% of the way there?

Or after spending 15 minutes building a structure, the Chief says that we are 75% to seeing the structure to completion. How much more time is required to finish the structure?

• AFAIK the original idea behind percentages was to compare more easily various fractions by converting them to a common denominator:

Last week, Ahote used 15 arrows to kill 4 preys while Takola killed 6 preys with 26 arrows.

The same evening, like every hunter ever, they argue over bragging rights. Who’s the most accurate hunter? (i.e. if you have only 3 arrows and you have to hit a target, who’s your best bet?)

Using percentages, they can figure out who is the most accurate.

They could also use percentages to figure out the food reserves available compared to their needs or the ratio of trained fighters compared to the size of the tribe. etc.

Decimals could be explained as another way of writing percentages, being more convenient to use when the number is higher than 100% (60% is easy to visualize, but 6550% doesn’t immediately ring a bell, whereas 65.5 is easy to understand)

• Those are some brilliant ideas. Thank you very much

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