Number Sense 039

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Saturday February 04, 2012 · 10:18 AM PST

2012/02/04 · 10:18

Last week, in Number Sense 038, Awkward Goat proved that a complete list of prime numbers could not be made, because there was no end to prime numbers: more could always be found and added to any supposed complete list of prime numbers. He didn't phrase it quite this way, but he proved there are an infinite number of primes. This week, the weather is unseasonably warm, daffodils are poking their buds above the ground, and spring is in the air.

Orinoco

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Saturday January 28, 2012 · 7:47 AM PST

2012/01/28 · 07:47

Last week, in Number Sense 037, Awkward Goat proved that all counting numbers (numbers of goats in formation for the Marching Goat Society) were either prime numbers or the product of prime numbers (although he called them primary numbers, analogous to primary colors) much to Billy Goat Gruff's dismay. This week, the goats got together to discuss these awkward numbers a bit more

Orinoco

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Saturday January 21, 2012 · 7:15 AM PST

2012/01/21 · 07:15

Last week, in Number Sense 036, Awkward Goat challenged the Marching Goat Society to disprove his conjecture that every time they got into formation, their rows and their columns were awkward numbers, or the product of awkward numbers. The Marching Goats couldn't do it with only ten goats, but they vowed to return this week, with many more goats, to prove Awkward Goat wrong.

Orinoco

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Saturday January 14, 2012 · 12:38 PM PST

2012/01/14 · 12:38

Last week, in Number Sense 035, we took a look at a proof for the formula we developed for adding up series of numbers. I really wasn't happy with the way it turned out, so we are going to shift gears a bit, and bring back the goats.

The goats joined a close order drill society and learned how to march in formation.

Orinoco

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Saturday January 07, 2012 · 9:08 AM PST

2012/01/07 · 09:08

Last week, in Number Sense 034, we developed a formula for figuring out the sum of a series of numbers. We tried out our formula on a couple of examples, and it worked. We also came up with a diagram showing how the formula found the sum for one of the examples. But we didn't prove the formula was true. Two or three examples of it working does not prove it will always work. In order to do that, we must be a bit more rigorous.

Orinoco

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Saturday December 31, 2011 · 9:12 AM PST

2011/12/31 · 09:12

Last week in Number Sense 033, we took a look at an equation that produced a parabola when it was plotted on Cartesian coordinates. This opens up the possibility of a situation having two solutions, or no solutions. This week I'd like to change course a bit, and begin a discussion about how we know mathematical things.

Orinoco

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Saturday December 24, 2011 · 9:30 AM PST

2011/12/24 · 09:30

Last week, in Number Sense 32, we took two linear equations and plotted them on a graph, and discovered that the intersection of the two lines gave us a solution that worked for both equations. This is a very powerful idea.

Neither of the linear equations had a single solution. We could pick many different values for the amount of liquid milk, and then use one of the linear equations to calculate how much we had left to make cheese, and still not know how much was actually used.

If we used the other equation, again, we could pick many different values for the amount of liquid milk, and calculate the amount of milk used for cheese, and still not know how much was actually used.

But! when we combined those two equations, there was only one combination of liquid milk and cheese milk that worked for both. There was AN ANSWER! A single, gotta be this, honest to god answer, just like the answers we got in arithmetic when we were asked to add 3 plus 6.

Orinoco

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Saturday December 17, 2011 · 8:37 AM PST

2011/12/17 · 08:37

Last week, in Number Sense 31, we made a graph of a more continuous function: how much grass a herd of goats might eat each hour. We also took a look at what the graph might look like if it were an inequality, rather than a strict equality. This week we are going to solve a problem using a graph.

Orinoco

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Saturday December 10, 2011 · 8:47 AM PST

2011/12/10 · 08:47

Last week, in Number Sense 030, we took a look at a situation where two quantities were related to each other. We used Cartesian coordinates, commonly called a graph. This week I'm going to expand on the graph a bit, and take a look at what else we can do with it.

Orinoco

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Saturday December 03, 2011 · 12:44 PM PST

2011/12/03 · 12:44

Last week, in Number Sense 029 we added and subtracted nothing from our equations, and found that to be a useful technique.

Up until now, we have been dealing with one unknown, one goat, and we have come up with methods for finding the value of that goat. But what do we do when we have more than one unknown?

Real problems are considerably messier than the simple problems we set up to teach basic ideas, simple problems are rarely encountered in the real world, or, when they are, can be solved with the most simple mechanical methods.

Have you ever played cards? When you dealt the cards, did you think your were dividing a certain number of cards by the number of players? Probably not. You just dealt the cards, one at a time, to each player in turn. A simple real world mathematical problem, solved so simply that few people even think they are doing math when they solve that problem.

This week we will begin to look at problems where there are two unknown quantities, somehow related to each other.

Orinoco

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Saturday November 26, 2011 · 8:20 AM PST

2011/11/26 · 08:20

Last week, in Number Sense 028 we put some goats on a scale to solve an algebra problem. This week, we are going to play tricks on the scale, by adding and subtracting nothing.

Orinoco

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Saturday November 19, 2011 · 10:40 AM PST

2011/11/19 · 10:40

Last week, in Number sense 027, we outlined the rules of the algebra game.

It was some pretty rough sledding, and there weren't any goats around to liven things up. This week, I'm going to see how we can use these algebra properties and to solve some problems

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