12 of 63 Items .... Type: Explainer

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Say you had data that told you that
The proportion of all US public school students whose families are low-income:
In 1989, less than \(\frac{1}{3} \)
In 2013, more than \(\frac{1}{2} \)

Interpret this in a positive way.
Interpret this in a negative way.

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The last of the three related-rate geogebra problems from Kate Nowak. It's the related rate problem from calculus: the conical tank being filled with water.

Adjust the slider and... wait, what is changing and how?

For every click of the slider:
Is the depth increasing at a constant rate?
Is the radius increasing at a constant rate?
Is the volume increasing at a constant rate?
How can you tell?

• Where or how, in the RealWorld^tm, could we see the constant increase in volume?


• Where or how, in the RealWorld^tm, could we see the constant increase in radius, or depth?

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The problem speaks for itself.

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You've been asked to shade one-third of this triangle.




And how do you know?

Here's a response:

• Is this a valid way to get one-third of the triangle?


• Does this technique require that we stipulate a right triangle?


• Does this technique require that we stipulate an isosceles one?


• Do the lines have to be parallel to each other?


• Do the lines have to be parallel to a side for this to work? 


• Perpendicular to a side for this to work?

• How might we generalize this method (if it can be generalized)?

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The sum of \(\frac{1}{4}\) and a number is equal to the product of \(\frac{1}{4}\) and the number.

(a) Explain why the number must be negative.

(b) What's the number ?

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If you are parked during any part of the time indicated, then you need to pay, even if it's only for a few minutes at the beginning or end of your shopping. (If you only are there for the five minutes between 8:00 and 8:05, you only pay a pro-rated fee.)

If you park at any random time and leave your car there for an hour, are you more likely to pay or more likely to not pay?

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What positive and negative shapes (and their dimensions) go into making this yellow figure?

3

On a side note: isn't it cool that I can say the phrase "negative shape" and no one bats an eye?

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What shapes (positive or negative) go into making the shaded area?

Include important dimensions.



How about here?



What shapes (positive or negative) go into making this figure?

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Can you explain how this is possible? Qatar is only 23.5% women?

Before we get into these issue-specific statistics, we can see in basic demographics something that’s different about living in Saudi Arabia as a woman: Only 42.5 percent of the population is female.

There are only five countries in the world (for which we have data) with a smaller percentage of female residents, according to the World Bank:

Qatar (23.5 percent of the population is female)
United Arab Emirates (29.9 percent female)
Oman (36.4 percent female)
Bahrain (37.8 percent female)
Kuwait (40.2 percent female)

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You only get to make one and you've only got 6 sides. What are the six most important items of math in your opinion? What would you put on your Minimal Math Cube?

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Everyone seems to have an opinion and now, students, we're asking for yours.

Scott Macleod says, "We now live within multidirectional conversation spaces in which 12-year-olds can reach audiences at scales that previously were reserved for major media companies, large corporations, and governments. We all now can have a voice. We all now can be publishers. We all now can find each other’s thoughts and ideas and can share, cooperate, collaborate, and take collective action."

So how should addition, and by extension subtraction, be taught? The standard algorithm or by piecewise addition?

Weigh in on the "Letter to Jack".




How would you teach these two problems?

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Once upon a time, the world's smartest person (Marilyn vos Savant, IQ: 228) received a question for her newspaper column.

Suppose you're on a game show, and you're given the choice of three doors. Behind one door is a car, behind the others, goats. You pick a door, say number 1, and the host, who knows what's behind the doors, opens another door, say number 3, which has a goat. He says to you, "Do you want to pick door number 2?"

Is it to your advantage to switch your choice of doors?
Craig. F. Whitaker, Columbia, MD