## Monday, March 31, 2014

### 78: That Set

An updated version:

And a video zooming in ... 2 * 10275

## Sunday, March 30, 2014

### 77: Some Probability Calculations are All Wet

Because it's Sunday, here's another:

So ... what do you think? How likely is it that you'll get wet if you walk outside today?

### 76: Fractions and decimals

Which do you think works better?
"Decimals are a subset of fractions." OR "Fractions are a subset of decimals."

Say What?

## Friday, March 28, 2014

### 74: The One where we discuss Size.

After we laugh at the joke,

Consider:

Here is the NPR discussion on this.

## Thursday, March 27, 2014

### 73: Four-Squares

2² ends in a 4
12² ends with 44
Find a square that ends with 444.
Find another that ends with 4444.

## Wednesday, March 26, 2014

### 72: Trends in the Data

FiveThirtyEight had this graph and the comment. "It looks to me as if Mr. Cain had been on a positive trajectory before, perhaps having moved up to about 28 percent of the Republican vote."

Is that blue trendline reasonable?

Some background information. From Wikipedia, "Cain ran as a Washington outsider and became a front-runner in the race in the fall of 2011. However, Cain's support plummeted after several women alleged that he had engaged in sexual harassment or, in one case, a 13-year extramarital affair. Cain and his wife unequivocally said the accusations were false, but Cain, citing the toll the allegations had taken on his family and his political support, suspended his campaign on December 3, 2011."

## Tuesday, March 25, 2014

### 71: Is it easier to be wrong?

Which is easier ... a completely correct bracket or a completely wrong one?

## Monday, March 24, 2014

### 70: Logarithmic Fun

What is $log_2 3 * log_3 4 * log_4 5 *log_5 6 * log_6 7 * log_7 8$ ?

## Sunday, March 23, 2014

### 69: Triangular Fibonacci Numbers

1, 3, 21, 55 only triangular Fibonacci numbers.

Any tetrahedral beyond 1?

## Saturday, March 22, 2014

### 68: The cool pythagorean triangle.

I lied. It's not a Pythagorean triangle. It's TWO Pythagorean triangles that make up a Heronian triangle.
What other Pythagorean Triangle combinations make a triangle like this?

## Friday, March 21, 2014

### 67: Two Questions of Average Difficulty

From Gabriel Rosenberg via email

True or False?
If my stock increases in value by 28% one year, and then decreased in value by 2% the following year, then on average it increased by 13% per year.

If I powerwalk to school at a constant speed of 4 miles per hour, and then saunter home at a constant speed of 2 miles per hour, then I averaged 3 miles per hour for my trip.

## Thursday, March 20, 2014

### 66: Go Fish with Primes

3 William Carey, on a Dan Meyer post:
We play Prime fish with the sixth and seventh graders. You need a special deck of cards, but it’s an easy deck to make (edited, - ed.):
Ten cards with a "2" on them (or two fish)
Ten cards with a "3" on them (or three squid)
Eight cards with a "5" on them (or five eels)
Five cards with a "7" on them (or seven sea-slugs)
Two cards with a "11" on them (or eleven shrimp)
Each player draws four cards. They multiply their hand together, and announce only the product (!) to the group. They then play go-fish.

It’s fun to watch the kids debate whether there’s a strategy to the game. It’s more fun to watch them work out the strategy once they decide that there is a strategy.

What's the strategy?

## Wednesday, March 19, 2014

### 65: Square Fibonacci Numbers

What are the only square Fibonacci numbers?
How can we show that these are the only ones?

## Tuesday, March 18, 2014

### 64: Who's Better at Packing

Which student would you choose to pack your parachute?

## Monday, March 17, 2014

### 63: Who's Better at Doodle Jump?

Dan might not even remember this ...

How many different ways can you compare these two to decide that Dan is better?

How many different ways can you compare these two to decide that Mike is actually better?

Posted years ago by @ddmeyer

I think my pre-algebra came up with seven different ways to decide.

## Sunday, March 16, 2014

There are 68 teams in the U.S. College Basketball Tournament.  The bottom eight play an extra round; the winners get the bottom seeds in the main tournament.  The main bracket has 64 teams in a single elimination tournament.

In the main bracket, how many games will be played, total?

If you just flipped a coin, what is the probability that you'd win them all?

Warren Buffet has offered $1 Billion Dollars to anyone who does pick all the games. What are the chances he will lose 1/60th of his money? If you'd like to join the fun. with the rest of the Mathtwitterblogosphere. ## Saturday, March 15, 2014 ### 61: Textbook Error You can tell by the font this is a textbook. You can tell by my tone that this is an error. Fix that Graph ... Fix That Question. ## Friday, March 14, 2014 ### 60: We watch someone else talk about pi Well, recite it, actually ... 3.14159265 3589793238 4626433832 7950288419 7169399375 1058209749 4459230781 6406286208 9986280348 2534211706 7982148086 5132823066 4709384460 9550582231 7253594081 2848111745 0284102701 9385211055 5964462294 8954930381 9644288109 7566593344 6128475648 2337867831 6527120190 9145648566 9234603486 1045432664 8213393607 2602491412 7372458700 6606315588 1748815209 2096282925 4091715364 3678925903 6001133053 0548820466 5213841469 5194151160 9433057270 3657595919 5309218611 7381932611 7931051185 4807446237 9962749567 3518857527 2489122793 8183011949 1298336733 6244065664 3086021394 9463952247 3719070217 9860943702 7705392171 7629317675 2384674818 4676694051 3200056812 7145263560 8277857713 4275778960 9173637178 7214684409 0122495343 0146549585 3710507922 7968925892 3542019956 1121290219 6086403441 8159813629 7747713099 6051870721 1349999998 3729780499 5105973173 2816096318 5950244594 5534690830 2642522308 2533446850 3526193118 8171010003 1378387528 8658753320 8381420617 1776691473 0359825349 0428755468 7311595628 6388235378 7593751957 7818577805 3217122680 6613001927 8766111959 0921642019 8938095257 2010654858 6327886593 6153381827 9682303019 5203530185 2968995773 6225994138 9124972177 5283479131 5155748572 4245415069 5950829533 1168617278 5588907509 8381754637 4649393192 5506040092 7701671139 0098488240 1285836160 3563707660 1047101819 4295559619 8946767837 4494482553 7977472684 7104047534 6462080466 8425906949 1293313677 0289891521 0475216205 6966024058 0381501935 1125338243 0035587640 2474964732 6391419927 2604269922 7967823547 8163600934 1721641219 9245863150 3028618297 4555706749 8385054945 8858692699 5690927210 7975093029 5532116534 4987202755 9602364806 6549911988 1834797753 5663698074 2654252786 2551818417 5746728909 7777279380 0081647060 0161452491 9217321721 4772350141 4419735685 4816136115 7352552133 4757418494 6843852332 3907394143 3345477624 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1651511685 1714376576 1835155650 8849099898 5998238734 5528331635 5076479185 3589322618 5489632132 9330898570 6420467525 9070915481 4165498594 6163718027 0981994309 9244889575 7128289059 2323326097 2997120844 3357326548 9382391193 2597463667 3058360414 2813883032 0382490375 8985243744 1702913276 5618093773 4440307074 6921120191 3020330380 1976211011 0044929321 5160842444 8596376698 3895228684 7831235526 5821314495 7685726243 3441893039 6864262434 1077322697 8028073189 1544110104 4682325271 6201052652 2721116603 9666557309 2547110557 8537634668 2065310989 6526918620 5647693125 7058635662 0185581007 2936065987 6486117910 4533488503 4611365768 6753249441 6680396265 7978771855 6084552965 4126654085 3061434443 1858676975 1456614068 0070023787 7659134401 7127494704 2056223053 8994561314 0711270004 0785473326 9939081454 6646458807 9727082668 3063432858 7856983052 3580893306 5757406795 4571637752 5420211495 5761581400 2501262285 9413021647 1550979259 2309907965 4737612551 7656751357 5178296664 5477917450 1129961489 0304639947 1329621073 4043751895 7359614589 0193897131 1179042978 2856475032 0319869151 4028708085 9904801094 1214722131 7947647772 6224142548 5454033215 7185306142 2881375850 4306332175 1829798662 2371721591 6077166925 4748738986 6549494501 1465406284 3366393790 0397692656 7214638530 6736096571 2091807638 3271664162 7488880078 6925602902 2847210403 1721186082 0419000422 9661711963 7792133757 5114959501 5660496318 6294726547 3642523081 7703675159 0673502350 7283540567 0403867435 1362222477 1589150495 3098444893 3309634087 8076932599 3978054193 4144737744 1842631298 6080998886 8741326047 2156951623 9658645730 2163159819 3195167353 8129741677 2947867242 2924654366 8009806769 2823828068 9964004824 3540370141 6314965897 9409243237 8969070697 7942236250 8221688957 3837986230 0159377647 1651228935 7860158816 1755782973 5233446042 8151262720 3734314653 1977774160 3199066554 1876397929 3344195215 4134189948 5444734567 3831624993 4191318148 0927777103 8638773431 7720754565 4532207770 9212019051 6609628049 0926360197 5988281613 3231666365 2861932668 6336062735 6763035447 7628035045 0777235547 1058595487 0279081435 6240145171 8062464362 6794561275 3181340783 3033625423 2783944975 3824372058 3531147711 9926063813 3467768796 9597030983 3913077109 8704085913 3746414428 2277263465 9470474587 ### 59: In which we talk about pi on pi-day From Gabriel Rosenberg via email: If Ï€ is a non-repeating and non-terminating value, is it a number? ### 58: It's not Hump Day.$3+\dfrac{4}{2*3*4}-\dfrac{4}{4*5*6}+\dfrac{4}{6*7*8}-\dfrac{4}{8*9*10}+ ....$### 57: 10,000 Random Dots. To repeat the experiment, refresh the page or ... Do it Again. Your browser does not support the HTML5 canvas tag. ### What are we looking at, here? Feel free to steal the code. I converted to javascript from the Original python code by @rjallain. ## Thursday, March 13, 2014 ### 56: Squaring the Circle I don't care if it's a RealWorld question. It's still fascinating. Exactly when are the two areas equal? From @ddmeyer ## Wednesday, March 12, 2014 ### 55: The Fastest Way Down. Where is the steepest part of this bowl? What is that slope? What is the angle in degrees? (Click to embiggen) ## Tuesday, March 11, 2014 ### 54: Cheating Is this evidence of cheating? ## Monday, March 10, 2014 ### 53: Right six, CARE, tightens, gnarl. Jiggy Jiggy, Fifty, crest. Right three minus Go full size: The 7.6-mile-long Mt. Washington Road is lined with trees, drop-offs, and winds on the way to the 6,288-foot summit. Travis Pastrana in a 2011 Subaru Impreza WRX STI rally car, with an officially timed run of 6 minutes 20.47 seconds. There are questions all over the place. 1. Average speed 2. Average slope of the road. 3. What do the calls mean? 4. Add more in the comments. This one includes rally notes system details. "Increases the radius, decreases the radius" "Can you take it wide open?" "If the notes are wrong, we go off a cliff." ## Sunday, March 9, 2014 ### 52: Pythagorean Triples If you've worked with the Pythagorean Theorem, you've come across some integer solutions. 3-4-5 and 5-12-13 come to mind, especially if you've studied for the SAT; 8-15-17 is another good one. How many can you find? Which one is your favorite? Is there a way to find as many as you want? (For those who haven't seen this trivia snippet) pick distinct positive integer values for u and v: perhaps 3 and 4. The three sides are 2*u*v, u² + v², and |u² - v²|, thus 24, 25, 7 The hypotenuse is simply the longest of the three sides, but won't be generated by the same expression all the time. ## Saturday, March 8, 2014 ### 51: Dividing by a fraction Why is dividing by a fraction equivalent to multiplying by the reciprocal ... Here's one explanation, from my other blog: We "invert and multiply", "multiply by the reciprocal" or insist on using the fraction key because we can't remember or were never really taught the reasons or the algorithm. Is there a simple explanation for the method we old farts memorized years ago in third or fourth grade? Why does it work? Let's start with a problem:$\frac{3}{4} \div \frac{5}{6}$and change to a compound fraction:$\dfrac{\frac{3}{4}}{\frac{5}{6}}$Now what? Dividing by a fraction is confusing, but dividing by 1 is obvious. So we turn$\frac{5}{6}$into unity by multiplying by its reciprocal. Of course, you can't just multiply part of our problem by$\frac{6}{5}$without changing its value, so we multiply by 1:$\dfrac{\frac{6}{5}}{\frac{6}{5}}$All in one image:$\dfrac{\dfrac{3}{4}}{\dfrac{5}{6}} \rightarrow \dfrac{\dfrac{3}{4}}{\dfrac{5}{6}} \cdot \dfrac{\dfrac{6}{5}}{\dfrac{6}{5}} \rightarrow \dfrac{\dfrac{3}{4} \cdot \dfrac{6}{5}}{\dfrac{1}{1}} \rightarrow \dfrac{3}{4} \cdot \dfrac{6}{5} \rightarrow \dfrac{18}{20} \rightarrow \dfrac{9}{10}\$

Divide by one. Seems simple to me.

## Friday, March 7, 2014

### 50: Rectangle made up of Squares

"A perfect fit with no overlapping"

Take the squares as defined below and fit them into one big rectangle with no gaps or spaces between the squares or in the corners.

The squares have sides of the following lengths 2, 5, 7, 9, 16, 25, 28, 33, & 36.

## Thursday, March 6, 2014

### 49: Pizza, pizza

Pizza ... makes you hungry doesn't it?
What if you had ten toppings available. How many different two-topping pizza variations can you make ...

What definition did you have to "adjust" in order to get David's answer of 55?

Do you agree that this is a fair interpretation of the problem?

source:

## Wednesday, March 5, 2014

### 48: The One Where We Label Axes.

Why are coordinate axes perpendicular?
Do they have to be?
What if there are more than two dimensions?

## Tuesday, March 4, 2014

Submitted without comment:

Oh, the Humanity ...

## Monday, March 3, 2014

### 46: The Dinosaur Bone

What questions does this image bring up?

What part of the dinosaur is that?

How big was it?

What measurement system are we using?

## Sunday, March 2, 2014

### 45: Complicated Crossings.

Explain WHY this works for adding fractions.

Three very similar-looking, but very different, ideas: