jeremy and emily factor a quadratic

I’m here at Cafe Wifi, with my triple latte and chocolate scone, thinking about my algebra students sitting there listening to me (or not), and I wondered: What about teaching a concept or giving out a problem, using the students themselves as tutors, in the following way:

Say a couple of students already know how to do something; for example, factoring the difference of cubes. They each explain it to someone, then those two explain it to two others, while the first two explain it to two other others.

As new students learn the skill, they move from the “don’t know” side of the room to the “know” side, with the explaining taking place at the interface where the tables are. From time to time, the newer knowers must explain it back to the early knowers to check they know it, and to gain insight into how the process changes.

Within a short number of generations, the whole class knows and the “don’t know” section is empty. Mission accomplished.

One concern is when a student doesn’t get the explanation and then gets bogged down trying to explain it to the next person. Maybe helping with that could be the role of the teacher, if there’s even one present.

Any comments on how you think this might or might not work? It wouldn’t have to be limited to math classes, right?

small stellated dodecahedron

the second set of my daily twitter math problems, #26-50. answers can be found by scrubbing my twitter feed at  twitter.com/dansmath

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Problem 26 (dan’s prime code):
Label the letters with first 26 primes; A=2, B=3, . . . , Z=101. What’s the value of DANSMATH? (eval. as in algebra)

Problem 27:
Review ‘dan’s prime code’, then find the (real) word whose prime code is closest to a million. (rules: two tweets max, closest=1.5, next5=1, rest=0.5.)

Problem 28, a perfect number:
a) Find the next two. b) How do they involve mersenne primes? c) How many digits in largest known perfect number?

Problem 29:
An abundant number n is one whose proper divisors (incl 1 not n) add to > n. Find, on your own, the smallest ODD abundant number.

Problem 30:
Ten people put their names into a hat, then each randomly removes one name. Find the probability nobody gets their own name.

Problem 31:
Mersenne prime 2^5 – 1 = 31. Find the first three primes p such that n = 2^p – 1 is not prime, and factor those three n’s.

Problem 32:
If a roll of scotch tape has outer diam 2″, inner diam of 1″ to tape, & thickness of tape is .004″, how long is the tape?

Problem 33:
I just heard four gunshots outside, and it took six seconds. How long would a full clip (of 16 shots) take to empty?

Problem 34:
This is my 700th tweet! What percentage of the numbers from 1 to 700 are the product of two distinct primes? (HNY! ans jan 2)

Problem 35:
Let spf(n) = sum of all prime factors of n: spf(12) = 2+2+3=7. Find two consecutive 3-digit integers with the same spf.

Problem 36:
A student once “cancelled 6’s” in 16/64 to get 1/4, the right ans! Find 2 other “good-bad cancellings” (no 33/44 etc).

Problem 37:
A semicircular arched doorway is 6 ft high (above the floor) 1 ft from the edge. find the height of the arch 5 ft from the edge

Problem 38, tweet #800:
Find smallest positive integer that’s odd, 2 more than a mult of 15, and 3 more than a mult of 38. (try to avoid excel)

Problem 39:
I am an integral right triangle. my legs are consecutive integers, and my perimeter has three digits. find my three sides.

Problem 40:
What is the max product of any number of positiv integers whose sum is 40? and what are the numbers? and how many numbers?

Problem 41: “The primagical formula”
How many consecutive n’s, starting with n=1, give a prime number answer when plugged into n^2-n+41?
.
Problem 42:
How do you divide a herd of 17 sheep in the proportions 1/2, 1/3, and 1/9? (without any slicing up of sheep, if you please!)

Problem 43:
43 is prime. Figure out all 3-digit primes ending in 43. Whose theorem guarantees an infinite # of primes end in 43?

Problem 44:
Using exactly four 4’s, and regular math symbols, but no other numbers, can you make 41? [e.g. 46 = 4 + 44 - sqrt(4).]

Problem 45:
One point: how many 1″ diam circles can fit into a circle of diam 7″? Bonus point: into a circle of diam 17″?

Problem 46:
Numberebuses from @cnansen – http://twitpic.com/18ifp – tweet me all four! (esp. the answer to the last one?)

Problem 47:
Chris and Pat are siblings. Chris has twice as many brothers as sisters, but Pat has as many bro as sis. two questions arise: 1. What sex(es) are Chris and Pat? 2. How many siblings total? 3. How many boys & how many girls? (ok that’s 3 questions)

Problem 48:
What are: a) the smallest sum, and b) the largest sum, of three non-negative real nos x,y,z such that x^2 + 2y^2 + 3z^2 = 48?

Problem 49:
x: How old are your three kids? y: The product of their ages is 36. x: I still don’t know their ages. y: The sum of their ages is your house number. x: I still don’t know their ages. y: The oldest one has red hair. x: Now I know their ages! How old are they?


Problem 50:
My phone number is xxx-xxxx. the prefix, subtracted from half the square of the rest, is the whole number! What’s my number?
  


.

icosahedron with 'sierpinski gasket' faces

here is a list of my first 25 daily math problems; follow me at twitter.com/dansmath.

remember there’s a 140-char lim on tweets so some r “dense” stmts. thanks to barry fulk @fulkb for pulling these from my twitter feed. 

there are also answers if you scrub my twitter feed; please leave a comment if you want me to post them here. 

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@dansmath daily twitter problems Nov/Dec 2008:
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One dansmath point for each correct answer. First to a million wins!
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Problem 1:
2x^2 + 5xy – 12y^2 = ( ? )( ? )
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Problem 2:
Write 391 as the difference of squares, then factor it as such.
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Problem 3:
What’s the equation of the parabola (vertical axis) thru the pts (0,3), (1,4), (3,0)?
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Problem 4:
What number, 200 or less, has the most divisors? How many does it have?
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Problem 5:
Among the numbers “one” to “one hundred” which is alphabetically LAST when spelled out?
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Problem 6:
A ball is thrown upwards at 80 ft/sec from a 96-ft-tall tower. how long will it take to hit the ground?
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Problem 7:
If I have twice as many tweets as followers, I follow three people for each 16 tweets, and the sum of my followers, followees, and tweets is 26^2 – 1^2, how many people am I following?
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Problem 8:
What is the integral of 3(ice)^2 d(ice) ? Simplify your answer.
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Problem 9:
What’s the most, and fewest, friday-the-13ths there can be in one calendar year?
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Problem 10:
How many different ways can you arrange the letters of “dansmathcast”?
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Problem 11:
Kevin Rose can drink a gallon of tea in 6 hrs & Don McAllister can drink a gallon in 4 hrs, how long drinkng together? … that is, how long will it take them, drinking together, to finish one gallon o’ tea?
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Problem 12:
There are 68 bugs in my kitchen, all ants and spiders, with a total of 506 legs. how many of each bug?
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Problem 13:
How many 1″ circular disks can you fit in an 8×8 square?
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Problem 14:
A truck goes from A to B at 40 mph and returns along the same road at 60 mph. What’s its average speed for the round trip?
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Problem 15:
My new 500GB hard drive loses 5% of its capacity each day due to rust. how many bytes will be left a year from today?
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Problem 16:
What is the next number in this sequence, and why? 2, 4, 6, 12, 24, 36, . . . hints at http://www.dansmath.com
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Problem 17:
What’s the first multiple of 17 after 17 to end in the digits 17?
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Problem 18:
If I had 6 more eggs I’d have twice as many eggs as I’d have if I had 3 dozen fewer eggs than I have. How many eggs do I have?
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Problem 19:
What one yes/no question can you ask to determine whether someone is a faithful truth-teller or a perennial liar?
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Problem 20:
Name the first perfect square Fibonacci number after 1. Bonus point for the one after that.
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Problem 21:
I bought three items at the 7-11: what three prices have a product of 5.70 and a sum of 5.70?
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Problem 22:
On the 12 days of xmas, what was the total number of presents my true love gave to me?
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Problem 23:
Pecans, almonds, cashews have 13, 7, 9 calories & weigh 1.7, 1.4, 1.5 gms each. i have 51 nuts, 469 cal, 77 gms. how many of each nut do I have?
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Problem 24:
I ran 6 miles round trip (downhill then back up) in 1 hr. down i’m 1 mph faster’n level, up 1 slwr’n. what’s my 6-mi time on level?
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Problem 25:
A snail climbs 1 meter up a wall, slides back 1/2, climbs 1/3, slides 1/4, etc. where does it end up? 

* * * * * * * * * * * * * *

If you like these please leave a comment and/or suggest a new problem!

And try my ongoing ProblemOfTheWeek on my website www.dansmath.com

– i’m not sure how long i’ll keep these up, but i am posting quick contest problems on twitter, such as factoring puzzles and the like. winners are limited to the first few each day. one was to factor 391 as the difference of squares; the answer is 17 times 23 when the dust settles. do you know what that means? follow me at www.twitter.com/dansmath for more updates!

welcome to dansmathworld

i have just scripted, animated, produced, and uploaded a promo for my site and podcast through a webapp called xtranormal, the self-titled “text-to-movie” company.

it was a fun and painless experience: i just typed in the dialogue, dragged in some camera angles, looks, and backgrounds, uploaded to the xtranormal page, and easily put the video on my youtube as well.

watch my shameless self-promotion now!

dan in front, algebra in back

recently i was interviewed by bill palmer of iProng magazine about my website and podcast. you find it at www.iprong.com ; you click it, you download it as pdf, you read it, you know all about me! please feel free to comment here, or at dansmath.libsyn.com , or in itunes!

dan inside a polyhedron

i am often accused by others of being, of all things, a ‘math nut.’ i accept the label, but wonder if it is said in admiration or with sarcasm. does anyone have thoughts, events, or stories to relate about this?

mathematics for the masses

are you a math nerd? a math-phobic? 

everyone is welcome at dansmathblog. 

post your math questions, thoughts, ideas, or stories here!