Since we're trying to get out of town for the weekend, Casa Free-Ride is a hive of activity. (As we seem to be passing another cold back and forth, it's also a hive of mucus. Ew.) But we have time to update you on recurrent topics of conversation this week around the Free-Ride kitchen table.
This week, it's been all about math.
The younger Free-Ride offspring has been finding the math in the second grade classroom a little ... boring. They're doing multi-digit addition and subtraction, and while "carrying is OK, borrowing is boring!" I wonder whether this is an issue that could be addressed with better branding -- maybe by calling borrowing "reappropriating" or "seizing for the people" or something.
In any case, there have been non-boring loci of math at home to suck the younger Free-Ride offspring in. As the elder Free-Ride offspring's fourth grade class is working on fractions, the younger sibling has been glomming on, and last night sort of grokked multiplying fractions by whole numbers in a discussion of pizza. (If A piece of pizza is a tenth of the pie, multiplying that by ten gives you a whole pie. And, if you have two tenths of a pizza pie, multiplying that by ten gives you two whole pizza pies. But sorry, pizza's not on the dinner menu tonight.)
The elder Free-Ride offspring, meanwhile, was playing around with decimals (which are really just fractions with kind of boring denominators) and showing off by quickly delivering the results of multiplying or dividing by powers of ten. Of course, the younger offspring wanted to get in on the act, too, so we talked about how multiplying 9.3 by 10 was the same as (9 x 10) + (0.3 x 10). If 0.3 is just three tenths (and if you know how to multiply fractions of pizzas), you see that 9.3 x 10 is (90 + 3), which is 93.
"When you're multiplying or dividing by powers of ten," said the elder Free-Ride offspring, "you're changing which digit is in the ones place, which is in the tens place, which is in the tenths place, and so on." At this point, the Free-Ride parental units reveal that we think about the operation as "pushing the decimal point" to the right or to the left.
It's possible that while we were discussing this I may have been doing a finger-twirling, hip-shaking dance to illustrate the concept. But you'll never prove it in a court of law.
Of course, a question came up: "In 9.3 x 10 = 93, where did the decimal point go?" We noted that the decimal point was safe and sound, between the 3 in the ones place and the zeroes in the tenths, hundredths, thousandths, ... "So, it's really 93.0. At least, until you learn about significant figures, when it goes back to being 93."
The kids have been browsing through a new book in the house (Real World Algebra). One result of this is that the elder Free-Ride offspring now tries to set up (and solve) systems of equations in two variables without any paper. (This makes my head hurt. Maybe I'm more of a visual learner than I thought I was.) Another is that the younger Free-Ride offspring now has a time-saving strategy in the event of being kept after class to write a googol on the whiteboard one hundred times. (The secret is exponents, and now the younger Free-Ride offspring has the power to , uh, understand how to write the powers.)
Meanwhile, the younger Free-Ride offspring wants to know why XXXXXXXXXIII isn't a perfectly legitimate way to write 93 using Roman numerals.
Anyone know any good math games we can play during our long drive this afternoon?
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Hexadecimal isn't just fun, it's useful! I'd start there although you may want to start out with pencils and paper. Or I guess you could start with binary.
XXXXXXXXXIII = 93 is a 'legal', if rare, use of Roman numerals. You might use it if you were working with a nine or ten bead per row abacus.
Not using the subtraction rule is relatively common, (many clocks still use IIII and VIIII for instance), but skipping the five counts is what makes that 93 frowned upon.
Car cricket
Involves both maths AND the greatest game ever invented by man:
http://en.wikipedia.org/wiki/Pub_cricket
If your car has a digital clock, try this one:
At a given time, count the number of segments in the time display (for example, 12:59 has 2+5+5+6=18 segments). Then try to use the digits of the time in an expression that evaluates to the number of segments.
For example, off the top of my head, Using the digits 1, 2, 5, and 9 from 12:59:
18 = 15 + \2/9
That is, fifteen plus the second (i.e., square) root of nine.
There's a new game every minute! Some times are obviously much easier than others.
My daughter used to play this while trying to go to sleep, in lieu of counting sheep.
Equation Jam!
I came up with this a while ago, but never was on any sufficiently nerdy road trip to test play it.
Take any arbitrary string of numbers that comes along outside the car (phone numbers on billboards, license plates, addresses). Paper and pencil/pen will help for longer strings and keeping track of points.
The goal is to create a simple equation with the digits in that order provided by adding +,-,/,x,^, and the necessary "=" with minimal duplication of digits. The less duplications the better the answer. If someone makes a pristine equation or the 5 min time limit is up that round ends, that person gets a point, and you go on to the next string.
You see a licence plate 3BA4321.
1) Toss out the letters, that's 34321
2) One answer may be 34-32=1+1 which requires one duplication which may win that person a point, if someone else cannot come up with a better equation in the time allowed.
3) (3+4)*3=21 would win over the previous because it doesn't duplicate any number, IF it was found in time. Though to be fair it does require the use of parenthesis, but that convention can be ignored easily enough for this game.
Please, I would like to know if you used it how it worked out.
I totally love the Sprog Blogging! Keep it up. Thank you!
maybe you should give them chocolate. that might change their mindsabout math.
http://www.livescience.com/health/090403-chocolate-mind.html
have a great trip.
Keep this up, and they'll pass on science and become mathematicians... or even (the horror!) theoretical mathematicians!
You think you're getting headaches now (as a visual learner), wait until the younger Free-Ride offspring starts showing you topology theorems...
I used to try to figure out square roots in my head on car rides, using a method similar to the higher/lower game on wheel of fortune. But that's more of a solitary game. And not much of a game, actually ...
Meanwhile, the younger Free-Ride offspring wants to know why XXXXXXXXXIII isn't a perfectly legitimate way to write 93 using Roman numerals.
It's legitimate, but it's a much longer route to get to destination 93 than route XCIII.
Anyone know any good math games we can play during our long drive this afternoon?
How about this:
1. Choose a number using some random procedure (e.g., number on speed limit sign; let's say 49)
2. Each person spends a designated time (e.g. 30 seconds) calcuating how to get to the number using the shortest calculation they can imagine:
Examples:
49 can be: 7-squared, 7*7, 98/2, 50-1, 19+30, etc
3. Person using the least number of symbols for the calculation wins. In this case, 7-squared wins (2 symbols), 7*7 (3 symbols), 98/2 (4 symbols), 50-1 (4 symbols), 19+30 (5 symbols)