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?