Must-see Common Core math problems of the day [pics]

Twitchy ^ | 10/4/13

[JediJones]

Coincidentally that household budget shows almost exactly how much of the debt each individual taxpayer owes. Because, in 2005, only about 99,880,223 paid federal taxes, and you divided the total debt by 100 million (8 zeros). Each taxpayer owes about $140 grand in federal debt.

[Hoodat]

Are they trying to make kids stupid?

[Pajamajan]

I have a second grader in my house. They are teaching her this Common Core crap at school.

Trying to help her with her homework is an exercise in frustration.

What the hell is the point of this?

I don't get it.

Seems like a recipe for increased numbers of school dropouts.

[Moltke]

Note that he/she got the “total budget cuts so far” figure wrong: it should be $385.00. I guess removing 8 zeros proved too difficult for him/her. *sigh*

[Hoodat]

Here is the correct mental calculation for 26 + 17:

17 --> 1 + 7 = 8
26 - 8 = 18

18 --> 8 - 1 = 7
Take the square of 7:
7 * 7 = 49

Put the two numbers in bold together:
18 & 49 --> 1849

Now take the square root of 1849 and you get 43. Simple.

[Attention Surplus Disorder]

“Conclusion: “Math is too hard and I’ll never understand it. Will the government take care of me if I promise to vote Democrat?”

Perfect.

[NativeSon]

and that's why I said that this should not be taught to the kids.

For math on paper "carry the one", when doing it in your head on the fly, breaking up and reassembling: this works for me.

[trubolotta]

You are wasting your talents here. You should be writing for CC math book publishers!

[InterceptPoint]

Now take the square root of 1849 and you get 43.

Simple.
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Indeed. Occam’s Razor triumphs again. :)

[Hoodat]

Things were a lot different for me back when I was growing up in the back wood mountains of Virginia. These are the kinds of questions we faced:

1. A pulpwood cutter has chain saw that operates at 2700 rpm. The density of the pine trees in a plot to be harvested is 470 per acre. The lot is 2.3 acres in size. The average tree diameter is 14 inches. How many Budweiser Tall-Boys will it take to cut the trees?
   
   
2. If your uncle builds a still that operates at a capacity of 20 gallons of shine per hour, how many car radiators are necessary to condense the product?
   
   
3. A front porch is constructed of 2x8 pine on 24-inch centers with a field rock foundation. The span is 8 feet and the porch length is 16 feet. The porch floor is 1 inch rough sawn pine. When the porch collapses, how many hound dogs will be killed?

[discostu]

There’s nothing dangerous about being able to do math without electronic devices. Not being able to do math in their head is where the danger lies, that’s what makes a person the victim of fast talkers. People who can do math in their head understand the numbers that make up their life (paycheck, tax rate, budget, can I buy all this stuff in my cart) a heck of a lot better.

I never learned the tables and I’m glad I didn’t. The tables will tell you that 5x4 is 20, but working it tells you WHY 5x4 is 20 and gives you a better understanding of what those numbers do and how they work so someday when some guy at a store tries to charge you $125.46 for 5 $19.89 items you’ll know he’s screwing you because you get 5, and you get multiplying, and you understand that 19.89 is basically 20 so it should be coming out near 100 plus sales tax which ain’t 25% and it doesn’t bother you that many of these numbers weren’t on those tables you memorized.

Sure give the kid a pencil and paper for 431+564, but teach them that there’s more to the answer than 3 trips to the addition table to get 995, teach them that these numbers have meaning, teach them that they’re part of an overall system, put the foundation work in place so when they move on to algebra it doesn’t come at them as a completely foreign concept. Teach them MATH not chanting.

I’m betting they did a lot in their heads, that’s how math works. You really do it ALL in your head, you just happen to write some of it down. If they were dealing with simple numbers they were probably part of a larger equation, so you work the numbers in your head because that’s the easy stuff. Anybody that can’t do simple arithmetic in their head is simply not on path for advanced math.

[Praxeologue]

Why don’t they just ask for the answer?

[DungeonMaster]

Proving that the island might tip over and capsize.

[trubolotta]

I agree entirely with your first paragraph but after that I draw a line.

I learned stick addition and subtraction in the 1st grade before learning that memorizing a table was a lot easier than adding sticks. The same goes for multiplication and learning it was noting more than addition. It was a lot easier to memorize that 4x5=20 than taking 5 piles of 4 sticks (or 4 piles of 5 sticks) and adding them together in your head. Learning tables does not mean you didn’t learn the reason.

The same principle applies to the use of geometric theorems, trigonometric identities and theorems of calculus. You learn the derivation and then memorize the results as simple rules to solve more complex problems.

This aversion to memorization doesn’t make sense.

[discostu]

If my choice had been sticks or tables I’d probably have gone with tables, but we never used sticks. We used number lines for addition and subtraction, and just working the numbers for multiplication and division.

I did very little rote memorization in school, but what I did left my brain almost immediately upon being tested. Most of my learning was method based, and that all gave me the foundations for later. I can see the number line roots in how I do math, that core understanding of what these numbers mean is still there, add that to my algebra teacher’s lesson on how to eyeball a number to see what it’s divisible by other numbers (especially the rules for 4, 6, 8 and 9, those taught me a new way of thinking about numbers which informs probably 75% of how I do math now).

In geometry and beyond I didn’t memorize the results, I learned the concepts and their implications. That was all waterfall to me, a logical path where one theorem followed after another through understanding not memorization. Of course again it was teacher method, my geometry teacher emphasized the meaning of the theories over the names, she was much more interested in us knowing why a squared + b squared = c squared and what could be intuited from that and what you could do with that than us remembering who it was named after.

I can’t even tell you what I learned rote because it’s just plain gone. Memorization might be OK for history, but even then it works better if you can build a narratives rather than just trying to go with disembodies meaningless dates and names. I don’t know, maybe if memorization had been how I learned more stuff I’d see its use, but most of my teachers shied away from it and I like the results of how I was taught, and the few that did use it are on my list of bad teachers from whom I didn’t actually learn.

[wastedyears]

When and where did you learn to do math like that?

[Leaning Right]

There’s nothing dangerous about being able to do math without electronic devices.

I completely agree with that. In fact, I don't think students should even be given calculators until the 8th grade or so.

And I actually agree with much of the rest of your post. In-your-head math skills are very important, especially when it comes to estimating.

But I guess were we somewhat disagree is with the value of memorizing things. Someone once said "through memorization comes understanding." I very much agree with that.

But as you said, some numbers theory must be taught also. I would want my child to instantly know that 7x5=35. That instant knowledge is only gained through memorization.

But I would also want my child to understand, and visualize, that 7x5 really means 7 groups of 5.

The problem with much of today's "new math" (and "new science", for that matter) is that both memorization and traditional theory is discarded in exchange for gimmickry.

[trubolotta]

Memorization has its utility whether it is history or mathematics. I will never forget SOHCAHTOA as a mnemonic for trigonometry. These are definitions and must be committed to memory or you go back to the book.

As another example, I don’t know of any calculus instruction that does not derive the Chain Rule, but I also have never seen a requirement that the rule must always be derived before it can be applied. Learn why it works and use it; that’s straight forward. More importantly, all the fundamental theorems leading to the derivation must be memorized because they too are based on definitions. Memorize what a limit is and use it. It is not a big deal.

So too for all those axioms and postulates you learned in geometry. Had you not learned them, grasped the importance and committed them to memory, doing geometric proofs would have been an exceedingly tedious process.

Even the problems illustrated to start this thread at some basic level resort to memorization that for example, 10+30=40. You can picture the number line all you want to understand the “process” but the idea there is no memorization involved is simply not true. How did you remember where the tic marks are, what the symbols mean and how the process itself works? Why is memorizing that 1+3=4 detrimental as opposed to seeing it on a number line? It isn’t; it is quite useful.

I am not at all disputing learning the underlying fundamentals, but I think there may be enough space in my brain to hold a simple multiplication table in addition to the fundamentals. I don’t see where these CC illustrative problems teach any fundamentals but focus on method, and not necessarily a very good one. Should we assume place holders were taught earlier? If they were, what a convoluted way to use them.

[discostu]

It all really depends on what’s being repeated. I did the math enough time to memorize a lot of the little stuff, which taught me what to do with it while memorizing it. That’s always the thing that struck me as wrong about the tables, it seems (remember I did almost know rote memorization of any kind in school) to me you learn the results without the method.

I don’t know if it’s really gimmicky. I mean OK when I do it I refer to it as “stunt math”, but really it’s all build around number theory and basic arithmetic. The big benefit I personally get from it, and I think students will probably get, is it makes hard numbers seem easy. In a normal situation if I tell you to multiply 7569 by 2686 you’re seeing some annoying math that must be paper and pencil, and seeing it as tough makes you more prone to mistakes. I see a number that’s a 75 and a 70-1 two easy numbers to work with, and another number that’s got a 2, two 6s (which are really a 2 and a 3 and I’ve already got a 2) and an 8 ( which is really 2 three times) all super easy multipliers made easier by their relationship to each other, to me the problem is a third solved by knowing 15138, I can multiply those numbers while driving. You actually probably could too, I’d just enjoy it more. I think there’s a definite benefit in learning a method that has as one of its grounding lessons “it’s easy if you let it be easy”. Too many people think math is hard, this method might fix it... or it might not. But the old ways of teaching math clearly didn’t, might as well try something new.

[InterceptPoint]

When and where did you learn to do math like that?
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Sometime around the 4th grade. I doubt seriously if it was taught to me. I think I just started doing it for simple additions and subtractions. After awhile it seems quite natural.