They don't know that this isn't a novel and 50,000 words was never a goal. I remind myself I have at least an extra thousand 'words' when you include the code. Whatever that means. But I appreciate the email reminders to write, so I stay connected with that organization. The time I spend formatting and making images and researching the parts of a book aren't represented in this graph though, I have been working a lot! The only remaining productive procrastination option would be to figure out how an index works in LaTeX, but mostly all I have left is the regular writing so I'm hoping things move quicker the second half of the month.
I think this week I convinced the linked text to stay active. It definitely works on scribd, maybe while embedded as well. [Update: the links to sections of the document work, but not the ones to the world wide web. Intriguing.]
Two things:
Michael did an amazing job of matching up math mistakes with tricks, but he didn't have one to match every trick. For the new chapter I'm seeking: 1) messing up order of operations by multiplying before dividing 2) cancelling a square and a square root
Editors. Doesn't appear that I'm going to get much feedback by posting here. You want to be an editor? I'll put your name on the verso! (Check out that lingo I learned.)
When I am more awake, I'll send more comments. Thanks for this work, Tina!
ReplyDeleteIt's looking great!
ReplyDeleteIs it too late to comment on the content?
You wrote: "There is a reason for the order of operations, but it is beyond the scope of most K-12 classes. "
I don't think it is. If you think of which operations are more powerful, and take that as your ordering principle, you don't need a mnemonic. (I always hold my arms up to show my muscles as I talk about who's more powerful.)
mrdardy- thanks!
ReplyDeleteSue: no way! I love learning new things, I'd never even thought about why the order of operations was the way it was, someone wrote that it was beyond K-12 and I thought "Must be since I don't know it." Nice to know there's something else I don't have to take on faith.
I don't know the history of it, but if you think about polynomials like 7*x^3-3/2*x^2-4*x+5, they'd need a lot of parentheses if we weren't using order of operations. The only way to avoid parentheses on something like that is to use the convention we have - that exponents are the first (so don't do 7*3 and then cube it), then multiplication and division, then addition and subtraction. We change the order with grouping symbols. It all seems perfectly logical to me, so I never really understood the pemdas thing.
ReplyDeleteThat polynomial may not be a good example for the K-8 crowd. But once students start taking algebra, I think it would make sense. What do you think?
Dang. I wrote another comment, then hit sign out by mistake. I can offer more comments if you'd like. My email is mathanthologyeditor on gmail.
ReplyDeleteOrder of Operations has to do with the Distributive Property. Because multiplication distributes over addition:
ReplyDelete6 x (2 + 4) = (6 x 2) + (6 x 4)
Children can understand this: We have 6 rows of fruit in the produce section, with 2 apples and 4 oranges in each row. We will end up with a total of 6x2 apples AND 6x4 oranges.
But if we were thinking about meaning, we would never write:
(2 x 4) + 6 = (2 + 6) x (4 +6) ???!
How could we make sense of that? We move over to the vegetable counter, where there are 2 rows with 4 squash in each, and we want to add 6 more squash to the display. That would NEVER be the same as 2+6 rows with 4+6 squash in each.
Because multiplication distributes, we have to use parentheses in the first instance, if we want the 6 to multiply the whole row, both the 2 and the 4. Leaving out the parentheses would make a difference. But because addition does not distribute, we could write the second expression without parentheses:
(2 x 4) + 6 = 2 x 4 + 6
...and it still means the same thing, as long as we remember order of operations.
This is true at all the levels of the order of operations hierarchy. It's all based on which operations distribute over other operations. Which is another way of saying, it's based on understanding the meaning of the numbers and how they work, not just memorizing rules.
[I am the same as letsplaymath.net above. The comment form is being glitchy and keeps switching my name to "Anonymous" whenever I turn my back.]
ReplyDeleteA few minor notes:
(1) The word "verso" just means "left-hand page." ("Recto" is the right-hand page, and the recto pages should always have the odd page numbers.) If your book just has one verso, your font is too small! I'm assuming you meant a certain particular left-hand page?
(2) Don't put a period after your sub-title. It is not a sentence. And even if it were grammatically a sentence, it would still be a title, which doesn't take a period.
(3) I've never heard of "BEMDAS" until I saw it in your table of contents. Everyone I've heard that uses "B" says "BODMAS" [example, http://www.mathsisfun.com/operation-order-bodmas.html] but Wikipedia mentions BEDMAS, BIDMAS, and BOMDAS as alternatives.
Well, I told you they were minor notes. I should have said "nitpicky".....
Based on google search hits BIDMAS wins. Not sure that's the best way to choose but I'm going with that one until I get more complaints!
ReplyDelete