# Halfway there!

Posted on April 22, 2013

So.  We have confusion and frustration over these “percent” exercises that have a four column chart:  price, tax percent rate, tax amount, and total price.

So confused!  How do you tell which is part, which is whole?  How do you remember whether to add or subtract?

Welp… let me ask you, when it’s a tax, is it going to cost you more, or cost you less?   Oh.  More.   Then what math should you do?  Oh. Add.   And you then inform me that, of course, the price is always going to be the whole, right?

Why, you ask, did it all seem *so* confusing at home?

The tax is always going to be the part… it’s starting to make sense…

Oh, but this “rounding” thing… you have to do that, too?  And… what on earth do you do when it’s 4 1/2 percent?  **fractions**????

First was the revelation that since those decimal things stood for tenths, and five was half of ten, that 4 1/2 could be written as 4.5 .   The number line was necessary for convincing. And then… well, tell me, just how would you pay me \$2.193 ?   Oh… Again, I used a number line to show the principle of rounding; all of this had been procedures with nothing to do with reality.   Now, she’s ready to tackle ’em…

I tell her, don’t even *begin* the next page’s problems without talking to me.

Yea, the next page is the page where they’re figuring out tips… and the teachers always just assign the problems, including the “estimate the 15 %” and “estimate the 20%” tip that the *text* has explained back there somewhere, but it’s not included in the lecture.   They’re expected to figure it out on their own — not something they’ve been expected to do in the first 13 weeks of the semester.

THere *is* that cool thing about finding 10% by bumping the decimal over… which, of course, is a whole lot easier to remember if you actually comprehend that 10% would be 10 out of a hundred, which would be a tenth, and you have some idea what that quantity means and what splitting it into ten equal chunks would look like.  However, we’re not going there.   Let’s get that “halfness” idea in there a little more solidly.

If you already knew the connection between halfness, you could prob’ly make the connection to tenthness… but If you don’t have that one yet, these are all that many straws on your camel’s backpack of procedures…

So, I decided my focus would on that “half is in the middle” idea — we figured out 10%, and the idea t 20% was twice as much as ten percent was also a minor revelation… but that was successfully applied to whatever the numbers were… and then … how do we get  that 15% tip?   Fortunately, her first assigned problem had 10% at \$2… I drew number lines to show that 15 was halfway between 10 and twenty and… what was halfway between 2 and 4?

The thing that made me *happy* was that she decided that the best way to “show her work” was to draw a number line with 2, 4 and 3 and underneath the 10, 20, and 15 percent… and she did the same with the other examples.

The thing that doesn’t make me happy is that the curriculum isn’t designed to develop that comprehension of basic ratio relationships; it takes active intervention… and it has to be done all on top of the forty-seven details of procedures that you’re stuffing in at the same time.

On the other hand, if today’s work has you thinking that you can figure out a whole lot by  reading and thinking and oh, drawing a number line, things are moving forward…