Two Substituting Firsts, This Week

[ProfessorGAC]

Remember, my wife worked in the school system for 30 years, so these surprised her, too.
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On Tuesday, I was supposed to sub 6-8 math, because teacher was involved in meetings. Monday, they call & tell me meeting are only half-day, so I told them I was out, because I don't do half-days.
An hour later they called to tell me they'd find something else FOR THE REGULAR TEACHER TO DO, and I could do the class for the whole day!
I was shocked! My wife said she never heard of that happening. Certainly a first for me in the 3 years I've been doing it.
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Wednesday I was playing golf & the school by my house called because the 7th grade math teacher had to go home. (Sick toddler.)
I told them I had partners, so I had to play the last 4 holes but could get there by 11:30.
So, I go home, let doggie do his biz, changed from shorts to pants & went there. Got there at 11:20. School gets out at 2:50.
They told me that since this was such a big help, they were putting it in as a full day. So I worked a half day, but got paid full boat.
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BTW: at that school Wednesday, the 7th graders are working on algebra. In early October. Not just the advanced kids, all of them.
And, I don't mean 2x + 1 = 5. One problem I remember was 9x - 31 = 6x + 1. The accelerated classes were working on tougher problems.

[brush]

1. What's the answer to the harder problem. I was never good...

at algebra. Did well in geometry though.

[royable]

2. Subtract 6x and add 31 to each side

You’re left with 3x=32
Divide each side by 3
X=32/3=10 plus 2/3

[brush]

8. Is the x and unknown or multiplication simbol?

[royable]

9. In this case, the x is the unknown. It could by y or z or a or gamma or a box.

I remember doing worksheets in 2nd grade where we had to write the answer inside a big open box of triangle or circle.

[BOX] + 7 = 12

3 * [CIRCLE] = 18

(where the "*" above is a multiplication sign)

Little did we know that we were being mentally prepared for 7th grade pre-algebra.

So in 7th grade we're given problems like

x + 7 = 12

3 * x = 18

and the very same classmates I'd had in 2nd grade were getting all bent out of shape. "Oh, algebra, it's SOOOO hard!" And I'd remind them we did this in 2nd grade, except we got to write the number inside a hollow shape instead of writing "x = whatever" on a separate line.

[ProfessorGAC]

3. Ten & Two-thirds

I had to help several kids with that one. And, I did it their method, and the way I'd do it, and if we got the same result it has to be right!
But, a few in each class got it without much problem.
That school is far ahead of the other 8 schools in which I've subbed math this year. And, its convenient. It's 4 blocks from our house!

[PoindexterOglethorpe]

4. I was likewise able to solve that second one.

Hooray for me! I actually enjoy the odd algebra problem. But then, I'm weird because I like math, and at the age of 47 actually took calculus for fun.

[ProfessorGAC]

5. Good For You!

Doing math, especially in one's head is supposed to help keep us sharp as we age.
I'll sometimes randomly pick a time period (let's say, 14 years) and then, calculate the rate of return to double & triple the investment, without calculator, paper or pen.
Or, I might look at the radio and see 97.1 and decide to extract the cube root while I'm driving somewhere.
I hope that "stay sharp" works. I'd hate to think I'd be this geeky and have no fringe benefit! LOL!

[PoindexterOglethorpe]

6. I never did learn to do cube roots.

I remember how painful and time consuming it was to do square roots.

And quadratic equations without a calculator.

As for doubling an investment, I know the rule of 72. That's what you're using, right?

And I often do simple addition and subtraction in my head, and do like to think it's keeping me sharp also.

[ProfessorGAC]

7. No Rule of 72

I insist on knowing the answer (to 2 decimals, at least), not an estimate, and the rule of 72 is of no help with tripling or quintupling the principal. It only works for doubling.
For me, it's all in setting up the problem mentally so I can iteratively zoom in on the answer.
My wife thinks I'm nuts.

[PoindexterOglethorpe]

10. Ahh, you want the exact answer. I get that.

I'm fussy that way about other sorts of factual things, so I understand.

Just got done chatting with My Son The Astronomer and he clarified for me just how long astronomical observing, other than purely visual light, has been done. Apparently by the late 19th century astronomers were branching out beyond just looking through a telescope. These days, astronomers rarely do actual in person observing.