Eliminating Geometry from High School?

Are we sure? 1+1+1+1+1+1+1+1+1+1-1+1+1+1+1+1+1x0
PEMDAS
1+1+1+1+1+1+1+1+1+1-1+1+1+1+1+1+0
10-6
=4

At least that's what I get...
 
Are we sure? 1+1+1+1+1+1+1+1+1+1-1+1+1+1+1+1+1x0
PEMDAS
1+1+1+1+1+1+1+1+1+1-1+1+1+1+1+1+0
10-6
=4

At least that's what I get...

You have the first part right, the first set of 1's (until the - sign) equal 10. Then subtract 1 from that 10; equal 9. Then, add another 5 to that 9; equals 14. Then, multiply 1 by 0; yields 0. Add that 0 to the running summation; equals 14.
 
Adding brackets to highlight the order of operation may help:

(1+1+1+1+1+1+1+1+1)+(1-1)+(1+1+1+1+1)+(1x0)
= 9 + 0 + 5 + 0
= 9 + 5
= 14

Do they teach order of operations any more?
 
Adding brackets to highlight the order of operation may help:

(1+1+1+1+1+1+1+1+1)+(1-1)+(1+1+1+1+1)+(1x0)
= 9 + 0 + 5 + 0
= 9 + 5
= 14

Do they teach order of operations any more?

In Washington it is on the 7th grade WASL, now MSP. I was taught that in Sixth.

Please Excuse My Dear Aunt Sally

And Multiplication/Division & Addition/Subtraction go in the order they come in the equation, not Multiplication, THEN division. Same for Add. & Sub.
 
Adding brackets to highlight the order of operation may help:

(1+1+1+1+1+1+1+1+1)+(1-1)+(1+1+1+1+1)+(1x0)
= 9 + 0 + 5 + 0
= 9 + 5
= 14

Do they teach order of operations any more?

I didn't think this was difficult at all. Maybe it can be blamed on Texas Instruments since they are the downfall of RPN calculators?

Edit: Let me expand on my comment for those of you who don't know what RPN calculators are. RPN calculators require you to enter the equation in the way you go about solving it by hand. For for the above equation, you need to enter the 1x0 first, then start on the far left and go about adding it. The first question everyone says when they try to use an RPN calculators is "where is the equals/enter button?". TI calculators don't require any thought; they use an algebraic method to solve equations.
 
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The correct answer is clearly 14. The questions is:

"What is the answer? 1+1+1+1+1+1+1+1+1+1-1+1+1+1+1+1+1x0 "

1+1+1+1+1+1+1+1+1+1-1+1+1+1+1+1+1x0
is
1+1+1+1+1+1+1+1+1+1-1+1+1+1+1+1+0
2+1+1+1+1+1+1+1+1+1+1+1+1
3+1+1+1+1+1+1+1+1+1+1+1
4+1+1+1+1+1+1+1+1+1+1
5+1+1+1+1+1+1+1+1+1
6+1+1+1+1+1+1+1+1
7+1+1+1+1+1+1+1
8+1+1+1+1+1+1
9+1+1+1+1+1
10+1+1+1+1
11+1+1+1
12+1+1
13+1
14

Easiest way to show it on a forum. Red Denotes First in sequence and the -1 is done right after to avoid confusion.
 
I don't use RPN calculators, if they are the graphing calculators. I am well aware of order of operations but the calculators hurt my head. Of course, I'm not too swift with a ten key either. I can use a regular or even a scientific calculator but others baffle me.
 
I don't use RPN calculators, if they are the graphing calculators. I am well aware of order of operations but the calculators hurt my head. Of course, I'm not too swift with a ten key either. I can use a regular or even a scientific calculator but others baffle me.

I've used RPN calculators, and I hated it. My mom (a former accountant) loves it.

I've found another reason for geometry. I'm in Intro to Engineering Design and currently we are working on different shapes and measurements. (Triangles, Octagons, Rhombus, etc..) and during lunch, I need to go talk to my geometry teacher abut a few of the questions. Things that we work on later in the year in geometry.
 
I've used RPN calculators, and I hated it. My mom (a former accountant) loves it.

I've found another reason for geometry. I'm in Intro to Engineering Design and currently we are working on different shapes and measurements. (Triangles, Octagons, Rhombus, etc..) and during lunch, I need to go talk to my geometry teacher abut a few of the questions. Things that we work on later in the year in geometry.

I'm a civil engineer so I see geometry as crucial to any education. Just about everything can be solved by similar triangles.
 
Are we sure? 1+1+1+1+1+1+1+1+1+1-1+1+1+1+1+1+1x0
PEMDAS
1+1+1+1+1+1+1+1+1+1-1+1+1+1+1+1+0
10-6
=4

At least that's what I get...

Adding and Subtracting are the same thing, thus there is no implied first operation, basically you dont do all of one type first then the other.
 
Adding and Subtracting are the same thing, thus there is no implied first operation, basically you dont do all of one type first then the other.

The order they appear in the problem is what we were told.

This almost should get moved into its own thread in QotD!
 
Under no circumstances should you have to write an explanation of process.
Which is why when I took my PE exam you had to show all your work even if you already knew the answer or shortcuts. There were several times I actually had to go back and and fill in some of the steps from what I normally did.

As already stated, the point was showing that you could not just get the right answer but more importantly that you actually understood the underlying concepts, thus showing that you might be able to apply those same concepts to other problems.
 
Which is why when I took my PE exam you had to show all your work even if you already knew the answer or shortcuts. There were several times I actually had to go back and and fill in some of the steps from what I normally did.

As already stated, the point was showing that you could not just get the right answer but more importantly that you actually understood the underlying concepts, thus showing that you might be able to apply those same concepts to other problems.

I have to show work on tests in my AP Chemistry class to receive credit. Even if you get the wrong answer, showing work will yield partial credit, including on the real AP test. While that doesn't happen in the real world, you or someone else can pick it apart to see where you went wrong.
 
I freely admit that in higher math or science you have to show what your are doing, however, in elementary school you need to be graded on what you do, right or wrong. Learning the basics of addition, subtraction, multiplication and division are right or wrong. There are no signs to worry about, no abuquities at all. Higher math is also right or wrong but getting there is much more complicated so work needs to be shown.
 
So, would you admit that the above example was not higher math, but elementary math? Even still, by showing work we were able to (through different means) show how to obtain the correct answer. Showing work, even on basic math, is an element of problem solving, to verify a correct answer. If there were no need for showing how to do the math, then how would a teacher be able to know if the student misunderstood the concept or made a clerical error?

Showing your work for math problems and knowing your times tables should be taught as an exercise of good practice. By learning that discipline at an early age, students will have a solid foundation as they get older and into more advanced subjects. I would liken this to a musician learning their scales. There are many self taught musicians who do not practice their scales, or never learned them, but you will not find very many playing in a major symphony orchestra.
 
Math teaches so much more than just math. It is (arguably) the only subject where someone must actually understand all of the concepts and why the numbers work they way they do. Tests aren't multiple choice (multiple guess) for a reason and partial credit is the key to passing most exams. Even more, every solution has a proof for the solution.

With all of that being said, every situation in life has a solution that needs to be found. This solution needs to be understood and a (type of) proof can then be established. Even the simplest of situations can be interrupted incorrectly (as shown above in my picture). Math should be teaching students to think through a problem, whether it be a math problem, economic problem, theatre related issue, etc. What other subject teaches you to think?

There is an old saying that goes something like this... "When a client tells an engineer he/she needs a ladder, a good engineer will ask how long, but a great engineer will ask 'why a ladder?'"
 
So, would you admit that the above example was not higher math, but elementary math? Even still, by showing work we were able to (through different means) show how to obtain the correct answer. Showing work, even on basic math, is an element of problem solving, to verify a correct answer. If there were no need for showing how to do the math, then how would a teacher be able to know if the student misunderstood the concept or made a clerical error?

Showing your work for math problems and knowing your times tables should be taught as an exercise of good practice. By learning that discipline at an early age, students will have a solid foundation as they get older and into more advanced subjects. I would liken this to a musician learning their scales. There are many self taught musicians who do not practice their scales, or never learned them, but you will not find very many playing in a major symphony orchestra.
The reason the thread took this turn was my example of an elementary school state test. There was no work to show, it asked to list three fractions in order, smallest to largest. Then they wanted the process to be explained. I did it one way and the test example did it another. Both were sound methods but when I asked if my answer would be marked wrong because I did it differently the answer was,"I would hope not." If the answer isn't yes or no then the test is flawed.
Let me ask a question. You are taking a math test, and they do exist on job apps, they ask you to figure the total for 6 tickets at $17.50 per ticket without a calculator. Many would just multiply it out, I prefer to make it an easy number to work with. I add 17.5 to itself to get 35 and triple it, $105.00. That is done in seconds in my head but I think it be wrong a state test.
 
Let me ask a question. You are taking a math test, and they do exist on job apps, they ask you to figure the total for 6 tickets at $17.50 per ticket without a calculator. Many would just multiply it out, I prefer to make it an easy number to work with. I add 17.5 to itself to get 35 and triple it, $105.00. That is done in seconds in my head but I think it be wrong a state test.

By doing it "your way", you essentially just multiplied $17.50 by 6. Doubling the number and then tripling that answer yields the exact same result. A standardized test has multiple choice answers, thus if you mark the correct answer, your method of arrival cannot be invalid as long as it produces the correct answer. I see no reason as to why this could be marked "incorrect".
 

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