Sunday, December 14, 2008

Survey Says.....

After watching the Heisman awards show the other night, I started thinking about my classes recent attempts at verifying the validity of surveys. The way that I see it, the Okie QB should not be holding the hardware right now if Superman got the most first place votes, and I am not a Gator fan at all, as the picture should prove! -----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
At any rate, our class has determined that a valid survey should represent exactly 100% of the group that was surveyed. That seems to make sense, as, if there were five people asked to respond, you should have five responses, not 4 or 12 ;-}-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
However, we determined that this all becomes a little trickier if we blend the way that the results are recorded into a mush of fractions, percents, and decimals. ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Now the challenge ensues. See if you can figure out if the following survey could be valid. ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
All of the teachers at CCE were asked to provide one response each to the following question; How could CCE best improve the CCE experience for our students?------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
0.22 of the teachers replied that Mr. P. and Mr. D. should not be allowed to wear Steelers football clothing.--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
1/5 of the teachers replied that Mrs. H. should hold no more than 12 tech meetings a week.-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
30% of the teachers stated that Mrs. Phillips should lobby for overtime pay for time spent scoring diagnostic tests. --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
0.125 of the teachers said that Coach Hall should have a Character Ed. class for the teachers.------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
1/8 of the teachers said that Mrs. Phillips, the math teacher, should write all lesson plans for all math teachers.------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
3% of the teachers said that lunch should be catered by P.F. Changs.------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
1/4 of the teachers said that there should be no more surveys ever.-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
Please look for combinations that "simply must go together". Are there any amounts that are equivalent? Would it help to know that 0.125 could be read as one hundred twenty-five thousandths or 12 and one half hundredths or 12 1/2% ? ----------------------------------------------------------------------------------------------------------------------------------------
Well, is it mathematically valid? -----------------------------------------------------------------------------------------------------------------------------------------------------------------
Peace and Happy Holidays!
T-Cubed ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- Sorry for all of the dashed lines. This post scrunches all of my hard returns together leaving no space between the lines.

Sunday, December 7, 2008

Please have some flexibility!


Imagine playing a game with the following three decimal number cards:

0.4 = Four tenths

0.45 = Forty-five hundredths

0.375 = Three hundred seventy-five thousandths

You might be asked to put these in order from least to greatest. You might be asked to add these all up to find a final sum. You might be asked to shade in a 10 X 10 grid in a way that represents the amounts shown. In fact, students will be asked to all of the above.

A few simple things will always makes matters work out better:

First, since out students are so tuned in to comparing fractional amounts through conversion to equivalent percents, why not convert decimals to percents? But how?

Well, it's easy enough for most kids to see that 0.4 (four tenths) could be written as 4/10, and most know that we could multiply 4/10 X 10/10 to get 40/100. Once we have a denominator of 100, we have a percent (parts per hundred). So, 0.4 = 40%.

For 0.45 (forty-five hundredths) we just think 45/100, and we have our percent. 45%

Now for the challenging one, not really, if we look at .375 (three hundred seventy-five thousandths) we could write 375/1000. If we divide 375/1000 by 10/10 we get 37.5 /100 or 37 1/2 percent. so, if you were shading in a 10 by 10 grid, you would simply shade thirty-seven and one half blocks.

If I was asked to add these decimals, I would rewrite them so that they all have the same number of digits on the right hand side of the decimal point. 0.4 = 0.40 = 0.400 = 0.4000000000000000000000000000000000000000000.

0.45 = 0.450 etc.

I'd end up with:


From there, I would add the largest place value (the tenths) .4 +.4 +.3 = 11/10 or 1.1
Next, I would add the hundredths .00+.05 +.07 = 12/100 or .12
Finally, I would add the thousandths .000 + .000 +.005 = 5/1000 or .005

+ .005 = 1.225 or 1 22/1000 or 1 22.5/100 or 122 1/2 %

Have Fun :-}