Sunday, December 14, 2008
Sunday, December 7, 2008
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 :-}
Sunday, November 23, 2008
Be you a student, a teacher or an interested guardian, please ask yourself if you could come up with any more profound statements about the fractions 2/3 and 3/4. Also, please challenge yourself to create accurate models of each as well. To the mathematically uninterested, this may not seem like a grand accomplishment, but to a well-trained math geek, this is poetry!
Sunday, November 9, 2008
Sunday, November 2, 2008
Hello again. Once more, a student has shown how working "smarter" makes for a better and more efficient math student!
Sunday, October 26, 2008
I'd be willing to bet that you read that as 25 "times" 41.
The students were given four choices as a correct answer:
B) (20 X 40) + (40 X 1)
C) (25 X 40) + ( 25 X 1)
D) ( 25 X 40) + (26 X 1)
Now, before you put on your number crunching hat, consider the rereading the "times" sign in the original problem. If you read the X as "groups of", you become aware that we are looking for some combination that is equivalent to 25 groups of 41 or 41 groups of 25.
Do you see a choice that makes 41 groups of 25? I do! Decompose the 41 into 40 and 1. Does that help? The answer is C, and I'll C U L8TR.
Sunday, October 19, 2008
Sunday, October 12, 2008
The two scans above, starting with the top scan (uh, not the pug), represent some of the most efficient strategies around when it comes to multiplication and division. Perhaps, the best thing about these strategies is that most of the calculations can be carried out mentally and do not rely on the rote memorization of many math "facts". Truly, this is how most mathematicians think, smarter not harder!
Parents, students, fellow countrymen, and all other living beings, please challenge yourself to see if you can find the beauty in this kind of thinking. You may just find your inner math geek after all!
As a footnote, I wish that I could say that I "hired" a student to write this for me, but that would not be honest. I wrote this myself! Bad hand writers of the world unite! We shall rule.
Sunday, October 5, 2008
Sunday, September 28, 2008
Monday, September 22, 2008
Sunday, September 21, 2008
I wish that I could make this uploaded work a bit more clear, but it still is great to emphasise my point.
This work comes from our last Mini-Quiz, and it is a great example of how organizing your work in a very simple way can lead to a great outcome. K did an amazingly simple but powerful thing when she drew lines to separate her problems. She made it easier for her brain to focus on the tasks individually. Separate spaces for separate thoughts. Simple but very important.
I also noticed something else really cool. K did not use ultra-small writing. While I like saving trees as much as the next teacher, I know that simply writing bigger and using more space often creates better results.
I also love love love love love love the expanded notation in the addition problem, the open number line in the subtraction problem, the generic rectangle in the multiplication problem, and the misconception corrected in the division problem. This work ROCKS!!!!!!
Monday, September 1, 2008
We will be starting our investigations in the area of number sense tomorrow, and our unit starts with a look at subtraction. You know, where you find the difference between two numbers.
What if I changed that to read "find the distance between two numbers"? Does that sound any easier?
Here's my point: If I ask a kid to subtract 95 from 100, I hate to see the kids that are driven by traditional thinking as they line up their numbers in columns and subtract to find the distance. Wouldn't it be easier to just think about how far it is from 95 to 100? You can use an open number line if you wish as well, for all of you visual learners out there. Hopefully, you'll just think about the distance and know that the distance is five.
Many teachers that I talk to say "That's great for easy small numbers, but I don't want my kids to rely on that for bigger numbers!" I think that you might want to rethink that stance if you've taken it already.
Using an open number line or "counting up" works well with any numbers, and it prepares kids to make estimates far better than traditional thinking. We all know that "in the real world" folks will use calculators to deal with big numbers anyway. So why not build some audacious number sense now.
$1,000,000 - $257, 665 can be solved as follows:
257,665 +35 = 257,700 +300 =258,000 +2,000 = 260,000 +40,000 = 300,000 +700,000=
So, if I add the numbers in bold that I "added on" I get a sum of $742,335 which is the distance between the two numbers. The beauty is that I did it in my head for the most part:-} Another beautiful thing is that there are an infinite number of ways to "add on". Kids choose the number combinations that they like. I would, of course, make sure to lead them into using landmark numbers (usually numbers that end in 0, 00, 000...) as targets to add up to.
Peace, and try it...
T-Cubed P.S. Do you know the man in the picture?
Sunday, August 24, 2008
Then, T.S. Fay toppled a huge Oak tree onto my house and I lost phone service, cable, Internet, and electricity. At that moment, 3:00 A.M. 08-21-08, I started to think about math! Some of my thoughts: Is there still a $5,000 hurricane deductible? How much do carpenters charge per hour? How much does plywood cost per sheet? Exactly how hot will it get in my house without AC? How long will my generator run on one five-gallon tank of fuel?
Math may not always be pretty, but it is always around us!
Thursday, August 14, 2008
To be short, I found some burlap on the ground. I made my daughter wear it for a gorgeous shot. She took a photo of me, and then the Park Ranger screamed at us for bothering the burlap. Really, it was just resting on the ground.
Monday, August 11, 2008
Monday, June 23, 2008
What is it larger than?
What is it half of?
What is half of 25?
What if it were a percent, what would it look like?
What landmark numbers is 25 close to? How close?
What's a landmark number?
If it was money, what could I buy?
Now you try.........
Thursday, June 12, 2008
Wednesday, June 11, 2008
Please remember that you can start thinking this way using really small numbers to help understand. We all know that 10-4 = 6, but if you think about the distance between 4 and 10, it becomes easy to see how we can add-on to 4 until we get to 10 (4 + 6 =10)