MATHEMATICS is a way of approaching a problem by using one’s own logic and powers of observation. It is not a recipe for problem solving, but rather a collection of ways of using reasoning, models, evidence, examples and counter examples to discover meaningful patterns in numbers, in 2-D and 3-D space, and in data.
Challenge: ADDING FOUR CONSECUTIVE NUMBERS MENTALLY (no pencil, no paper)
Some people say that to add four consecutive numbers, you add the first and the last numbers and multiply by 2. What can you find out about that? Start with 5, 6, 7, 8. (5 + 8 = 13, and 13 x 2 = 26) Does that work?
Now try these: 10, 11, 12, 13. What about 21, 22, 23, and 24?
Next: 100, 101, 102, 103 - can you now add these 4 consecutive numbers "in you head" ?? CONGRATULATIONS!
(Something to ponder...what if you added the two MIDDLE numbers?????)
ALL LIFE IS A CONCATENATION OF EPHEMERALITIES.
Moose on Sherman Ave. - CDA, Idaho
Just how long is a second? A second is equal to 9,192,631,770 oscillations of a Cesium-133 atom! So, next time someone calls to you, say,"I'll be with you in 9 billion, 192 million, 631 thousand, 770 oscillations of a Cesium-133 atom!"
Want to know the EXACT time? Go to
SKYSCRAPERS by Rachel Field
Do skyscrapers ever grow tired Of holding themselves up high? Do they ever shiver on frosty nights With their tops against the sky?
Do they feel lonely sometimes Because they have grown so tall? Do they ever wish they could lie right down And never get up at all?
We are Americans. As enduring as Rushmore. As strong as the Tetons. As refreshing as the geysers of the West. As vast as the Grand Canyon. As raw as the prairies of Texas and the Everglades of Florida. We are the land of purple mountain majesties above the fruited plains. (Thomas Kincaid)
We human beings are not mechanical, timeless creatures that can grind on endlessly at work. We need quality time to collect our thoughts and our dreams. We need time to "cease" and to wonder abut the deep meanings of life. We need to remember our history and to worship the Lord of life. (Earl F. Palmer)
June 7, 1976 is an interesting date. It can be written 6-7-76, or, ignoring the dashes 6776. Notice the sequence of the digits is the same in BOTH directions -so it is a PALINDROMIC DATE.
How many dates can you find in the twentieth century that are palindromes when written in the form month-day-year?
Is October 1, 1901 a palindromic date? How about December 11, 1921?
THE CASE FOR INVENTED STRATEGIES VS STANDARD ALGORITHMS:
Invented Strategies are: a. number oriented rather than digit oriented b. left-handed rather than right-handed, which provides some sense of the size of the eventual answer in just one step c. flexible rather than rigid
EXAMPLE: When asked to find 1/2 of 96 cents, a mathematician would NEVER use the standard algorithm for division..she would simply take the larger number apart so that she can solve the problem without paper or pencil! Her Thinking: 96 = 80 + 16, so I will just add half of 80 to half of 16! My answer is: 40 + 8 = 48 cents! Another strategy is to find half of 100 cents: 50 + 50, then take 2 cents from each amount to get 48 cents.
THESE are examples of flexible thinking!
A hiker walks from one town to another. On the first day he walks 1/3 of the total distance. The next day he covers 1/3 of what is left. The following day he covers 1/4 of the remaining distance. The fourth day he covers 1/2 of the remaining distance. Now he has 15 miles left to travel. HOW FAR HAS HE TRAVELED ALREADY?
Artwork by the Creator of the Universe
CALCULATOR CHALLENGE COUNTING: Students press any number on the calculator (e.g., 17), then + 8.
They say the sum before they press = .
Then they continue to add 8 mentally, challenging themselves to say the number
before they press = . They should see how far they can go before making a mistake!
SOMETHING TO THINK ABOUT -
Would you rather work for 7 days and be paid $20 each day - OR - would you rather be paid $2 the first day, $4 the second day, etc. (your salary would double each day for a week).
FIRST - write down your choice.
NEXT - do the calculations.
FINALLY - was your choice the best one????? Why or why not?
Click on the photo on the right (a tall tree in Kelsey Creek Park - across the street from where I live) - and you will be "whisked" to the next page in this website!