Problem Solving is Fun and I Can Prove It! October 14, 2004 David Rock [email protected] University...
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Transcript of Problem Solving is Fun and I Can Prove It! October 14, 2004 David Rock [email protected] University...
Problem Solving is Fun and I Can Prove It!
October 14, 2004
David Rock
www.faculty.umassd.edu/david.rock
University of Massachusetts Dartmouth
The Straight Line of Wonder
Mem Fox1997
There is a circular pond with a diameter of 200 feet. Dead in the center of the pond is a frog on a lily pad. The average leap of a frog is two feet, and there are plenty of other appropriately spaced lily pads in the pond on which to jump.
What is the minimum number of leaps it will take the frog to jump completely out of the pond?
Frog in the Pond
200 feet
Strategies students use
Repeated addition
Repeated subtraction
Groundwork for multiplication
How Much Dirt
How many cubic inches of dirt are there in a hole that is one foot deep, two feet wide, and three feet long? Multiple Levels.Variety of Concepts.
Why is it important to make problem
solving fun?
Interest towards MathematicsMathematical EnthusiasmInspirationProblem solving is one of our most important standards – key to success in other subjectsWe tend to succeed at things we enjoyWe tend to enjoy things at which we succeed
Cute Little BookwormThere is a three-volume set of books sitting on a shelf. The front and back covers of the books are each one-eighth inch thick. The page section inside each book spans exactly two inches. A cute little bookworm starts eating at page one of volume one and eats, in a straight line, through to the last page of volume three.
How far will the little worm travel?
Strategies
The answer is not six and one-half inches.
HINT: Try the problem!
Drawing a diagram is a great strategy – but you are not physically trying the problem!
Card Tricks are Fun
Pick a card and concentrate on that card!
It’s Magic!
I threw out your card!
Handy ManA man walks into a hardware store and buys:
1 for $120 for $2 300 for $3
What is the man buying?
Not Tic-Tac-Toe
Toe-Tac-Tic The object of the game is to get three in a row! What skills are used to play this game?
Not-Toe-Tac-Tic The object of the game is to NOT get three in a row! What skills are used to play this game?
Numeric Phrase
What number does the following phrase represent? TTTTTTT9 Seven Ts and a 9Say it fast.
Old Age
A person was born on September 28, 31 B.C. and died on September 29, 36 A.D. How many years did the person live? What skills are needed?
19 – 1 = 20
How can you take one away from nineteen and get twenty?
Roman Numerals?
XIX is 19
Take away the I
and you get XX which is 20
A Perfect TenObserve the four straight line segments below. Add 5 more straight line segments to make 10.
T E N
Problem Solving Board
Create a problem solving bulletin board for the classroom.Post 1-2 weekly contest problems.Provide incentives and recognition for correct work.Encourage outside help.
White House Math Challenge
www.whitehouse.org/kids/math
Four Distinct Levels
Elementary SchoolMiddle SchoolHigh SchoolOpen Challenge
Math Curse
Scieszka, John Smith, Lane1995
Seminar Materials
Web Addresswww.faculty.umassd.edu/david.rock
Visit Seminar Materials
E-mail: [email protected]