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A lone goose was flying in the opposite direction from a flock of geese. He cried: "Hello, 100 geese!' The leader of the flock answered: "We aren't 100!" If you take twice our number and add half our number, and add a quarter of our number, and finally add you, the result is 100, but --- well, you figure it out!
The one goose flew on, but could not find the answer. Then he saw a stork on the bank of a pond looking for frogs. Now among the birds the stork is the best mathematician. He often stands on one leg for hours solving problems. The goose descended and told his story.
The stork drew a line with his beak to represent the flock. Then, he drew a second line of the same length, a third line half as long, another line a fourth as long, and a very small line, rather like a dot, to represent the goose.
"Do you understand?" the stork asked.
"Not yet."
The stork explained the meaning of the lines: The first and the second represented the flock, the third half of the flock , the next a quarter of the flock , and the dot stood for the goose. He rubbed out the dot, leaving the lines that now represented 99 geese. "Since a flock contained four quarters, how many quarters do the four lines represent?"
Slowly the goose added: 4 + 4 + 2 + 1. "Eleven," he replied.
"And if 11 quarters make 99 geese, how many geese are in a quarter?"
"Nine."
"And how many in the entire flock?"
The goose multiplied 9 by 4 and said "Thirty-six."
"Correct! But you couldn't get the answer yourself, could you? You ---- goose!"
This story is from Russia where it is has been told in schools for over 50 years.
from The Moscow Puzzles, p. 95
(see bibliography)
Assignment Exercises
Readings Bello & Britton,
Sections 5.5-5.6
Web Resources These web resources have links to
algebra problem-solving sites.
1. Make up any number trick or puzzle that uses algebra to solve. (Check out the Proofs page for ideas)
2. Complete the following exercises:
1. . pp. 319 - 322, Ex. 5, 17, 19,29, 30, 32, 40 44
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2. pp. 330 - 333 , Ex 2, 6, 7, 15, 16, 18, 24, 30, 35, 48, 49
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3. Prove that the sum of any 3 x 3 array of dates from a calendar is always 9 times the middle number:
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4. In Week 4, you created a number pattern using the Hundred Number Pattern Chart.
Prove your number pattern or create another one that you then prove. Link here for a fresh Hundred Number Pattern Chart.
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5. Given the number chart below, complete the four step process:
Step 2) Circle another number that has not been crossed out and cross out the remaining numbers in its row and column.
Step 3) Repeat Step 2 until there are 4 circled numbers.
Step 4) Add the four circled numbers.
Step 5) Subtract 66 from the sum and divide that number by 4.
What is the result and how does that link to the chosen square?
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6. Prove your result using algebra.
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7. Add the numbers of the day, the month, and the year you were born (Use all of the numbers in the year!). Subtract 23 times the day. Add 21 times the month. Add your age on December 31, 1991. If this result is divisible by 11, you were born on a lucky day!
Use algebra to show why everyone is born on a lucky day!!!!
Calculator City with Algebra Calculators
http://www.1728.com/Cut-the Knot Algebra Puzzles
http://www.cut-the-knot.com/algebra.htmlEasy Start Algebra Menu - has tutorials on various topics in algebra
http://www.gcse.com/Maths/algmen.htmGraphing Calculator
http://www.geocities.com/CapeCanaveral/Launchpad/2426/calculator.htmlInteractive Algebra
http://www.accessone.com/~bbunge/Algebra/Algebra.htmlLinear Functions with applet
http://id.mind.net/~zona/mmts/functionInstitute/linearFunctions/linearFunctions.htmlMath Forum's Resource Page on Algebra
http://forum.swarthmore.edu/library/topics/algebra/Ms. Lindquist : The Tutor- a Free Web-Delivered Intelligent Tutoring System For
Tutoring Students In Writing Expressions For Algebra Word Problems
http://www.algebratutor.org/The Quadratic Solver
http://id.mind.net/~zona/mmts/miscellaneousMath/quadraticFormula/quadraticRealSolver.htmlQuickMath Automatic Math Solutions - an online calculator to solve equations and numerical operations
http://www.quickmath.com/S.O.S. Math - Algebra
http://www.sosmath.com/algebra/algebra.htmlWebmath Tutorials on Pre-Algebra through Calculus
http://school.discovery.com/homeworkhelp/webmath/WebAlgebra -Tutorials and Interactive Exercises
http://albert.math.uiuc.edu/algebra.htm
Syllabus | Home | Assignments | Bibliography
