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This page contains syllabus and homework problems. Starting from the fifth class (October 31) we will also post solutions to the problems. New material will be added about once in a week. Check for updates. For overview of our program, please, see letter to the parents. |
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February 6:
In class:
We count squares and small cubes, rebuild house from matches and walk through a maze.
Homework 12, due February 13
First term classes (October-December 2004)
October 3
In class: We add numbers by counting money (we have our own currency called fishka). You can get extra fishkas by answering questions in class and doing your homework.
We also learn ancient Egyptian hieroglyphs.
Homework 1.
October 10
In class:
We count rabbits in a bush by their ears.
We color maps and learn the notion of odd and even numbers.
For instance, is the sum of two odd numbers
even or odd?
Homework 2.
October 17
In class:
We count small cubes and solve
logical problems. These
problems are based on the following fairy tale. Once upon a time there was a king who had many beautiful
daughters. There were many dangerous tigers in his kingdom as well.
A knight came to the king. He wanted to marry a princess.
The king decided to test how clever the knight was. He offered the following test.
There were two doors leading to two rooms. In each room, there was a princess OR
there was a tiger. The problem was to decide which door leads to a princess
(and go through that door, if the knight preferred a princess to a tiger).
The king placed labels on the doors to help the knight to choose.
These labels could be true or false.
Homework 3.
October 24
In class:
We do geometry with matches.
Homework 4.
October 31
In class:
We solve logical problems about twins Tom (who always tells the
Truth) and Luke (who always Lies).
We also solve apple problems. Then we come back to
Tom and Luke.
Homework 5 (
Part 1,
Part 2).
November 7
In class:
We cut different geometric figures into equal pieces. Two pieces are equal if you can put one
onto the other so that they coincide. We also continue sequences of numbers. It is easy to guess
what the next number is in the sequence 1, 2, 3, 4, 5,... . Now what about 1, 3, 2, 4, 3,...?
Homework 6, due November 14
Here is the list of all problems. Homework consists
of all problems from this list that we have not yet solved in class. Some problems are
marked with (*). That means they are very tricky. It is great if you can solve at least
one of them.
November 14
In class:
We make false equalities true. We also play the following game. One player thinks of some number,
and you should guess what number he has in mind. You can ask him "Yes or No" questions (that means that
the answers to these questions can be only Yes or No). Your objective is to guess his number by asking
as few questions as possible. Can you think of a good strategy to win this game?
Homework 7, due November 21
November 21
In class:
We play the same game as we played last time. It is a little bit harder now because
you may only ask 5 questions to guess a number from 1 to 30.
What questions would you ask to win for sure? Do not count on your good luck!
We also save cabbage from goats by drawing fences.
Homework 8, due December 5
December 5
In class:
We count bottles of Pepsi and distribute water between three cans. The common feature of all this problems is that
to solve them you need to do more than one step (sometimes 5 or 6), although each step is easy. So it is helpful
to keep track of all these steps by writing or drawing separately what happens after each step. In this way, even if your last step is wrong you can come one step back and try again.
Homework 9, due December 12
December 12
In class:
This class is very special because we start Math Olympiad. You can continue to solve these
problems at home (this is your homework). Try to solve as many problems as you can to win the Olympiad and get a prize! It is thus very important that you solve the problems by yourself. Next time (December 19), do not forget to bring your SOLUTIONS!
Next time we will also have an auction. Remember to bring all your FISHKAS!
Homework 10, due December 19
November 7
How to continue sequences, turn unequal sums to equal etc. pdf.
How to cut into equal parts jpg
How to cut a pie jpg
November 21
How to separate goats from cabbage, find the price of the book etc. pdf
December 5
Solutions to the problems about Pepsi and water.
