3.5

2564103*13
142857143*7=
14285714286*7=
142857142857*7
2564103*13

p-adic arithmetic:

...6666666666667*3=1

...666666667*9=3

....6666666667^2=?

Bulls and cows

2.26

multiplication

666667x3

37x3

divisibility by 3 rule

142857x7

p-adic arithmetic

...142857143x7

Opening the brackets

1001x107

(a+b)x(c+d)

Bulls and cows

Dragon curves

Phases of the moon

February 26, 2017 - Math Circle 2.0

Warm up

1 + 0 = _
4 +1 = _
2 + 3 =  1 + _
1 + 6 =  3 + _
6 + _ = 2 + 8
6 - 5 = 1 + _
7 - 2 = 2 + _

Coordinates

Coordinate review























Homework review - make a 6 pointed star using the coordinate system.  How can we make the star bigger?  

Homework - How do we make a 8 pointed star?


Logic question


There are three brothers named John, James, and William.  John and James always lie, but William always tells the truth.  The three are triplets and you cannot tell them apart.  You meet one of the three on the street and you want to find out if he is John.  You can only ask him one yes or no question.  The question you ask him can only have three words.  What do you ask him?

We made a truth table:

feb 19

Recall powers of 10.

Multiplication rules - explain distributivity (bracket opening).

Other usages for bracket opening: explains -x-=+.

Puzzle - ?

Knots/unknots?

February 19, 2017 - Math Circle 2.0

Warm up
Speed review.

The kids ran 83 feet from the steps of Altgeld hall to the Alma Mater statue.  The kids ran the distance in the following times: 6 sec, 6 sec, 7 sec, 10 sec, 11 sec.  How do these times compare with certain animals:

A tortoise will travel the same distance in 56 seconds
A cheetah will travel the same distance in 1 second


Coordinates with graph paper

Re-affirm degree coordinate system.  

Homework answer - Calculate the corresponding degrees of the southwest direction and the northwest direction.
Southwest - 225
Northwest - 315

At defined starting point on graph paper, draw lines using the following direction.

0 deg - 3 spaces
90 deg - 10 spaces
180 deg - 3 spaces
270 deg - 10 spaces
0 deg - 3 spaces
90 deg -2 spaces
45 deg - 2 spaces
90 deg - 2 spaces
135 deg - 2 spaces

What did you make if you add wheels to the bottom?

Homework - make a 6 pointed star using the coordinate system.  List the instructions that you used to make the star.

February 12, 2017 - Math Circle 2.0

Warm-up - Last week's Logic Problem

From http://brainden.com/logic-puzzles.htm

There are three switches downstairs. Each corresponds to one of the three light bulbs in the attic. You can turn the switches on and off and leave them in any position. 

How would you identify which switch corresponds to which light bulb, if you are only allowed one trip upstairs?  Hint:  The lightbulbs generate heat.


Drawing on Graph Paper

Re-affirm degree coordinate system.  

At defined starting point on graph paper, draw lines using the following direction.

90 deg - 10 spaces
0 deg - 10 spaces
270 deg - 10 spaces
180 deg - 10 spaces

where do you end up?

If the square that we built was a house, how would you draw the roof?  Have the kids figure out the degrees in between.

0 deg - 10 spaces (to return to top)
45 deg - 5 spaces
135 deg - 5 spaces

Homework - Calculate the corresponding degrees of the southwest direction and the northwest direction.

Speed for now ... because velocity is a vector

Are we faster than animals?
A tortoise moves less than 1 mph 
A cat can run at 29 mph
A horse can run at 30 mph
A dog can run at 45 mph (Greyhound)
A cheetah can move at 70 mph

How fast can you run?  How can we calculate it?  Hint:  The distance from the steps of Altgeld Hall to the Alma Mater statue is roughly 80 feet.  Using this distance and a stopwatch, the kids ran between 5 mph and 8 mph.

feb 12

Multiplication

Powers (compare 2^(3^2) and (2^3)^2 etc). More about bracket forming.
Guess number trick:
- think of a number;
- add 5;
- double the result;
- subtract the original number;
- add 10;
- subtract the original number again.

Solar eclipse (start at 0:45)

Lunar eclipse (start at 0:30)

Homework:

1. Invent your own number trick
2. Compare: 2²²²²² and 3⁽³³⁾
3. Find: 1111111 * 1111111; 11111111*11111111
4. What is the phase of moon during the lunar eclipse? solar eclipse?