April 2, 2017 - Math Circle 2.0

Warm up

Sequences with numbers and letters.

2 4 6 8 _
B D F H _

Review equality and letter substitution:

6 = x + x
10 = y + y
3 + n = 8
10 - z = 2

Try 2 equations:

a + b = 7
2 + a = 4
Solve for a and b

Speed and Time

The sphero robot needs three parameters to travel:

• Direction (in the coordinate system we learned)
• Speed 
• Time (in seconds)

Program sphero to hit a target in the room.  Set sphero at a fixed speed, choose a direction, and then figure out the amount of time sphero needs to travel to hit the target.


Sequence problem

Bulls and Cows

Always a favorite, we wrapped up math circle with a nice game of bulls and cows.

april 4

- Find:

• 2x4-1x5=3;
• 3x5-2x6=
• 4x6-3x7=
• ....
• 322x324-321x325=
• ....
• (a+1)(a+3)-a(a+4)=

- Look up the lunar eclipses over the past 20 years. On what months do they happen?


- Puzzle: guess what's in the picture?

Try to make your own picture of something that is hard to guess...

March 12, 2017 - Math Circle 2.0

Warm up

Focus on equality and operation sign:

Does 5 + 7 = 11?
Why not?

5 = _ + _
10 = _ + _
2 = _ - _


Substitute a symbol

6 = x + x
10 = y + y

Game

Bulls and Cows - mathematical game.  There is a secret code n digit code with all the digits  being different.  The kids then guess the code.  If they have a digit that is present in the code, it is a cow.  It they have a digit that is both present and in the correct position, they have a bull.  The number of bulls and cows are reported after each guess.  The game stops when the code is guessed correctly.

The kids picked a code for Sanjay and Darrin to solve that was 3 digits long.  The kids then stumped the adults with a 4 digit code.

March 5, 2017 - Math Circle 2.0

Warm up

Focus on equality and operation sign:

* + 0 = _
**** +* = _
**** - * = _
** + *** =  * + _
* + ****** =  *** + _

Game

Bulls and Cows - mathematical game.  There is a secret code 2 digit code with all the digits  being different.  The kids then guess the code.  If they have a digit that is present in the code, it is a cow.  It they have a digit that is both present and in the correct position, they have a bull.  The number of bulls and cows are reported after each guess.  The game stops when the code is guessed correctly.

Coordinates

Homework review:  How do we get an eight pointed star using squares?  

New homework:  Can we make a 10 pointed star using squares or triangles?

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: