April 9, 2017 - Math Circle 2.0

Warm up

Calculating the number of triangles in an object....

There are 4 math circle students:
Count the total number of items that the students have:

Shirts?
Shoes?
Fingers?

Max was able to bake cookies.  He put a the cookies in 3 rows, with 4 cookies in each row.  How many cookies did he make? Are there other problems that can be solved like this?

Cabbage Patch Problem:

Divide the cabbage patch into 6 sections that contain only two cabbages in each section using only 3 straight lines.

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 make start at a point, move to a second point, and then move to a final point at speed of 50.

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