May 21, 2017 - Math Circle 2.0

Multiplication review

Use graph paper to solve:

3 x 2 = 
5 x 1 =
8 x 4 =
9 x 6 =

7 x y = 21
solve for y

Number Sequences

Predict the next number in the triangle number sequence and the square number sequence.


Logic Problem One

You are at a picnic and there is a cooler full of juice.  There are five apple juices, three grape juices, and three fruit punches.  You really want an apple juice.  Without looking at package of juice, what is the smallest number of juice packages that you need to take out of the cooler in order to make sure you get one apple juice.  What is the smallest number if you really wanted fruit punch?

Logic Problem Two

From Raymond Smullyan's To Mock a Mockingbird

Suppose I offer one of three prizes: Prize A, Prize B, and Prize C.  Prize A is the best prize.  Prize B is an ok prize, and Prize C is the worst prize.  If you say a true statement to me, for example, 2+2 = 4, I will give you prize A or B.  If you say a false statement, I will give you Prize C.  You really want Prize A.  What could you say to me to force me to give you Prize A, the best prize.

May 14, 2017 - Math Circle 2.0

Warm Up

Using graph paper and a pencil, graphically solve the following multiplication problems:

2 x 3 = 
4 x 3 =
4 x 4 =
5 x 6 =
7 x 7 =


Sphero

Make a square and a triangle with the Sphero.  

May 7, 2017 - Math Circle 2.0

Word problem

Cathy has 6 pair of black gloves and 6 pair of blue gloves in a drawer.  She needs to pick out a matching pair of gloves in complete darkness.  How many gloves does she need to pull in order to make sure she gets a match (one left hand glove, one right hand glove of the same color)?

Logic

Three friends and a missing cookie.  Based on the friends responses, who stole the cookie?

2-variable constraints

In the land of gnomes and dwarfs, there are seven total that came to a party.  Using that the dwarfs ate three more cookies than the gnomes, each being ate one cookie, and some graph paper, how many dwarfs and gnomes were at the party.

Bulls and Cows

April 30, 2017 - Math Circle 2.0

Warm up

4 + e = 10  what is e?
9 - f = 3  what is f?
10 - g = 2 what is g?

1 + 8 = x
x - 5 = y
x + y = z
what is z?

i + 5 = 10
j + j = 14
j - i = k
what is k?

Number sorting

Sort the numbers in ascending order

8 2 10 15 13 4
18 5 22 11 9 40
d a j x s k

Sort the numbers in descending order

9 1 3 11 5 8


Sphero

Let's make a path around the classroom and see if we can program the sphero to navigate the path.  The kids picked a route and programmed the sphero to navigate the classroom.

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...