Aug 23 Math Circle 2.0

Symmetry

1. Which shapes are symmetric? Which are asymmetric?

Students were asked to fold figures along axis of symmetry

How many ways can the robot get from point A to point B?

2. Fill in the missing half of each shape 

Robots In Urbana

Following Math Circle 1.0 Sept 29 2013

The robot only understands two instructions:

1. "Go North"
2. "Go West"

A robot starts at the corner of Vermont and Race. What instructions can you give it so that it will move from the corner of Race and Vermont to the corner of Carle and Pennsylvania?

How many ways can it get there?

Can you give it instructions to get back?

Algebra

Each kid has one head and two legs. 

• How many heads and how many legs do three kids have?
• If there are two heads and four legs, how many kids are there?
• If there is one head and six legs, how many kids? (no correct answer here, see below)

An ant has one head and six legs.

• If there is one head and six legs, does the head belong to a kid or to an ant?
• If there are two heads and eight legs, how many kids? How many ants?

Experiment

What happens if you put a pack of mentos in a 2 L bottle of diet coke?

august 30 - circle 2.0

For the lesson of August 30, 2015.....

1. Symmetry

The 2.0 group reviewed the symmetry lesson of last week.  We also worked together to complete a pattern on a grid using the symmetry worksheet below.


2. Number line

After symmetry, we introduced the concept of the number line.  We identified numbers on the number line.  We then used the number line to determine which number was greater. At the end of the topic, we tried simple addition.

3. Money

The 2.0 group sorted a bag full of pennies, nickels and dimes into the three types of coins.  We then learned that one nickel is equal to five pennies.  For homework - how many pennies are needed to have the same value as 5 nickels?

august 30

• Work out the cross problem: tile the plane; find an integer lattice; cut the cross. 
• What is the area of a square: 1, 4, 9,... But the cross's area is 5; how we can make a square of the area 5?
• Try the same trick with other pentaminos? P, T,  
• Take white and black stones, same number of each. Place them on a circle; find a place so that when you start from there and add 1 for each black stone, and subtract 1 for each white stone, you never go below 0...
• Try to do the trains (using the Boston Metro visualization widget)
• Slice of bread with two cuts can be split into 3 pieces. What about a bagel? A pretzel?

Homework

• A family is crossing a dark narrow bridge; at most two of them can cross at a time, and the family has just one flashlight. Mom can run across in 1 minute, dad in 2 minutes; son in 5 minutes and their pet sea lion in 6 minutes. Can they all cross the bridge for 13 minutes?
• Here is a solution (there are many!) of the cross puzzle.
  
  
  
  Can you cut and reassemble each of these two pentaminos, to get squares?

OK, train again: if it makes 100 miles per hour, how many miles it makes in 15 minutes? 30 minutes? 45 minutes? One hour and 15 minutes?

august 23

Warm-up:

• 100 heavy guys want to cross a wide river. Two kids happened to be around with a boat which can carry no more that two kids or one adult. Can one get all the big guys across?
• Alice, Bob and Clara ate apples. Alice and Bob together ate 5 apples (we call it A+B=5). Further, A+C=3, B+C=6. How many apples ate each of them?

Same if A+B=3, B+C=2, C+A=2.

Graphs of functions: 

• Train moving from A to B...

Homework:

• Partition the cross with straight cuts into several parts from which make a square:

• Solve:
• A+B=5, B+C=5, C+A=4;
• A+B=5, B+C=5, C+A=6;
• what about A+B=5, B+C=5, C+A=5?
• A train goes with speed 100mph. 
• Plot where it will be in 1h, 2h, 3h, 4h. 
• What about 30min? 1h30min? Draw as many points on the graph as you can...
• What if the train makes a 1 hour long stop after two hours? Show where it will be after 1, 2, 3, 4 hours...