Warm Up
Scale of the solar system. Watch movie:
https://www.youtube.com/watch?v=Kj4524AAZdE
Perimeter
Introduce perimeter of a square and a rectangle. How do we define a rectangle and a square? How many side lengths of a rectangle do you need to know to calculate the perimeter?
Puzzle
Cows in a field game
Homework puzzle
You need to capture precisely 4 gallons of water for some unknown experiment that requires precisely 4 gallons of water. The tools available to you are a 3 gallon container, a 5 gallon container and an unlimited water source that allows you to fill the 5 and 3 gallon containers. How would you fill the containers to get precisely 4 gallons of water?
Sunday, September 3, 2017
Saturday, August 26, 2017
August 20, 2017 - Math Circle 2.0
Warm Up
Welcome back to Math Circle. Let's discuss the solar eclipse that will happen Monday, August 21, 2017 in the USA.
Pinhole Camera
Safety first! Never look at the sun directly without ISO 12312-2 compliant solar glasses. You may look at the sun indirectly by making a pinhole camera.
Follow the link below to get the directions.
https://eclipse2017.nasa.gov/sites/default/files/EclipseCerealBoxViewer.pdf
Size of Sun, Earth, and Moon
The following link has a summary of the sizes and distances of the sun, earth, and moon.
http://blair.pha.jhu.edu/scale.html
Almost four diameters of the moon span the earth.
109 diameters of the earth span the sun.
The distance from the earth to the moon is 110 moon diameters
The distance from the earth to the sun is 11759 earth diameters
What does that look like?
How can we create a model of this?
What is a diameter anyway?
Scale - 1 earth diameter = 1 inch
distance from earth to moon is 30 inches
distance from earth to sun is 11759 inches, or 980 feet, or distance to the top of right of the rectangle formed by the sidewalks north of Foellinger auditorium.
Welcome back to Math Circle. Let's discuss the solar eclipse that will happen Monday, August 21, 2017 in the USA.
Pinhole Camera
Safety first! Never look at the sun directly without ISO 12312-2 compliant solar glasses. You may look at the sun indirectly by making a pinhole camera.
Follow the link below to get the directions.
https://eclipse2017.nasa.gov/sites/default/files/EclipseCerealBoxViewer.pdf
Size of Sun, Earth, and Moon
The following link has a summary of the sizes and distances of the sun, earth, and moon.
http://blair.pha.jhu.edu/scale.html
Almost four diameters of the moon span the earth.
109 diameters of the earth span the sun.
The distance from the earth to the moon is 110 moon diameters
The distance from the earth to the sun is 11759 earth diameters
What does that look like?
How can we create a model of this?
What is a diameter anyway?
Scale - 1 earth diameter = 1 inch
distance from earth to moon is 30 inches
distance from earth to sun is 11759 inches, or 980 feet, or distance to the top of right of the rectangle formed by the sidewalks north of Foellinger auditorium.
Sunday, August 20, 2017
aug 20
...2857142857142857143x7=?
Quadrangles - what is the taxonomy:
Kites (pairs of neighboring sides equal) - Parallelograms (opposite sides <=> opposite angles are equal)-Trapezoids (pairs of neighboring angles are equal)
Rhombi (=diamonds) Rectangles
Squares
Midsides operations: take midpoint of all 4 sides of a quadrangle Q, get another quadrangle M(Q).
Turns out, - M(Q) is always a parallelogram!
Q-rhombus <=> M(Q) - rectangle, and vice versa.
Logics:
Two villages (Knights and Knaves), a person at the fork - which road goes to Knights village?
Larry, Leon, Tom, L's are liars, Tom tells truth. How to find if you speak to Larry?
When the angle between the hands is wider: 5 past 11, or 10 past noon?
$x^2 $
$x^2 $
Sunday, June 4, 2017
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.
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.
Sunday, May 21, 2017
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.
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.
Sunday, May 14, 2017
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
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
Sunday, May 7, 2017
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.
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.
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