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We adapt“Parable of the Polygons” (Vi Hart and Nicky Case), an online simulation on diversity and segregation, into an appropriate MTC session. The session is interactive, and offers multiple layers of content depending on the age and comfort level of students with conversations on social issues.
Imagine that all the numbers from 1 to 100 inclusive are written on the blackboard. At every stage, you are allowed to erase two numbers that appear on the board (let’s call the numbers you erased x and y) and in place of the two erased numbers, write the number x+y +xy. Repeat this operation until only a single number remains. What are the possible values for that remaining number?
A simplex lock is a type of combination door lock that involves pushing-in buttons. Given the set of rules for using a 5-button simplex lock, how many different combinations are there?
SET is a fun game that can be enjoyed by kids as young as 6 and is challenging even for adults. It is rich in counting problems and is great for getting people to pose problems. It is also an example of a finite geometry and interesting to explore how well one's geometric intuition works.
Plimpton 322 is a 5000 year old clay tablet that lists the short leg and hypotenuse of 15 right triangles with integer sides. We consider how Pythagorean triples might be generated and Eleanor Robson's explanation of the numbers.
This session asks participants to expand their notion of "distance," using a nontraditional taxicab metric instead of the usual Pythagorean notion.
In this session, participants will explore the Match-No Match game: two players each draw one chip out of a bag – if the color of the chips match Player 1 wins, if not Player 2 wins.
The divisibility rules are often "accepted without proof" by both teachers and students. The problem explored in this session involves a rich, novel way of looking at "amazing numbers," to authentically develop notions around patterns of divisibility as a solution strategy.
Kenken is a puzzle whose solution requires a combination of logic and simple arithmetic skills. The puzzles range in difficulty from very simple to incredibly difficult. Students who get hooked on the puzzle will be forced to drill their simple addition, subtraction, multiplication and division facts.
What is four times three? 12 you might say, but no longer! In a new type of math — intersection math— we will see that four times three is 18, two times two is 1, and that two times five is 10 (Hang on! That’s not new!).