A TOK Quiz for Mathematical Knowledge Choose the most appropriate answer(s) for each of the following. Discuss these answers with the people in your group and prepare to give supporting arguments for your selections.

Question 1 Mathematics is a subject about Logical thinking Illogical thinking Things that exist in nature Things that do not really exist at all Things that are certain Things that are not certain

Question 2 Problems in mathematics can be best solved by using Clever tricks Experiments Computers Graphic calculators Trial and error Investigations Discussion The answers in the back of the textbook

Question 3 Mathematics is a subject that should be studied by People who are interested in it Engineers and other people who want to apply it People who are challenged by it People who want to become better thinkers People who are intrigued by its aesthetic qualities People who want to become better artists People who want to improve their overall academic performance People who want to improve their college entrance exams All Diploma Program candidates People who are poor at it

Question 4 Which of the following best describes mathematics? A body of knowledge A practical tool A cornerstone of philosophy The perfection of the logical method The key to understanding nature An intellectual game An aesthetic experience

Question 5 One plus one is Always equal to two Sometimes equal to two Never equal to two Too philosophical to think about

Question 6 Parallel lines Never intersect Always intersect Do not exist

Question 7 Which of the following quotations best captures the essence of mathematics? “A mathematician is a blind man in a dark room looking for a black cat which isn’t there”. Charles Darwin “Pure math is a game. It’s fun to play. We play it for its own sake. It’s more fun than applying it. Most of the math that U teach is never used by anyone. Ever” Ted Williams, Prep School Mathematics Teacher “If you ask your mother for one fried egg for breakfast and she gives you two fried eggs and you eat both of them, who is better in arithmetic, you or your mother?” Carl Sandburg “Mathematics is a game played according to certain simple rules with meaningless marks on paper” David Hilbert

The University of Melbourne Entrance Examination (1875) Complete the addition below. Write your answers in words. 3,643,978 + 19,507,629 Twenty-three million, one hundred and fifty-one thousand, six hundred and seven. No hyphens, no commas, no “and” or wrong answer = no Uni !

Maths Questions???? A rabbit, chased by a dog, ran from a carrot patch into a nearby woods. How far did he run into the woods? 2. Two students played checkers. Each played 3 games and won 3. There were no draws. Explain how this could be. 3. Some months have 30 days. Others have 31. How many have 27? Half way; after that he is running out of the woods! They played other people! All of them!

“Pathetic” Maths 3,608,528,850,368,400,786,036,725 has 25 digits and divides by 25. BUT... if you just take the first n digits, the result will divide by n. For example, 360852 are the first 6 digits and 360852 divides by 6. 1729 is the lowest number that can be expressed as the sum of two cubes in two different ways! In other words, 1729 = 93 + 103 OR 13 + 123 If you multiply 21978 by 4 it turns backwards. 153, 370, 371 and 407 are all the "sum of the cubes of their digits". In other words 153 = 13 + 53 + 33 19 = 1 × 9 + 1 + 9 and 29 = 2 × 9 + 2 + 9. This also works for 39, 49, 59, 69, 79, 89 and 99.

Math is no more about equations than poetry is about spelling Math is no more about equations than poetry is about spelling. Equations and spelling exist to convey an idea. Understand that idea. Mickey Cheatham