1. TOK AND MATHS Туенок Ирина Анатольевна, Муниципальное образовательное учреждение Красноярская университетская гимназия «Универс» № 1

2. TOK AND MATHS How logical is mathematics? Consider the following: 0.1111….. = 1/9 0.2222.…. = 2/9. 0.8888…. = 8/9 0.9999…. = 9/9 = 1 Why can we say that 0.9999…. = 1?

3. TOK AND MATHS How important is it to be exact? How important is it to be exact? Discuss this with regard to different scenarios in mathematics and other areas of knowledge such as science, medicine, architecture etc. Discuss this with regard to different scenarios in mathematics and other areas of knowledge such as science, medicine, architecture etc.

4. TOK AND MATHS Is infinity a number? Is it ever correct to write Is infinity a number? Is it ever correct to write x =  ? x =  ? Do some infinite sets have more elements than others? Do some infinite sets have more elements than others? Give examples to back up your answer. Give examples to back up your answer. If infinite sets are not the same size then what does "infinite" mean? If infinite sets are not the same size then what does "infinite" mean? Can you count the elements of some infinite sets? Explain your answer as clearly as you can. Can you count the elements of some infinite sets? Explain your answer as clearly as you can. Can you think of an infinite set where it is not possible to count all the elements? Can you think of an infinite set where it is not possible to count all the elements?

5. TOK AND MATHS Do mathematical symbols such as , ,  etc. have meaning in the same sense as words have meaning? Do mathematical symbols such as , ,  etc. have meaning in the same sense as words have meaning? Can mathematical symbols be ambiguous or vague like certain words, (for example: free, poor, good etc)? Can mathematical symbols be ambiguous or vague like certain words, (for example: free, poor, good etc)?

6. TOK AND MATHS What is the difference between the empty set, , the number zero and nothing at all? What is the difference between the empty set, , the number zero and nothing at all? Can there be such a thing as a complete vacuum? Can there be such a thing as a complete vacuum? Do you think we can consider the universe to be the ultimate universal set U containing everything Do you think we can consider the universe to be the ultimate universal set U containing everything

7. TOK AND MATHS We must be very careful with brackets in Mathematics. We must be very careful with brackets in Mathematics. Are brackets in Mathematics more important than brackets used in other areas of knowledge? (e.g. History, Literature, Science etc?) Are brackets in Mathematics more important than brackets used in other areas of knowledge? (e.g. History, Literature, Science etc?)

8. TOK AND MATHS Why is order important in some areas of mathematics and not in others? Why is order important in some areas of mathematics and not in others? Do we really learn from our mistakes? Look at examples from Economics and History. Do we really learn from our mistakes? Look at examples from Economics and History.

9. TOK AND MATHS Often there are several different ways to arrive at an answer. Often there are several different ways to arrive at an answer. For each method there will be advantages and disadvantages. For each method there will be advantages and disadvantages. Sometimes one method may be more accurate than another. Sometimes one method may be more accurate than another. How do you decide what method is best? How do you decide what method is best? Do you think that everyone would agree with you? Do you think that everyone would agree with you? Are there different ways to arrive at an answer in other areas of knowledge such as the sciences, history, aesthetics? Are there different ways to arrive at an answer in other areas of knowledge such as the sciences, history, aesthetics?

10. TOK AND MATHS It is very important for the timing to be as accurate as possible in the Olympic Games. However, the same degree of accuracy is not necessary when timing the cooking of a pot of rice. So, how important is it to have “exact” values? It is very important for the timing to be as accurate as possible in the Olympic Games. However, the same degree of accuracy is not necessary when timing the cooking of a pot of rice. So, how important is it to have “exact” values? What do you understand by an “exact value”? What do you understand by an “exact value”? Can a measurement ever be exact? Can a measurement ever be exact? Is it more important to be “exact” in Mathematics and Science than it is in other Areas of Knowledge such as Science, History, Aesthetics? Is it more important to be “exact” in Mathematics and Science than it is in other Areas of Knowledge such as Science, History, Aesthetics?

11. TOK AND MATHS When conducting a survey how can you ever be sure that the replies given are true? When conducting a survey how can you ever be sure that the replies given are true? In a survey the people questioned could lie about the information they give In a survey the people questioned could lie about the information they give What type of questionnaire was used and to whom was it distributed? What type of questionnaire was used and to whom was it distributed? What difference could this make to the results? What difference could this make to the results?

12. TOK AND MATHS “Stem and leaf diagram”, “box and whisker plot”. “Stem and leaf diagram”, “box and whisker plot”. Does the name given to a mathematical process make a difference to the result? Does the name given to a mathematical process make a difference to the result? How do titles influence us in other areas of knowledge? How do titles influence us in other areas of knowledge?

13. TOK AND MATHS How do we know when two things are related? How do we know when two things are related? Can two sets of data have a very strong correlation and yet not be related? Can two sets of data have a very strong correlation and yet not be related? Try to think of your own examples. Try to think of your own examples. Can you find any examples in advertising? Can you find any examples in advertising?

14. TOK AND MATHS Why do we have different currencies? Why do we have different currencies? Would it not be easier to have one universal currency? Would it not be easier to have one universal currency? What would be the advantages and disadvantages? What would be the advantages and disadvantages?

15. TOK AND MATHS If mathematics is about following rules and we know that 10/10 = 1 and 4/4 = 1, If mathematics is about following rules and we know that 10/10 = 1 and 4/4 = 1, then why does 0/0  1? then why does 0/0  1?