conversations.from: human
conversations.value: What could be a title for a book about Based, Melbourne, Bill with the genre: Science & Math, Mathematics?
conversations.from: assistant
conversations.value: A title for this book could be 'Speed Mathematics'
conversations.from: human
conversations.value: Provide the first five paragraphs for this book.
conversations.from: assistant
conversations.value: Speed Mathematics
  In this third edition, I have included extra material on keeping numbers in your head, memorising numbers, working with logarithms and working with right-angled triangles. I have expanded the chapters on squaring numbers and tests for divisibility and included an idea from an American reader from Kentucky.
  My methods are not the same, although there are some areas where our methods meet and overlap. We use the same formula for squaring numbers ending in five. Trachtenberg also taught casting out nines to check answers. Whereas he has a different rule for multiplication by each number from 1 to 12, I use a single formula. Whenever anyone links my methods to Trachtenberg's, I take it as a compliment.
  Imagine being able to multiply large numbers in your head — faster than you could tap the numbers into a calculator. Imagine being able to make a 'lightning' mental check to see if you have made a mistake. How would your colleagues react if you could calculate square roots — and even cube roots — mentally? Would you gain a reputation for being extremely intelligent? Would your friends and colleagues treat you differently? How about your teachers, lecturers, clients, management?
  People equate mathematical ability with intelligence. If you are able to do multiplication, division, squaring and square roots in your head in less time than your friends can retrieve their calculators from their bags, they will believe you have a superior intellect.
  I taught a young boy some of the strategies you will learn in before he had entered Grade 1 and he was treated like a prodigy throughout primary and secondary school.
conversations.from: human
conversations.value: Provide five more paragraphs.. End with the sentence ' That is impressive.'.
conversations.from: assistant
conversations.value: We estimate the square root of the first digit pair. The first digit pair is 10. Three times 3 is 9. Four squared would be too high. The first digit of our answer is 3. Therefore, our divisor is 6.
  Three squared is 9. Subtracting 9 from 10 gives us a remainder of 1. Carry the remainder to the next digit. This gives us a new working number of 13.
  Our new working number is 4. We cross multiply. Twenty-one cross multiplied is 4 (2 × 1 = 2, 2 × 2 = 4). Subtract 4 from 4 for an answer of zero.
  Subtract 1 from 1. Our final answer is zero, so 103 041 is a perfect square. The square root is exactly 321.
  Also, with a little practice, you should be able to perform the above calculation entirely in your head. That is impressive.
conversations.from: human
conversations.value: Provide the last four paragraphs.
conversations.from: assistant
conversations.value: Instead of just giving a list of questions for students to answer, make the questions part of your conversation with the class. Work out problems with the class. Encourage the children to bring their own puzzles to class.
  See what you would do to solve a simple problem. (Instead of $47.36, what if it were $100.00, or $1.00?) Simplifying the numbers can often give you the clue you need. Note your method to solve the 'obvious' problem and apply it to your 'complicated' problem.
  Doing something, even if it seems to have nothing to do with the answer, will often give you the clue you need. Maybe you will find your step was an important part of solving the problem.
  This is often underrated. It is a valid strategy that will often give the clue to the correct method.
conversations.from: human
conversations.value: Reverse the sentences.
conversations.from: assistant
conversations.value: It is a valid strategy that will often give the clue to the correct method..
  This is often underrated. Maybe you will find your step was an important part of solving the problem.
  Doing something, even if it seems to have nothing to do with the answer, will often give you the clue you need. Note your method to solve the 'obvious' problem and apply it to your 'complicated' problem.00?) Simplifying the numbers can often give you the clue you need.00, or $1.36, what if it were $100. (Instead of $47.
  See what you would do to solve a simple problem. Encourage the children to bring their own puzzles to class. Work out problems with the class.Instead of just giving a list of questions for students to answer, make the questions part of your conversation with the class