Session One of Mathematical Flow. Page 2

Session One of Mathematical Flow. P a g e | 1 Flow . http://2015byod.wikispaces.com/Flow+Course Session 1. Pick any integer and multiply it by 5. Use the same integer and cube it. Add your two results together. Compare the result with your friends’ results. What do you notice? Can you explain what you have noticed? Will it always happen?

I have 9 dominoes. Can you arrange them so that by pushing one of them I can get 1,2,3,4,6,7,8 or 9 falling down? But not 5?

Mathex Question 2014 Year 10. Question 16. 89 72 14 4. 89 has a PERSISTENCE NUMBER of 3 [3 steps to reduce to a single digit]. Find the number between 70 and 79 with a persistence digit of 4. Session One of Mathematical Flow. P a g e | 2 Write out the sequence of 4 steps. More like this: http://www.funtrivia.com/playquiz/quiz36406029ad228.html

The answer is 2. What is the question? How many numbers can we make with 4 4’s? https://www.mathsisfun.com/puzzles/four-fours.html

The Wolf, Goat, and Cabbage A man has to take a wolf, a goat, and some cabbage across a river. His rowboat has enough room for the man plus either the wolf or the goat or the cabbage. If he takes the cabbage with him, the wolf will eat the goat. If he takes the wolf, the goat will eat the cabbage. Only when the man is present are the goat and the cabbage safe from their enemies. All the same, the man carries wolf, goat, and cabbage across the river. How? Puzzle provided by Kordemsky: The Moscow Puzzles (Dover) http://illuminations.nctm.org/BrainTeasers.aspx?id=4992 http://en.wikipedia.org/wiki/Cheryl%27s_Birthday Albert and Bernard just became friends with Cheryl, and they want to know when her birthday is. Cheryl gives them a list of 10 possible dates, shown in tabular format: May 15 16 19 June 17 18 July 14 16 Augus 14 15 17 t Cheryl then tells Albert and Bernard separately the month and the day of her birthday respectively. Albert: I don't know when Cheryl's birthday is, but I know that Bernard doesn't know too. Bernard: At first I don't know when Cheryl's birthday is, but I know now. Albert: Then I also know when Cheryl's birthday is. So when is Cheryl's birthday? http://www.mathsisfun.com/puzzles/great-picnic-puzzle.html Session One of Mathematical Flow. P a g e | 3 When they started off on the great annual picnic every wagon in town was pressed into service, each one carrying the same number of people. Half way to the picnic ground ten wagons broke down, so it was necessary for each of the remaining wagons to carry one more person. When they started for home it was discovered that fifteen more wagons were out of commission, so on the return trip there were three persons more in each wagon than when they started out in the morning. Now who can tell how many people attended the great annual picnic? Marvellous Matrix: http://nrich.maths.org/2064 Circle any number in the matrix, for example, 608 as below. Draw a line through all the squares that lie in the same row and column as your selected number. Circle another number which has not got a line through it, for example,343 and again rule out all squares in the same row and column. Repeat for a third time. Then circle the remaining number which has not got a line through it.

Add all the circled numbers together. Note your answer. Try again with a different starting number. What do you notice? 540 750 300 15 640 850 400 115 690 900 450 165 700 910 460 175

355 413 276 628 400 458 321 673 Session One of Mathematical Flow. P a g e | 4 465 523 386 738 543 601 464 816 Can you make another one, adding to a number of your choice?

“You are given four separate pieces of chain that are each three links in length. It costs 2¢ to open a link and 3¢ to close a link. All links are closed at the beginning of the problem. Your goal is to join all 12 links of chain into a single circle at a cost of no more than 15¢.”

http://peace.saumag.edu/faculty/kardas/courses/HonSem/criticalthinking.html

Meier’s String Problem: Your feet can not leave the floor. Session One of Mathematical Flow. P a g e | 5 You cannot reach both pieces of string at the same time. How do you tie them together?