Alphabet Blocks These two blocks are exactly the same, but they are turned in different ways. Each has 6 faces. The faces have the letters: A, B, C, D, E, and F. Look carefully at the blocks. What letter is on the opposite face of the letter D? How do you know?! Cathy Fillmore Hoyt 2006 MCC-4001
Bouncing Bubblegum In a tall skyscraper, Professor Chew is telling reporters about his new discovery. He has invented chewing gum so bouncy that when you drop it, it always bounces to exactly one-half the height from which it was dropped. If you drop it from 100 feet, it bounces up 50. If you drop it from 6 inches, it bounces up 3. To show off his invention, Professor Chew spit his gum out of a window that was 256 feet from the street below. Assume the gum doesn t get stuck on anything. How high will the gum bounce on its tenth bounce?! Cathy Fillmore Hoyt 2006 MCC-4004
Candle Math Here are 4 candles. Each candle takes a different amount of time to burn completely. The time is shown on each candle. Lily wants to light all four candles so that they will all burn out at exactly the same time. She wants them to burn out at midnight. At exactly what time should she light each candle? Cathy Fillmore Hoyt 2007 MCC-4017
Dinosaur Tracks A paleontologist found the tracks of a large dinosaur and a small dinosaur. The dinosaurs were running together. The scientist noticed that for every 3 steps the large dinosaur took, the small dinosaur had to take 5 steps to keep up. The paleontologist found 18 large dinosaur footprints. How many steps did the small dinosaur take to run the same distance?! Cathy Fillmore Hoyt 2006 MCC-4002
Emma s Birthday Today is Emma s birthday. Emma s mother is four times as old as Emma is today. In four years, Emma s mother will be three times as old as Emma. How old is Emma today? Cathy Fillmore Hoyt 2007 MCC-4015
Magic Square Each of the numbers from 1 through 16 must appear once in this magic square. When you put the numbers in the right place, every column, row, and diagonal will add up to 34. Some numbers have been put in the square for you. Where do the rest of the numbers go? Cathy Fillmore Hoyt 2006 MCC-4009
Maria s Cookies Maria baked cookies to sell. She put the cookies in 48 boxes. She paid $3 for the ingredients to make the cookies in each box. On Monday, Maria put a $5 price tag on each box and sold one-half of the boxes. On Tuesday, Maria changed the price tag on each remaining box to $4. She sold one-half of those. On Wednesday, Maria changed the price tag on the boxes that were left to $3. She sold one-third of those boxes. On Thursday, she changed each price tag to $2. She sold all the boxes that were left. On Friday, Maria went to the bank. She put all of the money that she had made into the bank. How much money did Maria put in the bank? $ $ $ $ Cathy Fillmore Hoyt 2006 MCC-4011
The Marvelous Magic Company Gnick the Gnome works at the Marvelous Magic Company. He makes magic wands for every occasion. Each wand comes in a case which measures 2 inches by 4 inches by 8 inches. Gagme the Great, a very powerful wizard, ordered 12 Wands of Mischief. Gnick needs to find a shipping box to send the wands. Gnick wants to find a box that will hold the wands and their cases with no extra space. What are the measurements of the box he needs? The MarvelouS Magic Company Cathy Fillmore Hoyt 2006 MCC-4010
More Trouble With Pigs A farmer has 5 pigs. He has one large pig pen in the shape of a rectangle. The measurements of the large pen are shown below. He has 4 pieces of fencing. Each piece is 10 meters long. How could the farmer put the fencing in the rectangle so that each pig will have its own pig pen? (Hint: The pens don t have to be the same size.) 12 meters Extra piece of fencing. There are 4 of these. 16 meters 10 meters Pig. There are 5 of these. Cathy Fillmore Hoyt 2007 MCC-4016
Paper Folding The large rectangle below is made from 8 smaller rectangles. The rectangles have letters from A to H. How could you fold the large rectangle so that the small rectangles lie on top of one another and are in alphabetical order? Write the directions in words. C D B G F E A H Cathy Fillmore Hoyt 2006 MCC-4014
Six Coins Ty has exactly six American coins in his pocket. The total of the coins is $1.15. Ty is going to give you some clues. Your job is to figure out exactly which coins are in Ty s pocket. Ty s Clues: Even if I use only a few of the coins, there are many amounts that I can t make. "# I can t make exactly $1.00. "# I can t make exactly 50. "# I can t make exactly 25. "# I can t make exactly 10. "# I can t make exactly 5. What six coins does Ty have in his pocket?! Cathy Fillmore Hoyt 2006 MCC-4005
The Smart Guards A king was afraid that a thief would sneak into his room at night and steal his crown, so he built a special bedroom with eight guard rooms all around. Then the king hired 24 guards. He put 3 in each room. Now I am completely safe, the king said. There are 9 guards on the north side of my room, 9 guards on the east, 9 guards on the west, and 9 guards on the south. Below you can see a diagram of the rooms. The king told the guards, Have all the fun you want, but remember, there must always be exactly 9 guards on each side of the building. The guards thought about the king s instruction. That night they invited 8 of their friends to visit. They dressed their friends in guard uniforms. 3 Guards 3 Guards 3 Guards 3 Guards King s Bedroom 3 Guards 3 Guards 3 Guards 3 Guards Before the king went to bed, he counted the guards on each side. He saw 9 guards on the north, 9 on the south, 9 on the east, and 9 on the west. My men must be doing a good job, he thought, and he went to bed. He didn t notice the extra men. What clever arrangement did the guards use to fool the king? Cathy Fillmore Hoyt 2006 MCC-4012
The Cardboard Cube Company For half a century, the Cardboard Cube Company made its cubes by folding this shape. Then Cathy came along. There are a lot of other shapes that can make a cube, she pointed out. She sketched out another example. In fact, besides the two shown on this page, Cathy explained, there are nine more shapes made from six squares that can be folded to make cubes. The company president was excited. She wanted to be on the cutting edge of cardboard cutting. Let s do it! she cried. Can you do it? Find all nine cube-making shapes. Cathy Fillmore Hoyt 2006 MCC-4006
The Cube Puzzle The three drawings below are of the same cube. Each drawing shows a different way of looking at the cube. Suppose you could unfold the cube to make the pattern below. Draw the remaining 4 faces of the cube where they belong.! Cathy Fillmore Hoyt 2006 MCC-4003
The Odd Pigs A farmer has 15 pigs. He has enough materals to build 6 pig pens. Now there is a new Farm Association rule. The farmer has to use all 6 of the pig pens, AND he has to put an odd number of pigs in each pen. How can the farmer fit the pigs in the pens? Cathy Fillmore Hoyt 2006 MCC-4008
The Painters Dilemma Twenty painters agree to paint a school. They tell the principal that it will take 20 hours if they all work at the same time. But now they ve got a problem. 15 of the painters are very sick. They won t be able to work on this job at all. How many hours will it take the 5 painters who are left to paint the school if they all work at the same time? Hint: How many hours would it take one person to do the job? Cathy Fillmore Hoyt 2006 MCC-4007
qüêéé=táëüéë= On Friday s math test, Jim once again got a bad grade. I ve got to get some help, Jim thought. So he went to visit a wizard he knew. I need help with my math, Jim told the wizard. Okay, I ll do what I can, the wizard said. You can have three wishes. Wow! Let s see, Jim thought hard. I wish for a magic potion of Math Smarts. Done! said the wizard. And he waved his wand, and suddenly there were 8 potions on a table. One of these is the Math potion. The rest are poison. But don t let that stop you. Go ahead and drink one. Hmm I ll just make another wish. I wish I knew how the math potion is different from the others, said Jim. Fair enough. That s your second wish. The poison potions all weigh the same. The math potion weighs more, explained the wizard. Then Jim made his third wish. I wish I had a balance scale to weigh the potions. Here s a balance scale, said the wizard, and here s the catch. The balance scale is mine and I m not good at sharing. I ll let you use it two times and that s all. Well, it turned out that Jim knew more about math than he thought because he used the balance scale twice, found the math potion, and lived mathematically ever after. How did he do it? =`~íüó=cáääãçêé=eçóí=ommt= j``jqmor=