EP3398 Mathological Liar Grade 5 Object of the Game In each round, players are given a case to solve. There are four suspects in each case. One or more of the suspects is guilty. Each player reads his or her suspect’s alibi. If the math or reasoning in the suspect’s alibi is correct, he or she is innocent. If the math or reasoning is incorrect, that suspect is lying and is guilty of the crime. Before You Play Do not shuffle the cards. Each round consists of four cards. When you take a round out of the box to play, make sure the case numbers on the cards match. When you are done with a round, place the used cards in a group at the back of the box. Before you begin, decide how many rounds you will play, or set a time or point limit for the game. Then, gather scratch paper, a pencil, and, if needed, a calculator for each player. Decide who will be the scorekeeper and keeper of the Answer Key. Directions (2 to 4 players) 1. Hand out a Case Card to each player. There are four cards for each case, each with a different alibi on the back. (If there are only two players, give each player two Case Cards.) 2. Have one player read the case on the back of the card out loud to the group. 3. Have each player read his or her suspect’s alibi silently. Each player will then write down whether or not his or her suspect is guilty or innocent. 4. One by one, each player reads his or her alibi out loud to the group. The player must then state whether the suspect is guilty or innocent, and why. The person with the Answer Key reveals the answers. Each player receives one point for correctly stating whether his or her suspect is innocent or guilty. If the suspect is guilty, the player can earn an extra point for correctly giving the reason why the suspect is guilty (why the math is incorrect). The scorekeeper writes down each player’s score. 5. The first person to reach the point goal, or the person who has earned the most points at the end of the set number of rounds or at the set time limit, wins the game! Answer Key Case #1: Miss Pincher did it. She added the numbers instead of subtracting. The correct answer should have been 13 balls of yarn. 20 – 7 = 13. Case #2: George is the Sailboat Spy. He said that 680 – 423 = 157. That’s not correct; it equals 257. Case #3: Scoop did it. He said 18 > 14. That’s wrong. 18 < 14. 30 = .03, but 30 = .3. Case #4: Betsy is guilty. She said 100 100 Case #5: Caleb and Leila are guilty. Caleb said the 8 in 398.2 stands for tens. It stands for ones. Leila said the 7 in 780.9 stands for thousands. It stands for hundreds. Case #6: Penny messed up the files. The number 10.99 does fall between the numbers 10 and 20. Case #7: Rick and Regina did it. He said 11 × 10 = 100, but 11 × 10 = 110. She said 12 × 6 = 62, but 12 × 6 = 72. Case #8: Olivia did it. She said 8 × 12 = 94, but 8 × 12 = 96. Case #9: Chef Patrick did it. The chef said 124 ÷ 31 = 8, but 124 ÷ 31 = 4. Case #10: Jenna did it. 285 ÷ 3 = 95, not 92. Case #11: Gabe and Vanessa did it together. Gabe said .3 = 33%, but .3 = 30%. Vanessa said .5 = 20%, but .5 = 50%. Case #12: Maddie did it. She said 14 = 40%, but 14 = 25%. Case #13: Ebony and Frank did it. Ebony said that 7 7 1 1 20 = 70%, but 20 = 35%. Frank said 20 = 20%, but 20 = 5%. Alternate Play Have each player read his or her suspect’s alibi out loud to the group. As a group, players determine whether or not the suspect on each card is guilty or innocent, and why. The person with the Answer Key reveals the answer. Each player whose suspect is innocent earns a point. The player with the most points at the end of the game wins! Individual, Small-Group, and Whole-Class Practice Put each four-card set of Case Cards in an envelope and place in a math center. Challenge students to individually work through the alibis on each case to determine who is the guilty party. Provide an Answer Key for self-checking. Encourage students to work through the cards in pairs or small groups and discuss their answers with each other. For a whole-class activity, project the cards on a screen to jumpstart math lessons. Read the case aloud, and then project the four alibis at the front of the room. As a class, have students help determine who is the culprit. Case #14: Nate, Larry, and Donna did it. Nate: If 12 × 5 = 60, then 60 ÷ 12 = 5. Larry: If 32 ÷ 8 = 4, then 8 × 4 = 32. Donna: If 70 ÷ 10 = 7, then 10 × 7 = 70. Case #15: Glory’s and Footloose’s owners did it. Glory’s Owner said there were about 600 people in the audience, but her estimate should have been 20 × 20 = about 400. Footloose’s Owner said they earned about $4,000, but his estimate should have been 320 × 10 = about $3,200. Case #16: Olivia and Rob are doing it. Olivia said each student would get about 10 pretzels, but 27 is about 25 and 200 divided by 25 would be 8. Rob said there needs to be a little more than 10 surprises a day when he should have said 7. You would round up 49 to 50 and 349 to 350. Then, divide 350 by 50 to get 7. Case #17: Luke and Kat jumbled the jigsaws. Kat said a quadrilateral must have equal sides and angles. A quadrilateral’s sides do not need to be equal. Luke said a circle is an irregular polygon. A circle has no straight sides or angles, so it is not a regular or an irregular polygon. Case #18: Wes didn’t go. Straws, shoe laces, and birthday candles all have beginning and end points. They are line segments. Case #19: Charlie and Glenn did it. Charlie called the path a ray, but a path between two points is called a line segment. Glenn said the parallel roads intersected. Parallel roads don’t intersect. Case #20: John did it. A slice of pie is a convex shape. A pie with a slice cut out of it is a concave shape. Case #21: Rita did it. She said isosceles triangles have rotational symmetry in all positions. You would have to turn one 360° to make it look like its partner. Case #22: Coach Carter stole the crown. He did not apply the law of distributivity correctly. 5 (16 + 9 + 10) = 5(16) + 5(9) + 5(10) = 175. Case #23: Cindy did it. The pattern would continue as aa bb cc, not as abc abc. Case #24: Chris, Julie, and Yana are the tricksters. Chris said Mr. Roberts belonged at the newsstand, but Mr. Roberts only goes to the newsstand every other day, and he went on Friday. Julie said he should have gone to the cleaners, but he only goes to the cleaners one day a week. Yana said he had to go to the market, but he only goes to the market one day a week. Case #25: Kevin rigged the race. Adding 100 three- or four-digit numbers quickly in your head would be too difficult, especially without estimating. The best way to do it would be to use a calculator. Case #26: Mr. DeMille and Mr. Meyer did it. Mr. DeMille should be able to do the math in his head. Mr. Meyer is working with very large numbers. It would be better to work with a calculator than a pencil and paper. Case #27: Mr. Rogers did it. He said he lived 30 yards, or 1 mile, from Mr. Fells, but 1 mile = 1,760 yards. Case #28: Holly did it. She said 30 mm was equal to 1 m, but 1,000 mm equals 1 m. Case #29: Lisa took the popcorn. She said 256 oz was not equal to 16 lbs, but it is. Case #30: Griffin, Joanie, and Walter did it. Griffin said 1 kg = 1,000 mg, but 1 kg = 1,000,000 mg. Joanie said 100 mg = 1 g, but 1 g = 1,000 mg. Walter said 1,000 kg = 100 g, but 1,000 kg = 1,000,000 g. Case #31: They all did it. Justin’s 1 pint should = 16 oz; Jerry’s 3 gallons should = 12 qts; James’s 16 cups should = 4 quarts; Jason’s 1 gallon should = 128 oz. Case #32: Susannah did it. She said 8 pints = 2 quarts, but really 8 pints = 4 quarts. Case #33: Grace did it. A cup would not be a large enough measure. Case #34: Stella did it. The formula to find the area of a parallelogram is base × height. 20 x 15 =300. Case #35: Kirk and Samantha did it. Kirk said the areas were the same. Actually the area of the square was 1,296 sq. in., while the area of the rectangle was only 720 sq. in. Samantha said both shapes had the same area. Actually the area of the square was 16 sq. ft., and the area of the rectangle was only 15 sq. ft. Case #36: Frank and Shaila are the budget busters. Frank should have estimated the cost of the print tablecloths at $4 each and the red one at $3. If he had, he would have figured the cost to be $11. Shaila could estimate the balloons at $2 and $1, but she would know they were actually a little more than that. Then, she would estimate the balloons to be more than her $15 budget. Case #37: Mary is the bad bidder. She said her bid of $320 was less than what the cups are worth. To come to that bid, she would have rounded the value of each cup up to $40. Since she rounded up, her bid would be a little higher than what they are worth, not a little less. Case #38: Lori did it. Six dimes, 2 nickels, and 1 penny only add up to 71¢, not 81¢. Case #39: Bunny did it. The bag should have weighed 24 ounces. She had only 22 ounces, which was 2 ounces too few. She should have taken out 4 ounces, not 6. Case #40: Serena and Zach made the too-short tunnels. Serena added 3 ½ feet, or 42 in., to 30 in. That would have made a perfect 6-foot-long tunnel without cutting any off. Zach’s equaled 70 in. Six feet equals 72 in., so Zach’s tunnel was too short even before he cut some off. Case #41: Maurice took the time. They would need 3 days and 18 hours, not 4 days and 18 hours, as he said. Case #42: Paris is the guilty party. If you add 8 hours to 3 a.m., you arrive at 11 a.m. If you subtract 3 hours for the time difference, you end up at 8 a.m., the customer’s time. Paris was off by an hour. Case #43: Eddie and Jon did it. Eddie said -12°F + 18° = -30°F, but -12°F + 18° = 6°F. Jon said 30°F – 35° = -65°F, but 30°F – 35° = -5°F. Case #44: Al is playing tricks. He said 6 + (-12) + 18 = 0, but 6 + (-12) + 18 = 12. Case #45: Fred did it. He said someone had a better chance entering the kids’ category. However, in the kids’ category, a person’s chances are 1 in 93. In the adults’ group, a person’s chances are 1 in 47. Case #46: Ann did it. She told her buddy the X stood for the number of people at the party. However, the number 50 represents the number of people. The X represents the number of carrot sticks each person will get. Case #47: Vinnie and Raven did it. Vinnie claims he predicted using the number of colors in the machine. That wouldn’t work. If there were 10 yellow gumballs and 190 other gumballs, it wouldn’t matter what color the others were. He would have a 1 in 20 chance. Raven said she made her prediction based on the number of yellows in the machines, but she also would have to consider the total number of gumballs. Case #48: Hannah dyed the poodle purple. There are only 8 colors, so there is only 18 of a chance of someone buying purple. Case #49: Rhea and Jill tinkered with the tugboats. Rhea said she was looking for multiples of 9 and needed the number 98. The number 98 is not a multiple of 9. Jill said 21, 96, and 51 were related, but not 81. However, 21, 96, 51, and 81 are all multiples of 3. Case #50: Ashton did it. The number 17 is not a factor of 24 or 48. EP3398 Mathological Liar, Gr. 5 © Highsmith LLC