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!
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
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
20 = 70%, but 20 = 35%. Frank said 20 = 20%, but 20 = 5%.
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
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
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
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