A Mathematical Medley
Activities for the CMS Regional Math Camp
Dalhousie University, July 9th, 2004
Richard Hoshino
INSTRUCTIONS:
– Get into groups of three. Once you have formed your group, pick a fun “Group Name”.
– You will visit seven different stations. You will have ten minutes to complete the activity at your station. Your team will receive up to 5 points for each activity.
– If your group has finished its activity early, then quietly go to the middle of the room and work on the “Sesquipedalian Expressions”. These are fun!
– The group with the most total points at the end of the session wins a special prize.
STATION #1
Missing Letters
You will be given ten clues, each of which will have some words with missing letters. Your job is to figure out what those missing letters are, and decode each of the clues.
For example,
“26 L of the A” is 26 Letters of the Alphabet
“7 D of the W” is 7 Days of the Week
“18 H on a G C” is 18 Holes on a Golf Course
Good luck!
When time is up, you will submit the Official Answer Sheet.
SCORING SYSTEM:
All 10 correct – 5 points
8 to 9 correct – 4 points
6 to 7 correct – 3 points
4 to 5 correct – 2 points
1 to 3 correct – 1 point
None correct – 0 points
STATION #1
OFFICIAL ANSWER SHEET
Group Name: ______
90 D in a R A: ______
7 W of the W: ______
29 D in F of a L Y: ______
54 C in a D (with the J): ______
9 P in the S S: ______
88 K on a P: ______
10 P and 2 T in C: ______
66 B in the B: ______
200 D for P G in M: ______
23 P of C in the H B: ______
STATION #2
The 9999 Game
Using each of the digits 9, 9, 9, 9, and any of the rules of arithmetic, try to form each of the numbers from 1 to 20.
For example, you can create the numbers 80 and 81 as follows:
9 ´ 9 – (9 ¸ 9) = 80.
99 – 9 – 9 = 81.
In this activity, you will try to create all the numbers from 1 through 20.
You may use any of the basic operations (+, -, ´, ¸), and to make things interesting, I’ll also let you use square root operation. Try to come up with as many numbers as you can. When time is up, you will submit the Official Answer Sheet.
SCORING SYSTEM:
20 numbers – 5 points
15 to 19 numbers – 4 points
11 to 14 numbers – 3 points
6 to 10 numbers – 2 points
1 to 5 numbers – 1 point
No numbers – 0 points
STATION #2
OFFICIAL ANSWER SHEET
Group Name: ______
1 = 11 =
2 = 12 =
3 = 13 =
4 = 14 =
5 = 15 =
6 = 16 =
7 = 17 =
8 = 18 =
9 = 19 =
10 = 20 =
STATION #3
Contest Problems
Here are various problems from old math contests. In this station, you will try to solve as many problems as possible. Only the final answer is required. Teamwork will be crucial for success.
When time is up, you will submit the Official Answer Sheet, with your completed answers.
The scoring is simple: one point for each correct answer.
STATION #3
OFFICIAL ANSWER SHEET
Group Name: ______
Problem 1: ______
Problem 2: ______
Problem 3: ______
Problem 4: ______
Problem 5: ______STATION #4
A Murder Mystery
Each of you will take a separate envelope, with several pieces of paper in it. They are clues to a murder mystery.
As a team, you will attempt to piece together the details of the crime. However, you may not show the clues in your envelope to anyone else – you may read them but you may not show them. Thus, teamwork is crucial.
Also, you will not be allowed to use a paper or a pencil until the last five minutes of the activity. Since other groups will be using the same clue sheets you are, please do not write on them.
You will submit a sheet, explaining the crime. Points will be awarded for accuracy and detail. A completely accurate, well-detailed description will earn your group 5 points, while a completely inaccurate description will earn you no points.
Before you move to the next station, please return your clues to your envelope, so that the next group can use them.
1. When he was discovered dead, Mr. Kelley had a bullet hole in his thigh and a knife wound in his back.
2. Mr. Jones shot an intruder in his apartment building at 12:00 midnight.
3. The elevator operator reported to the police that he saw Mr. Kelley at 12:15 A.M.
4. The bullet that was taken from Mr. Kelley’s thigh matched the gun owned by Mr. Jones.
5. Only one bullet had been fired from Mr. Jones’ gun.
6. When the elevator man saw Mr. Kelley, Mr. Kelley was bleeding slightly, but he did not seem to be badly hurt.
7. Mr. Kelley had destroyed Mr. Jones’ business by stealing all his customers.
8. A knife with Mr. Kelley’s blood on it was found in Miss Smith’s yard.
9. A knife found in Miss Smith’s yard had Mr. Scott’s fingerprints on it.
10. The elevator man saw Mr. Kelley’s wife go to Mr. Scott’s apartment at 11:30 a.m.
11. The elevator man saw Mr. Kelley’s wife go to Mr. Scott’s apartment at 11:30 p.m.
12. Mr. Kelley’s body was found in the park.
13. Mr. Kelley’s body was found at 1:30 a.m.
14. Mr. Kelley had been dead for one hour when his body was found, according to a medical expert working for the police.
15. The elevator man saw Mr. Kelley go to Mr. Scott’s apartment at 12:25 a.m.
16. It was obvious from the condition of Mr. Kelley’s body that it had been dragged a long way.
17. Miss Smith saw Mr. Kelley go to Mr. Jones’ apartment at 11:55 p.m.
18. Mr. Kelley’s wife disappeared after the murder.
19. Police were unable to locate Mr. Scott after the murder.
20. When the police tried to locate Mr. Jones after the murder, they discovered that he had disappeared.
21. The elevator man said that Miss Smith was in the lobby of the apartment building when he went off duty.
22. Miss Smith often followed Mr. Kelley.
23. Mr. Jones told Mr. Kelley that he was going to kill him.
24. Miss Smith said that no one left the apartment building between 12:25 and 12:45 a.m.
25. Mr. Kelley’s bloodstains were found in Mr. Scott’s car.
26. Mr. Kelley’s bloodstains were found in the hall outside Mr. Jones’ apartment.
STATION #4
OFFICIAL ANSWER SHEET
Group Name: ______
Explain what happened to Mr. Kelley that night. Give as many details as possible (e.g. chronological order of each of the activities, the actual murderer, and how his body ended up in the park).STATION #5
Human Calculator Tricks
In this section, you will read a handout on human calculator tricks, detailing how you too, can be a “mathemagician”.
Hint: the article is split into three sections. To save time, each of you should read one section, and answer the questions pertaining to your section. There likely won’t be enough time for all of you to reach each section individually and answer the questions.
You may keep the handout.
For this activity, you may not use a pencil/pen to do scratch work. Everything must be done in your beautiful mind.
You will only use the pencil/pen to fill out your answers on the Official Answer Sheet.
There are five questions on the Official Answer Sheet. You will get one point for each correct answer.
If you are caught with a calculator or are caught checking your answer using your pencil/pen, then your team will get 0 points.
STATION #5
OFFICIAL ANSWER SHEET
Group Name: ______
Answer the following questions:
(Remember: no pencil/pen for checking, and certainly no calculators are allowed!)
68 ´ 62 = ______
452 = ______
522 = ______
Cube root of 12167 = ______
Cube root of 778688 = ______
STATION #6
The Bridge Problem
The pop band “U2” must all cross a bridge to get to a concert. All four men begin on the same side of the bridge. They must get across to the other side. It is dark and it is impossible to see without a flashlight.
There is one flashlight. Since the bridge is really narrow, only two people can cross at one time. When someone is crossing (either by himself or with someone else), they must have the flashlight with them. The flashlight must be walked back and forth, it cannot be thrown, etc. Each band member walks at a different speed. A pair must walk together at the rate of the slower man's pace:
Bono – 1 minute to cross Edge – 2 minutes to cross
Adam – 5 minutes to cross Larry – 10 minutes to cross
How fast can all four of them get across? For example, here is a solution that takes 36 minutes:
Edge + Larry go across 10 minutes
Larry comes back 10 minutes
Adam + Bono go across 5 minutes
Bono comes back 1 minutes
Bono + Larry go across 10 minutes
Answer the following questions.
STATION #6
OFFICIAL ANSWER SHEET
Group Name: ______
Question 1: (2 points)
Explain how all four members can cross the bridge in 19 minutes.
Question 2: (3 points)
Get all four members to cross the bridge in 17 minutes.
(Yes, it can be done – there are no tricks involved!)
STATION #7
Paper Cutting
In this activity, you will take one piece of construction paper, and attempt to create a circle big enough that all three of you can fit through.
Your finished product must not have any loose ends that need to be taped or stapled together – it must be one big circle. Two examples are placed on the table. But both of these attempts are quite poor: can you do better?
There are several pairs of scissors on the table, as well as many pieces of (white) scrap paper that you can practice with. You will only be given one piece of construction paper – so make sure you do this very carefully! (You don’t get a second chance).
There is no official answer sheet in this activity – you just call one of the judges when your circle is complete, and s/he will give you points based on the following system:
5 points – all three of you can fit through the circle
4 points – two of you can fit through the circle
3 points – one of you can fit through the circle
2 points – one of you can stand in the circle
1 point – one of you can get your hand through the circle
0 points – the circle breaksSTATION #8
Extra Activities
For groups that are finished, here is a fun activity to do while you are waiting:
Sesquipedalian Expressions:
These are expressions that use unnecessarily big words. Your task is to translate each of these expressions into “common English”, i.e., cliches and phrases that you know.
For example,
“It is fruitless to attempt to indoctrinate a superannuated canine with innovative maneuvers”
is better known as:
“You can't teach an old dog new tricks”.
ENJOY!
Sesquipedalian Expressions
1. Pulchritude possesses solely cutaneous profundity.
2. Scintillate, scintillate, minute asteroid.
3. Members of an avian species of identical plumage congregate.
4. Surveillance should precede saltation.
5. It is fruitless to become lachrymose over precipitately departed lactose fluid.
6. Freedom from encrustation of grime is contiguous to divinity.
7. The stylus is more potent than the claymore.
8. Eschew the implement of correction and vitiate the scion.
9. The temperature of aqueous content of an unremittingly ogled saucepan does not reach 212 fahrenheit.
10. Neophyte's serendipity.
11. Male cadavers are incapable of yielding any testimony.
12. Individuals who make their abode in vitreous edifices would be advised to refrain from catapulting petrous projectiles.
13. All articles that coruscate with resplendence are not truly auriferous.
14. Where there are visible vapors having their province in ignited carbonaceous material there is conflagration.
15. Sorting on the part of mendicants must be interdicted.
16. A plethora of individuals with expertise in culinary techniques dilapidates the potable concoction produced by steeping comestibles.
17. Exclusive dedication to necessary chores without interludes of hedonistic diversion renders Jack a hebephrenic fellow.
18. A revolving lathic conglomerate accumulates no diminutive glaucous syrophytic plants.
19. The person with the ultimate cachination possesses, thereby, the optimal cachination.
20. Missiles of ligneous or petrous consistency have the potential of fracturing my osseous structure but appellations will eternally be benign.