The Lady or the Lions
Grade(s): 8
Strand(s): Data Management & Probability

Problem:
The King of a distant land arranged a marriage for his only daughter to a prince from a nearby kingdom. However, the Princess had already fallen in love with a handsome, clever, but unfortunately poor peasant. The king, upon learning of the Princess’s relationship with the peasant, ordered the suitor to be thrown in the lion’s den. His daughter pleaded with the king for mercy and the king offered a compromise. Her suitor could walk through a maze, with each path leading to one of two rooms. In one room there would be the Princess, but in the other would be a pride of very hungry lions. If the peasant entered the room with the Princess, they would be allowed to marry. If the peasant entered the room with the lions, well, that would be that. (Follow the link below for the remainder of this question and the answer). http://nrich.maths.org/591/index Printable Page Source:http://nrich.maths.org Posted by: Mark Ross, Norseman JMS A Dicey Situation Grade(s): 7 & 8 Strand(s): Data Management & Probability

Problem:
Jamie made up a new dice game. Two players each roll an ordinary six-sided die. Of the two numbers shown, the smaller number is subtracted from the larger. Scoring:- If the difference is 0, 1, or 2, player A gets 1 point.- If the difference is 3, 4, or 5, player B gets 1 point. The game ends after 12 rounds. The player with the most points wins the game. A) If you are given the choice of being Player A or Player B, which would you pick, assuming you want to win? (Remember to explain all the steps you use in making your decision.) B) Describe another way of scoring that is fair for this game of differences. Explain how you know it is fair. What to look for:
Students should be given the opportunity to play the game with a partner. Level four students might make the connection immediately as to who is more likely to win, but they can still be expected to calculate the individual probabilities.
.pdf download link here

Source: Intermediate Math ABQ Package – Summer 2009 (Compiled by Trevor Brown) Submitted by: Mark Ross, Norseman JMS The Monty Hall Problem Grade(s): 8, 7 and 6 Strand(s): Data Management & Probability, Number Sense (fractions)

Problem:
You are on a game show and you are presented with a choice of 3 doors. Behind one is a luxury car, and behind the two others are nothing. The game show host asks you to pick one of the doors. After you select one, and as part of the game, the host opens an unpicked door which he knows to be empty. You are asked if you would like to keep the door that you chose, or switch your choice to the remaining unopened door. Should you switch? Why or why not? What to look for:
This problem can be examined by using a tree diagram. If computers are available, students may try the link below. It is a Monty Hall Problem simulator that works quite well and keeps track of their choices so that they can work out the probabilities on the go. Links:http://www.grand-illusions.com/simulator/montysim.htm Links:http://www.youtube.com/watch?v=mhlc7peGlGg (an excellent 5 minute video providing a full explanation of the answer).

Source: Intermediate Math ABQ Package – Summer 2009 (Compiled by Trevor Brown) Submitted by: Mark Ross, Norseman JMS Burning Candle Grade(s): 8,7 Strand(s): Data Management & Probability

Problem:
Candle manufacturer companies advertise that their products are better quality and have the longest mean burning times. John decides to select same size candles form three different companies, Bright Candle, Fire Candle and Shiny Candle – and do an experiment with 15 candles in order to test which company has a better product. He recorded the number of minutes that each candle burned. (see .pdf for list of values and remainder of question). What to look for:
This question can be used to prompt a discussion about the most appropriate measure of central tendency (mean, median and mode).

## Probability Fair:

## A project for math, language and visual arts. Students apply their knowledge of probability to create a game.

The Lady or the Lions

Grade(s): 8

Strand(s): Data Management & Probability

Problem:The King of a distant land arranged a marriage for his only daughter to a prince from a nearby kingdom. However, the Princess had already fallen in love with a handsome, clever, but unfortunately poor peasant. The king, upon learning of the Princess’s relationship with the peasant, ordered the suitor to be thrown in the lion’s den. His daughter pleaded with the king for mercy and the king offered a compromise. Her suitor could walk through a maze, with each path leading to one of two rooms. In one room there would be the Princess, but in the other would be a pride of very hungry lions. If the peasant entered the room with the Princess, they would be allowed to marry. If the peasant entered the room with the lions, well, that would be that. (Follow the link below for the remainder of this question and the answer).

http://nrich.maths.org/591/index

Printable Page

Source:http://nrich.maths.orgPosted by:Mark Ross, Norseman JMSA Dicey Situation

Grade(s):7 & 8Strand(s):Data Management & ProbabilityProblem:Jamie made up a new dice game. Two players each roll an ordinary six-sided die. Of the two numbers shown, the smaller number is subtracted from the larger.

Scoring:-If the difference is 0, 1, or 2, player A gets 1 point.- If the difference is 3, 4, or 5, player B gets 1 point. The game ends after 12 rounds. The player with the most points wins the game. A) If you are given the choice of being Player A or Player B, which would you pick, assuming you want to win? (Remember to explain all the steps you use in making your decision.) B) Describe another way of scoring that is fair for this game of differences. Explain how you know it is fair.What to look for:Students should be given the opportunity to play the game with a partner. Level four students might make the connection immediately as to who is more likely to win, but they can still be expected to calculate the individual probabilities.

.pdf download link

hereSource:Intermediate Math ABQ Package – Summer 2009 (Compiled by Trevor Brown)Submitted by:Mark Ross, Norseman JMSThe Monty Hall Problem

Grade(s):8, 7 and 6Strand(s):Data Management & Probability, Number Sense (fractions)Problem:You are on a game show and you are presented with a choice of 3 doors. Behind one is a luxury car, and behind the two others are nothing. The game show host asks you to pick one of the doors. After you select one, and as part of the game, the host opens an unpicked door which he knows to be empty. You are asked if you would like to keep the door that you chose, or switch your choice to the remaining unopened door. Should you switch? Why or why not?

What to look for:This problem can be examined by using a tree diagram. If computers are available, students may try the link below. It is a Monty Hall Problem simulator that works quite well and keeps track of their choices so that they can work out the probabilities on the go.

Links:http://www.grand-illusions.com/simulator/montysim.htmLinks:http://www.youtube.com/watch?v=mhlc7peGlGg (an excellent 5 minute video providing a full explanation of the answer)..pdf download link here

Source:Intermediate Math ABQ Package – Summer 2009 (Compiled by Trevor Brown)Submitted by:Mark Ross, Norseman JMSBurning Candle

Grade(s):8,7Strand(s):Data Management & ProbabilityProblem:Candle manufacturer companies advertise that their products are better quality and have the longest mean burning times. John decides to select same size candles form three different companies, Bright Candle, Fire Candle and Shiny Candle – and do an experiment with 15 candles in order to test which company has a better product. He recorded the number of minutes that each candle burned.

(see .pdf for list of values and remainder of question).What to look for:This question can be used to prompt a discussion about the most appropriate measure of central tendency (mean, median and mode).

.pdf download link here

Source:Intermediate Math ABQ Package – Summer 2009 (Compiled by Trevor Brown)Submitted by:Mark Ross, Norseman JMS