Item Description - MC Phi - For the Teachers Please note: any activity that is not completed during class time may be set for homework or undertaken at a later date. MC Phi Rotation Lesson Activity Description: This lesson contains three Multiple Choice units comprised of questions testing the Phi Common Curriculum Elements. The first unit asks students questions based on the diagrams and table provided. In the second unit, students have to interpret the table in order to answer the questions about water levels in Minnesotan lakes. The third unit requires students to work with probability. They are provided with the formula for the probability of a certain outcome and must use this, as well as other information, to answer the questions. Purpose of Activity: This lesson allows students the opportunity to practise the Phi skills required in the multiple choice section of the QCS. CCEs: Calculating with or without calculators (Ф16) Estimating numerical magnitude (Ф17) Substituting in formulae (Ф19) Applying a progression of steps to achieve the required answer (Ф37) Suggested Time Allocation: This rotation lesson is designed to take one hour to complete approximately 20 minutes per unit. Teaching Notes: Students may need calculators to complete this lesson. After students have completed each section, go through the answers thoroughly with them to ensure they understand how to reach the correct answer. Encourage students to volunteer their own answers, and if possible, start a group discussion about different answers.
UNIT ONE Items 1-4 The head weatherman at the Weather Forecast Council (WFC) thinks he has come up with a method that will eliminate any discrepancies in forecasting the weather a week in advance. In order to find out whether it will be sunny, cloudy or raining in exactly one week s time, the weather of the previous three days must be taken into consideration. That is, yesterday, the day before yesterday, and two days before yesterday. This is best demonstrated by the three diagrams below. Day 4 Day three Day three Day 4 Next week Next week Day two = Day two = Day one Day one = = = = = = = = Day two Day one Day three Day 4 Next week = = = = = = = = = = = = = = = = =
Item 1 If it was raining on Monday and Tuesday and sunny on Wednesday, what will the weather be like next Thursday? A sunny. B raining. C overcast. D cloudy. Item 2 If it was cloudy three days ago, what is the probability that it will be cloudy in one week s time? A 22.22%. B 33.33%. C 44.44%. D 55.55%. Item 3 Evie only likes going surfing when it is sunny. Evie knows it has been raining for the past two days, but can t remember what the weather was like three days ago. What is the probability that she will be able to go surfing in a week? A 33.33%. B 44.44%. C 66.66% D 73.33%. Item 4 The information in the table below refers to item 4. What will the weather be like next Friday? This week s weather Monday Tuesday Wednesday Thursday Friday Saturday Sunday A B C D raining sunny raining not predictable
Item 1 If it was raining on Monday and Tuesday and sunny on Wednesday, what will the weather be like next Thursday? A sunny. B raining. C overcast. D cloudy. Item 2 If it was cloudy three days ago, what is the probability that it will be cloudy in one week s time? A 22.22%. B 33.33%. C 44.44%. D 55.55%. Item 3 Evie only likes going surfing when it is sunny. Evie knows it has been raining for the past two days, but can t remember what the weather was like three days ago. What is the probability that she will be able to go surfing in a week? A 33.33%. B 44.44%. C 66.66% D 73.33%. Item 4 The information in the table below refers to item 4. What will the weather be like next Friday? This week s weather Monday Tuesday Wednesday Thursday Friday Saturday Sunday A B C D raining sunny raining not predictable
Marking Scheme Unit One In order to successfully complete this unit, students were required to use the formula, diagrams and table provided and choose the most correct answer. CCEs Present in Unit: 16 Calculating with or without calculators. 17 Estimating numerical magnitude. 19 Substituting in formulae. 37 Applying a progression of steps to achieve the required answer. Unit One Item 1 D. Students simply had to use the diagrams provided to answer this question. Students should have used the diagram beginning with raining and then followed it through ( raining, then sunny ) to find that this combination of days produced a cloudy day in a week s time. Unit One Item 2 A. Students should have used the cloudy diagram to figure out the probability of a cloudy day in a week s time if it was cloudy three days ago. Two of the end results were cloudy, which is 2/9, or 22.22%. Unit One Item 3 C. Students should have used all three diagrams to determine the probability of a sunny day in one week s time if the past two days had been raining. This was a 2/3 chance, which equals 66.66%. Unit One Item 4 C. Students should have started by looking at Friday and the three days preceding it. Then they should have used the diagrams to work out that if it had been cloudy, rainy, rainy over the past three days, it would be raining on the next Friday.
UNIT TWO Items 5-8 The water levels of lakes in Minnesota are measured weekly. Figure 1 displays statistics on the water levels of these lakes at the start of the second week of March 2011 (08/03/2011), including any change in water volume that occurred since the previous measurement (01/03/2011). Lakes Winnibigoshish Bay Bemidji Lake of the Woods 30 24 54 64 23 17 43 58 498,630 223,000 324,170 600,110 385,940 167,120 276,200 530,870 77.40 74.94 85.20 88.46 Note: Item 5-0.98 +1.87 +2.34-1.34 Water height when full* (m) Current water height (m) Water volume when full (ML) Current water volume (ML) Current water volume** (%) Volume change***(%) * Height above max depth when full ** Current water volume as a percentage of water volume when full *** Volume change as a percentage of water volume when full m = metres ML = megalitres What percentage of the full water volume of Lake of the Woods is the equivalent of 7.85% the full volume of Winnibigoshish? A 6.68 C 7.66 B 5.65 D 6.52 Item 6 On the 1 st of March 2011 the volume of Lake Bemidji was approximately equal to A 269,000 ML B 283,000 ML C 290,000 ML D 265,000 ML
Item 7 The combined water of all four lakes on the 8 th of March 2011, as a percentage of the combined max volume of all four lakes is closest to A 80% C 82% B 83% D 79% Item 8 The overall change in volume of the four lakes combined since the 1 st of March 2011, as a percentage of the combined max volume of all four lakes is closest to A -0.07% C 0.09% B -0.06% D 0.08%
UNIT TWO Items 5-8 The water levels of lakes in Minnesota are measured weekly. Figure 1 displays statistics on the water levels of these lakes at the start of the second week of March 2011 (08/03/2011), including any change in water volume that occurred since the previous measurement (01/03/2011). Lakes Winnibigoshish Bay Bemidji Lake of the Woods 30 24 54 64 23 17 43 58 498,630 223,000 324,170 600,110 385,940 167,120 276,200 530,870 77.40 74.94 85.20 88.46 Note: Item 5-0.98 +1.87 +2.34-1.34 Water height when full* (m) Current water height (m) Water volume when full (ML) Current water volume (ML) Current water volume** (%) Volume change***(%) * Height above max depth when full ** Current water volume as a percentage of water volume when full *** Volume change as a percentage of water volume when full m = metres ML = megalitres What percentage of the full water volume of Lake of the Woods is the equivalent of 7.85% the full volume of Winnibigoshish? A 6.68 C 7.66 B 5.65 D 6.52 Item 6 On the 1 st of March 2011 the volume of Lake Bemidji was approximately equal to A 269,000 ML B 283,000 ML C 290,000 ML D 265,000 ML
Item 7 The combined water of all four lakes on the 8 th of March 2011, as a percentage of the combined max volume of all four lakes is closest to A 80% C 82% B 83% D 79% Item 8 The overall change in volume of the four lakes combined since the 1 st of March 2011, as a percentage of the combined max volume of all four lakes is closest to A -0.07% C 0.09% B -0.06% D 0.08%
Marking Scheme Unit Two In order to successfully complete this unit, students were required to use the formula, diagrams and table provided and choose the most correct answer. CCEs Present in Unit: 16 Calculating with or without calculators. 37 Applying a progression of steps to achieve the required answer. Unit Two Item 5 D. Students simply had to calculate what volume of water 7.85% of the max volume of Lake Winnibigoshish was and determine what percentage the max volume of Lake of the Woods this volume equated to. 0.0785 x 498,630 = 39142.455 39142.455 / 600,110 = 0.06522 0.06522 x 100 = 6.52% Unit Two Item 6 A. Students should have calculated what volume of water Lake Bemidji had gained in the since the 1 st of March and subtracted it from the volume reading taken on the 8 th of March. 0.0234 x 324,170 = 7585.578 ML 276,200 7585.578 = 268614.422 ML = 269,000 ML Unit Two Item 7 B. Students should have summed the measurements of volume on the 8 th and then summed the measurements of max volume and used these two values to determine what percentage the volume of the four lakes were with respect to the total volume. 385,940 + 167,120 + 276,200 + 530,870 = 1,360,130 498,630 + 223,000 + 324,170 + 600,110 = 1,645,910 (1,360,130 / 1,645,910) x 100 = 82.64%
Marking Scheme Unit Two Unit Two Item 8 A. Students should have calculated the total change in by converting from percentage form, and then found this as a percentage of the total combined max volume of the four lakes. -0.0098 x 498,630 = -4886.574 0.0187 x 223,000 = 4170.1 0.0234 x 324,170 = 7585.578-0.0134 x 600,110 = -8041.474 4170.1 + 7585.578 (4886.574 + 8041.474) = -1172.37 Max volume of combined lakes = 1,645,910 (-1172.36 / 1,645,910) x 100= -0.0712%
UNIT THREE Items 9-11 This unit deals with probability using a deck of cards. The probability of a particular outcome is equal to There are 52 cards in a deck. These cards are divided up between 4 different suits; hearts, diamonds, spades, and clubs. Hearts and diamonds are red, and spades and clubs are black. Each suit contains 13 cards; 9 numbered cards, 2 through 10 and four picture cards; the Jack, the Queen, the King, and the Ace which represents the number 1. Item 9 The percentage chance that the first card drawn from the deck is a heart or an 8 is closest to A 31% C 32% B 33% D 30% number of favourable outcomes number of possible outcomes At the beginning of a round of poker (5 card draw variant) all players are dealt 5 cards. They can then choose to discard as many cards as they want in return for the same amount of cards. Cards discarded are not shuffled back into the deck. Stan, Win and Alex have decided to play a game of poker.
Item 10 At the beginning of the round all three players have been dealt 5 cards. One of the players holds a Jack of Hearts, King of Diamonds, Queen of Diamonds, 3 of Diamonds and Ace of clubs. The probability that another player holds the Ace of Diamonds is closest to A 0.242 C 0.213 B 0.270 D 0.263 Item 11 Assume that after every player has now been dealt five cards and only Stan holds a spade. Stan s hand contains 4 spades and a diamond. Stan discards 1 card and is dealt another one. The probability that the card he is dealt is a spade is closest to A 0.243 C 0.256 B 0.245 D 0.254
UNIT THREE Items 9-11 This unit deals with probability using a deck of cards. The probability of a particular outcome is equal to There are 52 cards in a deck. These cards are divided up between 4 different suits; hearts, diamonds, spades, and clubs. Hearts and diamonds are red, and spades and clubs are black. Each suit contains 13 cards; 9 numbered cards, 2 through 10 and four picture cards; the Jack, the Queen, the King, and the Ace which represents the number 1. Item 9 The percentage chance that the first card drawn from the deck is a heart or an 8 is closest to A 31% C 32% B 33% D 30% number of favourable outcomes number of possible outcomes At the beginning of a round of poker (5 card draw variant) all players are dealt 5 cards. They can then choose to discard as many cards as they want in return for the same amount of cards. Cards discarded are not shuffled back into the deck. Stan, Win and Alex have decided to play a game of poker.
Item 10 At the beginning of the round all three players have been dealt 5 cards. One of the players holds a Jack of Hearts, King of Diamonds, Queen of Diamonds, 3 of Diamonds and Ace of clubs. The probability that another player holds the Ace of Diamonds is closest to A 0.242 C 0.213 B 0.270 D 0.263 Item 11 Assume that after every player has now been dealt five cards and only Stan holds a spade. Stan s hand contains 4 spades and a diamond. Stan discards 1 card and is dealt another one. The probability that the card he is dealt is a spade is closest to A 0.243 C 0.256 B 0.245 D 0.254
Marking Scheme Unit Three In order to successfully complete this unit, students were required to use the diagram provided and choose the most correct answer. CCEs Present in Unit: 16 Calculating with or without calculators. 19 Substituting in formulae. 37 Applying a progression of steps to achieve the required answer. Unit Three Item 9 A. Students were required to calculate the probability of drawing a heart or an 8. There are 13 hearts to a deck, and 4 eights with one of those eights being a heart. Therefore there are 16 favourable outcomes. With 52 cards in a deck, the probability is 16/52 = 0.307. 0.307 x 100 = 30.7% = 31% Unit Three Item 10 C. Students should have calculated the probability that one of the cards held by the other players was the Ace of diamonds. Since 10 cards were held by the other players the chances that one was the Ace of diamonds is equal to 10/47 (47 being the number of cards left in the deck after the first players hand has been dealt). 10/47 = 0.213 Unit Three Item 11 A. Students should have calculated the chances of drawing a spade. There are 4 spades no longer in the deck, and the deck only contains 37 cards (15 are in the players hands). Therefore the probability of drawing a spade is equal to 9/37. 9/37 = 0.243