NAP Mate is a registered trademark of Mighty Minds Educational Systems Pty Ltd. Cairns State High School

Transcription

1 NP Mate is a registered trademark of Mighty Minds Educational Systems Pty Ltd. airns State High School 1

2 NP Mate Please note: any activity that is not completed during class time may be set for homework or Q1 undertaken at a later date. M Phi Rotation Lesson ctivity escription: NP Mate is a registered trademark of Mighty Minds Educational Systems Pty Ltd. Mighty Minds Educational Systems Pty Ltd ll rights reserved. This lesson contains three Multiple hoice units comprised of questions testing the Phi ommon urriculum 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 ctivity: This lesson allows students the opportunity to practise the Phi skills required in the multiple choice section of the QS. Es: alculating with or without calculators (Ф16) Estimating numerical magnitude (Ф17) Substituting in formulae (Ф19) pplying a progression of steps to achieve the required answer (Ф37) Suggested Time llocation: 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. fter 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. M. Harland - airns State High School - Resource: th Jan

3 NP Mate Items 1-4 NP Mate is a registered trademark of Mighty Minds Educational Systems Pty Ltd. Mighty Minds Educational Systems Pty Ltd ll rights reserved. The head official at the Weather Forecast ouncil (WF) believes a method has been devised 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. Y 2 Y 1 loudy Y 3 Y 4 Next week = loudy = loudy = = loudy = = = = = loudy loudy = loudy loudy = = = Y 3 Y 4 Next week = loudy Y 2 loudy = = = loudy = Y 1 loudy Y 3 Y 2 Y 1 loudy loudy Y 4 Next week = loudy = = = loudy loudy = = loudy = loudy loudy = = loudy M. Harland - airns State High School - Resource: th Jan

4 NP Mate Item 1 If it was raining on Monday and Tuesday and sunny on Wednesday, what will the weather be like next Thursday? Overcast loudy NP Mate is a registered trademark of Mighty Minds Educational Systems Pty Ltd. Mighty Minds Educational Systems Pty Ltd ll rights reserved. Item 2 If it was cloudy three days ago, what is the probability that it will be cloudy in one week s time? 22.22% 33.33% 44.44% 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? 33.33% 44.44% 66.66% 73.33% The information in the table below refers to Item 4. This week s weather Monday Tuesday Wednesday Thursday Friday Saturday Sunday loudy loudy Item 4 What will the weather be like next Friday? loudy Not predictable M. Harland - airns State High School - Resource: th Jan

5 NP Mate Item 1 If it was raining on Monday and Tuesday and sunny on Wednesday, what will the weather be like next Thursday? Overcast loudy NP Mate is a registered trademark of Mighty Minds Educational Systems Pty Ltd. Mighty Minds Educational Systems Pty Ltd ll rights reserved. Item 2 If it was cloudy three days ago, what is the probability that it will be cloudy in one week s time? 22.22% 33.33% 44.44% 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? 33.33% 44.44% 66.66% 73.33% The information in the table below refers to Item 4. This week s weather Monday Tuesday Wednesday Thursday Friday Saturday Sunday loudy loudy Item 4 What will the weather be like next Friday? loudy Not predictable M. Harland - airns State High School - Resource: th Jan

6 NP Mate Marking Scheme Unit One: Multiple hoice In order to successfully complete this unit, students were required to use the formula, diagrams and table provided and choose the most correct answer. NP Mate is a registered trademark of Mighty Minds Educational Systems Pty Ltd. Mighty Minds Educational Systems Pty Ltd ll rights reserved. Es Present in Unit: 16 alculating with or without calculators 17 Estimating numerical magnitude 19 Substituting in formulae 37 pplying a progression of steps to achieve the required answer Item 1. 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 produces a cloudy day in a week s time. Item 2. 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%. Item 3. 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%. Item 4. 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 next Friday. M. Harland - airns State High School - Resource: th Jan

7 NP Mate 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). NP Mate is a registered trademark of Mighty Minds Educational Systems Pty Ltd. Mighty Minds Educational Systems Pty Ltd ll rights reserved. Lakes Winnibigoshish ay emidji Lake of the Woods Water height when full* (m) urrent water height (m) Water volume when full (ML) urrent water volume (ML) urrent water volume** (%) Volume change***(%) Note: * Height above max depth when full ** urrent water volume as a percentage of water volume when full *** Volume change as a percentage of water volume when full m = metres ML = megalitres Item 5 What percentage of the full water volume of the Lake of the Woods is the equivalent of 7.85% of the full volume of Winnibigoshish? 6.68% 5.65% 7.66% 6.52% Item 6 On the 1st of March 2011, the volume of Lake emidji was approximately equal to ML ML ML ML. M. Harland - airns State High School - Resource: th Jan

8 NP Mate Item 7 The combined water of all four lakes on the 8th of March 2011, as a percentage of the combined max volume of all four lakes, is closest to 80%. 83%. 82%. 79%. NP Mate is a registered trademark of Mighty Minds Educational Systems Pty Ltd. Mighty Minds Educational Systems Pty Ltd ll rights reserved. Item 8 The overall change in volume of the four lakes combined since the 1st of March 2011, as a percentage of the combined max volume of all four lakes, is closest to -0.07% %. 0.09%. 0.08%. M. Harland - airns State High School - Resource: th Jan

9 NP Mate 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). NP Mate is a registered trademark of Mighty Minds Educational Systems Pty Ltd. Mighty Minds Educational Systems Pty Ltd ll rights reserved. Lakes Winnibigoshish ay emidji Lake of the Woods Water height when full* (m) urrent water height (m) Water volume when full (ML) urrent water volume (ML) urrent water volume** (%) Volume change***(%) Note: * Height above max depth when full ** urrent water volume as a percentage of water volume when full *** Volume change as a percentage of water volume when full m = metres ML = megalitres Item 5 What percentage of the full water volume of the Lake of the Woods is the equivalent of 7.85% the full volume of Winnibigoshish? 6.68% 5.65% 7.66% 6.52% Item 6 On the 1st of March 2011, the volume of Lake emidji was approximately equal to ML ML ML ML. M. Harland - airns State High School - Resource: th Jan

10 NP Mate Item 7 The combined water of all four lakes on the 8th of March 2011, as a percentage of the combined max volume of all four lakes, is closest to 80%. 83%. 82%. 79%. NP Mate is a registered trademark of Mighty Minds Educational Systems Pty Ltd. Mighty Minds Educational Systems Pty Ltd ll rights reserved. Item 8 The overall change in volume of the four lakes combined since the 1st of March 2011, as a percentage of the combined max volume of all four lakes, is closest to -0.07% %. 0.09%. 0.08%. M. Harland - airns State High School - Resource: th Jan

11 NP Mate Marking Scheme Unit Two: Multiple hoice In order to successfully complete this unit, students were required to use the formula, diagrams and table provided and choose the most correct answer. Es Present in Unit: 16 alculating with or without calculators 37 pplying a progression of steps to achieve the required answer NP Mate is a registered trademark of Mighty Minds Educational Systems Pty Ltd. Mighty Minds Educational Systems Pty Ltd ll rights reserved. Item 5. Students simply had to calculate what volume of water 7.85% of the max volume of the Lake Winnibigoshish was and determine what percentage of the max volume of Lake of the Woods this volume equated to x 498,630 = / 600,110 = x 100 = 6.52% Item 6. Students should have calculated the increase in the volume of water contained in Lake emidji since the 1st of March and subtracted it from the volume reading taken on the 8th of March x 324,170 = ML 276, = ML = 269,000 ML Item 7. Students should have added the measurements of volume on the 8th together and then added the measurements of the max volumes of each of the four lakes together, and used these two values to determine what percentage the volume of the four lakes was with respect to their total volume , = = ( / ) x 100 = 82.64% M. Harland - airns State High School - Resource: th Jan

12 NP Mate Marking Scheme Unit Two: Multiple hoice Item 8. Students should have calculated the total change in volume by converting from percentage form, and then found this as a percentage of the total combined max volume of the four lakes x = x = x = NP Mate is a registered trademark of Mighty Minds Educational Systems Pty Ltd. Mighty Minds Educational Systems Pty Ltd ll rights reserved x = ( ) = Max volume of combined lakes = ( / ) x 100= % M. Harland - airns State High School - Resource: th Jan

13 NP Mate Items 9-11 This unit deals with probability using a deck of cards. The probability of a particular outcome is equal to number of favourable outcomes number of possible outcomes NP Mate is a registered trademark of Mighty Minds Educational Systems Pty Ltd. Mighty Minds Educational Systems Pty Ltd ll rights reserved. There are 52 cards in a deck. These cards are divided between four different suits: hearts, diamonds, spades and clubs. Hearts and diamonds are red and spades and clubs are black. Each suit contains 13 cards: nine 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 probability that the first card drawn from the deck is a heart or an 8 is closest to 31% 33% 32% 30% t the beginning of a round of poker (five card draw variant) all players are dealt five cards. Players can then choose to discard as many cards as they want in return for the same amount of cards. iscarded cards are not shuffled back into the deck. Stan, Win and lex have decided to play a game of poker. M. Harland - airns State High School - Resource: th Jan

14 NP Mate Item 10 t the beginning of the round, all three players have been dealt five 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 NP Mate is a registered trademark of Mighty Minds Educational Systems Pty Ltd. Mighty Minds Educational Systems Pty Ltd ll rights reserved Item 11 ssume that every player has now been dealt five cards and only Stan holds a spade. Stan s hand contains four spades and a diamond. Stan discards one card and is dealt another one. The probability that the card he is dealt is a spade is closest to M. Harland - airns State High School - Resource: th Jan

15 NP Mate Items 9-11 This unit deals with probability using a deck of cards. The probability of a particular outcome is equal to number of favourable outcomes number of possible outcomes NP Mate is a registered trademark of Mighty Minds Educational Systems Pty Ltd. Mighty Minds Educational Systems Pty Ltd ll rights reserved. There are 52 cards in a deck. These cards are divided between four different suits: hearts, diamonds, spades and clubs. Hearts and diamonds are red and spades and clubs are black. Each suit contains 13 cards: nine 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 probability that the first card drawn from the deck is a heart or an 8 is closest to 31% 33% 32% 30% t the beginning of a round of poker (five card draw variant) all players are dealt five cards. Players can then choose to discard as many cards as they want in return for the same amount of cards. iscarded cards are not shuffled back into the deck. Stan, Win and lex have decided to play a game of poker. M. Harland - airns State High School - Resource: th Jan

16 NP Mate Item 10 t the beginning of the round, all three players have been dealt five 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 NP Mate is a registered trademark of Mighty Minds Educational Systems Pty Ltd. Mighty Minds Educational Systems Pty Ltd ll rights reserved Item 11 ssume that every player has now been dealt five cards and only Stan holds a spade. Stan s hand contains four spades and a diamond. Stan discards one card and is dealt another one. The probability that the card he is dealt is a spade is closest to M. Harland - airns State High School - Resource: th Jan

17 NP Mate Marking Scheme Unit Three: Multiple hoice In order to successfully complete this unit, students were required to use their probability skills to calculate the most correct answer. NP Mate is a registered trademark of Mighty Minds Educational Systems Pty Ltd. Mighty Minds Educational Systems Pty Ltd ll rights reserved. Es Present in Unit: 16 alculating with or without calculators 19 Substituting in formulae 37 pplying a progression of steps to achieve the required answer Item 9. Students were required to calculate the probability of drawing a heart or an 8. There are 13 hearts to a deck and four 8s, with one of those 8s being a heart. Therefore, there are 16 favourable outcomes. With 52 cards in a deck, the probability is 16/52 = x 100 = 30.7% = 31% Item 10. 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 player s hand has been dealt). 10/47 = Item 11. Students should have calculated the chances of drawing a spade. There are four 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 = M. Harland - airns State High School - Resource: th Jan Powered by TPF (