Orange High School. Year 7, Mathematics Assignment 2

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1 Full name: Class teacher: Due date: Orange High School Year 7, 05 Mathematics Assignment Instructions All work must be your own. You are encouraged to use the internet but you need to rewrite your findings in your own words. Hand in this assignment and the spinner you have created. Place your name on both. Total marks 6 Introduction 4 marks Roulette 39 marks Personal reflection 5 marks Literacy 4 marks

2 Rationale To develop an appreciation of how probability can be used to guide decision making and in particular how Casinos design game rules to make a profit. To understand the relationship between theoretical and experimental probability. Engage Explore Explain Elaborate Evaluate Aim Students will discover applications of probability. Students will experience the difficulties with creating a truly random experiment and understand how random results can vary. Students will appreciate how probability can be used to guide decision making. Students will understand how Casinos use probability to develop game rules and make a profit. Students will learn to improve their thinking about thinking. Method Research on the internet, library or ask people. Create a spinner and conduct a chance experiment. Analyse the relationship between theoretical and experimental probability and develop their own strategy for winning. Answer reflection questions. Answer personal reflection questions. Year 7, 05 Mathematics Assignment P a g e

3 Probability Probability is the measure of likeliness that an event will occur. Probability can be used to guide decision making. For example, the gambling industry uses probability to design game rules ensuring casinos will make money in the long run. Activity List examples of probability in real life Find three other ways probability is used in real life. Ensure that you use correct grammar, punctuation and spelling.. 4 marks. 3. Hints Sport Hospitals Weather Year 7, 05 Mathematics Assignment 3 P a g e

4 Roulette Roulette is a casino game where a small white ball is dropped into a spinning wheel with numbered compartments (figure ). People bet on which compartment the ball will end up in, by placing chips on the betting table before the spin (figure ). Some of the bets you can make are listed in the table below. $ Bet Payout One number $36 Split (two numbers) $8 Even or odd $ Red or black $ Figure Roulette wheel Figure Roulette table Activity Construct a spinner marks Create a spinner similar to a roulette wheel. It should have the same numbers, in correct order and the same colour as a roulette wheel. You may use this video and instructions below or find your own design. Equipment o Template on last page of this assignment o Paper clip o Pliers o Sticky tape o Cardboard box Instructions. Write numbers and colour the circle segments in the same order as figure above.. Cut out the circle and the pointer. Paste them onto cardboard. 3. Bend a paper clip into an L shape and curl one end to protect fingers. 4. Push the other end through the centre of the pointer and then circle. Tape it to the bottom of the circle. Year 7, 05 Mathematics Assignment 4 P a g e

5 Activity 3 Conduct a chance experiment 9 marks Experimental probability (%) = number of times the event occurs total number of trials in the experiment 00 Use your spinner to conduct a chance experiment. Record your results in the table below.. Select one of the bets from the payout table on page 4.. Spin the wheel 0 times. Tally the number of times that you win. 3. Calculate the experimental probability of winning your bet. Show all working. 4. Spin a further 0 times. Calculate the experimental probability of getting your bet after 0 times. 5. Repeat steps & 3 until you reach 00. Bet selected: Trials Tally win Tally lose Running total win Running total trials Experimental probability (%) Example only I = 0% Year 7, 05 Mathematics Assignment 5 P a g e

6 Activity 4 Compare Theoretical and Experimental probability 4 marks Theoretical probability (%) = number of favourable outcomes total number of outcomes 00 Theoretical probability is useful for predicting what will happen before the experiment takes place. Calculate the theoretical probability for the bet you chose above. Show all working. As the number of trials increased, did your experimental probability get closer or further away from the theoretical probability? Explain your answer. Ensure that you use correct grammar, punctuation and spelling. Activity 5 Use probability to guide decision making Think of two different strategies for winning Roulette e.g. Always bet on even. Calculate the theoretical probability for each strategy. Show all working. 0 marks Strategy : Theoretical probability: 4 If you would like to create a more complicated strategy, you may want to research more of the rules on Wikipedia. Year 7, 05 Mathematics Assignment 6 P a g e

7 If your strategy involves more than one spin of the wheel, then you will need to combine probabilities together. e. g. Theoretical probability = probability of first spin probability of second spin Strategy : Theoretical probability: 4 Activity 6 Reflect on roulette 4 marks Why will the casino always win in the long run? Ensure that you use correct grammar, punctuation and spelling. Why do some casinos add a 00 to the wheel? Use an example to help support your answer. Ensure that you use correct grammar, punctuation and spelling. Year 7, 05 Mathematics Assignment 7 P a g e

8 Personal reflection Solving problems 5 marks. For activity 5, what were you being asked to find out?. What strategies did you use to help solve this activity? look for a pattern use objects to act out the problem guess and check brainstorm work backwards use logical reasoning by eliminating some draw a picture answers make a list other: make a table or diagram 3. Did you get anyone to help you solve these activities? 4. How do you rate the problem? o The problem was easy to solve. o The problem needed some brain power. o The problem was hard to solve and needed lots of brain power. Year 7, 05 Mathematics Assignment 8 P a g e

9 Connect Extend Challenge 6 marks Connect: How are the ideas and information connected to what you already know? Extend: What ideas did you get that extend your thinking in new directions? Challenge: What is challenging or confusing for you? What questions do you have? What puzzles you? Year 7, 05 Mathematics Assignment 9 P a g e

10 Worksheet reflection 4 marks What have I learnt? What did I do well? What did not go so well? What could I do to improve next time? Year 7, 05 Mathematics Assignment 0 P a g e

11 Assessment rubric Activity A B C / D E Above the standard: expert At the standard: practitioner Approaching the standard: moving forward Ungraded below standard: travelling required - List examples of probability in real life Three examples that are very different to each other and provide enough detail to demonstrate research has been conducted. 4 Three examples that may be similar or do not have much detail. 3 Two examples that have good detail and dissimilar. Or three examples that are similar and lack detail. One example with good detail. Or two examples that lack detail. - Construct a spinner The spinner has been numbered in order and coloured correctly. 4 There are one or two mistakes in the order or the colouring. 3 Most of the numbers are in order and coloured correctly. Some of the numbers are in order and coloured correctly. The spinner works freely to produce random results every time and is sturdy in construction. 4 The spinner works most of the time. 3 The spinner works some of the time. The spinner rarely works. The spinner looks excellent with neat writing, careful colouring and tidy edges. 4 The spinner looks good with mostly neat writing, careful colouring and tidy edges. 3 The spinner looks reasonable with some neat writing, careful colouring and tidy edges. The spinner looks poor with messy writing, careless colouring and untidy edges. 3 - Conduct a chance experiment In each row, the tally of wins and losses adds to 0. The running total includes the total of the previous row. 4 There are one or two rows where the tally and the totals are incorrect. 3 There are three to five rows where the tally and the totals are incorrect. Only some rows have been tallied and totaled correctly. In each row, the experimental probability calculation is correct and includes working. 4 In each row, the calculation is correct but does not include working. Or most rows are correct and working has been shown. 3 Most rows are correct but working has not been shown Or some rows are correct and working has been shown. Some rows are correct but working has not been shown Or one or two rows are correct and working has been shown. Year 7, 05 Mathematics Assignment P a g e

12 Activity A B C / D E Above the standard: expert At the standard: practitioner Approaching the standard: moving forward Ungraded below standard: travelling required 4 - Compare Theoretical and Experimental probability The theoretical probability has been correctly calculated and includes working. The answer is correct but does not include working or there is one mistake in the working..5 The answer is incorrect but most of the working is correct. The answer is incorrect and some of the working is correct. 0.5 The comparison reflects the chance results correctly. The reason supplied is valid and detailed. The comparison and reason are correct but not detailed..5 The comparison or the reason is correct and most statements are accurate. The comparison or the reason is correct and one statement is accurate Use probability to guide decision making A difficult strategy involves more than one spin. A simple strategy involves one spin. The strategy selected is difficult, the theoretical probability calculation is accurate and includes working. 4 The strategy is difficult, the calculation is incorrect but most working is correct Or the strategy is simple, the calculation is accurate and includes working. 3 The strategy is difficult and some of the working is correct Or the strategy is simple, the calculation is incorrect but most working is correct. The strategy is difficult and one part of the working is correct. Or the strategy is simple and some of the working is correct. 6 - Reflect on roulette The answer demonstrates an excellent understanding of how theoretical probability determines outcomes and how game rules favour casinos. The answer demonstrates a good understanding..5 The answer demonstrates a reasonable understanding. The answer demonstrates a poor understanding. 0.5 The answer demonstrates an excellent understanding of game rules and includes a valid example. The answer demonstrates an good understanding. Or an excellent understanding but no example..5 The answer demonstrates an reasonable understanding. Or a good understanding but no example. The answer demonstrates an poor understanding. Or an reasonable understanding but no example. 0.5 Literacy in activities, 4 & 6 All sentences have correct grammar, spelling and punctuation. 4 One or two mistakes in grammar, spelling or punctuation. 3 Three to five mistakes in grammar, spelling or punctuation. Many mistakes in grammar, spelling or punctuation. Year 7, 05 Mathematics Assignment P a g e

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