Probability: Game of Chance

Introduction

This online resource is to assist you in learning about Probability, Chance, exploring and investigating concepts such as presenting probabilities using fractions, decimals and percentages. You will conduct chance experiments physically and also using technology. Your prior skills developed in Year 5, for example chance experiments and equally likely outcomes and probability fractions will assist you in enhancing your skills of chance. This website is designed to be engaging, challenging and fun! These activities will build on your ideas and help you design your own game of chance. Please view this video to introduce the unit and also to reinforce your perspectives of chance...

The task for your Assessment will be to design your own game of probability/chance that will be used in an online 'Probability Fair'. You will view the videos, and participate in the online games. You will also complete the lessons provided under 'Process' which include worksheets. Using your prior and knowledge gained from the website, you will then attempt to design your own game of probability to conduct and play at your own classroom online fair!

Process

Lesson 1

http://www.scootle.edu.au/ec/viewing/L2637/index.html

Please click on the hyperlink and complete the activities. Participate in the bike race until all your answers are correct, you can refer to "What's the theory" for extra assistance. Once you have finished the activity, write a brief description about what you have learnt from this game.

Lesson 2

Student name:                                                                     Score:

Fair die Worksheet

A fair die is rolled.

 Find all possible outcomes   Answer:     Find the probability of finding an even number   Answer:     Find the probability of finding an odd number   Answer:     Find the probability of finding a prime number   Answer:     Find the probability of finding an even prime number   Answer:

Student name:                                                                        Score:

Fair coin worksheet

A fair coin is thrown.

Student name:                                                                              Score:

Probability of Numbers Worksheet

Numbers from 1 to 50 are written on a piece of paper and dropped into a box. A paper is chosen at random.

 Find the probability of choosing multiples of 10   Answer:           Find the probability of choosing an even number   Answer:         Find the probability of showing an odd number   Answer:         Find the probability of choosing an odd number Answer:         Find the probability of choosing factors of 36 Answer:       Find the probability of choosing neither odd nor prime. Answer:

Student name:                                                                                   Score:

A day is chosen from a week.

 Find the probability of choosing a Wednesday. Answer:           Find the probability of selecting a day that starts with the letter S   Answer:         Find the probability of selecting a day that starts with the letter T Answer:         Find the probability of selecting the weekends. Answer:         Find the probability of selecting a Sunday. Answer:

Student name:                                                                                         Score:

There are 25 students in grade 5. 15 are boys and the others are girls. A student is selected for a field trip at random. Find the

 Find the probability of selecting a boy Answer:           Find the probability of selecting a girl Answer:       Odds in favour of a boy Answer:       Odds in favour of a girl Answer:         Odds against boy and odds in favour of girl are the same. Is that right? Answer:

Student name:                                                                                                        Score:

Independent and Dependent

Two cards are drawn from a single deck of 52 cards one after the other.

 Find the probability of selecting a king from the first card. Answer:       If the first card is king and the card is not replaced, what is the probability of selecting a king from the second card? Answer:     Find the probability of selecting a king from the first card and a queen from the second card without replacing the first card. Answer:       Find the probability of selecting a king from the first card and a queen from the second card without replacing the first card Answer:         Find the probability of selecting a Jack from the first card and queen from the second card with replacement Answer:       Find the probability of selecting 6 or 7 in the first draw and 8 or 9 in the second draw without replacement Answer:

Student name:                                                                                                           Score:

Deck of Cards Worksheet

A card is drawn from a deck of 52 cards.

 Find the probability of drawing a black card Answer:       Find the probability of drawing a red card Answer:     Find the probability of drawing a red or black Answer:       Find the probability of drawing an ace Answer:         Find the probability of drawing either a jack or queen or king Answer:

Student name:                                                                                             Score:

Pair of Dice Worksheet

A pair of dice is rolled

 Find all possible outcomes Answer:       Find the probability of showing an even numbers on both dice Answer:     Find the probability of showing an odd number on the second die Answer:       Find the probability of not showing prime number on the first die Answer:         Find the probability of showing prime numbers on both dice Answer:       Find the probability of showing same numbers on both dice Answer:

Student name:                                                                                                Score:

Balls in a container

 There are 5 white balls, 8 red balls, 7 yellow balls and 4 green balls in a container. A ball is chosen at random Answer:       What is the probability of choosing red? Answer:     What is the probability of choosing green? Answer:       Find the probability of choosing either red or white? Answer:         What is the probability of choosing neither white nor green? Answer:       What is the probability of choosing other than yellow? Answer:       What is the probability of choosing black? Answer:

Student no.                                                                                                           Score:

Probability - Spinner

Make a spinner with sixteen segments, with the following number sequence, one on each segment: 2, 1, 4, 5, 4, 1, 4, 5, 3, 5, 2, 1, 2, 5, 1, 3. It is up to you how you would like to design this resource. Use this spinner to conduct these experiments

 What is the probability of choosing an odd number? Answer:       What is the probability of choosing an even number? Answer:     What is the probability of choosing a prime number? Answer:       Find the probability of choosing 1 or 5? Answer:         What is the probability of choosing 3 or 4? Answer:

Lesson 3

https://mrnussbaum.com/probability-fair-online-game

This fun game allows you to earn tokens by participating in probability games. You can start a new game, or choose a password so you don't lose your scores! Earn tokens to enter the fair by playing the first game. Once you are inside the fair, you can play a range of different probability games. See the demonstration video for more.

Evaluation

Student diversity

Referring to the Australian Curriculum, the lessons and assessment can be modified, using 'reasonable adjustments'. For example, students with learning disabilities sight or hearing impaired may have their screens adjusted to allow for larger text, higher volume or earphones, or teacher aide assistance. Children who are more hands on learners can physically perform the investigatory tasks on the worksheets. The Probability Fair can be used in between sections to alleviate boredom, or to work with students who tend to hyperfocus, or just to have a break from the more structured activities.

Gifted and talented students may complete the website activities at their own pace if wanting to move forward, or be given extra more challenging worksheet activities, or even design their own basic website or online game. They may make up their own experiments to carry out in the classroom.

For EAL/D students, after determining their learning progression, can make adjustments in the lesson and assessment, however, the bike race game uses numbers and is fairly universal, a teacher aide may assist them with the activities. The games on the website are not largely culturally loaded, for example, the Probability Fair is another general culturally inclusive task. Cultural games could be included in their lessons/worksheets, language modification online may also be a way for children to understand the tasks at hand. The activities are individual in nature, a conglomerate of ideas, so this allows for student adjustment.

Conclusion

By the end of Year 6, students recognise the properties of prime, composite, square and triangular numbers. They describe the use of integers in everyday contexts. They solve problems involving all four operations with whole numbers. Students connect fractions, decimals and percentages as different representations of the same number. They solve problems involving the addition and subtraction of related fractions. Students make connections between the powers of 10 and the multiplication and division of decimals. They describe rules used in sequences involving whole numbers, fractions and decimals. Students connect decimal representations to the metric system and choose appropriate units of measurement to perform a calculation. They make connections between capacity and volume. They solve problems involving length and area. They interpret timetables. Students describe combinations of transformations. They solve problems using the properties of angles. Students compare observed and expected frequencies. They interpret and compare a variety of data displays including those displays for two categorical variables. They interpret secondary data displayed in the media.

Students locate fractions and integers on a number line. They calculate a simple fraction of a quantity. They add, subtract and multiply decimals and divide decimals where the result is rational. Students calculate common percentage discounts on sale items. They write correct number sentences using brackets and order of operations. Students locate an ordered pair in any one of the four quadrants on the Cartesian plane. They construct simple prisms and pyramids. Students describe probabilities using simple fractions, decimals and percentages. (Australian Curriculum, n.d.)

The website encompasses the 'Big Ideas' about probability and chance, incorporating fractions, decimals and percentages as part of the whole number. The website is a tool to revisit ideas from Year 5, and to scaffold their learning further to lead into more advanced concepts by the end of Year 6.

Credits

There are no credits for this website.

Teacher Page

These proficiency strands are addressed in this unit of work: Year Level 6:

• understanding includes describing properties of different sets of numbers, using fractions and decimals to describe probabilities, representing fractions and decimals in various ways and describing connections between them, and making reasonable estimations
• fluency includes representing integers on a number line, calculating simple percentages, using brackets appropriately, converting between fractions and decimals, using operations with fractions, decimals and percentages, measuring using metric units and interpreting timetables
• problem-solving includes formulating and solving authentic problems using fractions, decimals, percentages and measurements, interpreting secondary data displays and finding the size of unknown angles
• reasoning includes explaining mental strategies for performing calculations, describing results for continuing number sequences, explaining the transformation of one shape into another and explaining why the actual results of chance experiments may differ from expected results.

The Content Descriptions involve:

Chance

Describe probabilities using fractions, decimals and percentages (ACMSP144)

Conduct chance experiments with both small and large numbers of trials using appropriate digital technologies (ACMSP145 )

Compare observed frequencies across experiments with expected frequencies (ACMSP146)

(Australian Curriculum, n.d.)

(These are explained in the Evaluation section)

This website provides students with opportunities to fulfill the proficiency strands. Understanding: students are experimenting with fractions and decimals using a rang of media. Fluency:  students solve problems using fractions and decimals, part of a whole. They are exposed to problem-solving data methods online. Reasoning: The website delves into calculations, prediction and comparing results of experiments.

Learning Trajectory process

* Students build on their prior knowledge and justify choices of likelihood by referring to past experience.

* Students enhance this knowledge and scaffold through the use of the website/lesson plans

* Students use their past learning about likely events and make predictions about probability experiments

* Students use decimals and fractions to answer problems

* Students compare their answers to the outcomes

* Students use data to compare events within their experience/knowledge and using the resources

* Students design a probability game to develop and demonstrate their understandings

Fair Die Worksheet: (1,2,3,4,5,6), 1/2, 1/2, 1/2, 1/6.

Fair Coin Worksheet: (H,T), 1/2, 1/2, 1, 0

Probability of Numbers Worksheet: 1/10, 1/2, 1/2, 9/50, 12/25

Probability Worksheet (Days of the week): 1/7, 2/7, 2/7, 2/7, 1/7

Probability Worksheet (boys and girls): 3/5, 2/5, 3:2, 2:3, yes

Independent and Dependent: 1/13, 1/17, 4/52*4/51 = 4/663, 4/52*4/52=1/169, 8/52*8/52=4/169

Pair of Dice Worksheet: (1,1), (1,2), (1,3), (1,4), (1,5), (1,6)

(2,1), (2,2), (2,3), (2,4), (2,5), (2,6)

(3,1), (3,2), (3,3), (3,4), (3,5), (3,6)

(4,1), (4,2), (4,3), (4,4), (4,5), (4,6)

(5,1), (5,2), (5,3), (5,4), (5,5), (5,6)

(6,1), (6,2), (6,3), (6,4), (6,5), (6,6)

1/4, 1/2, 1/2, 1/4, 1/6

Balls in a container: 1/3, 1/6, 13/24, 5/8, 17/24, 0

Deck of Cards Worksheet: 1/2, 1/2, 1, 1/13, 3/13

Probability - Spinner: 5/8, 3/8, 9/16, 8/16, 5/16

Cross Curriculum Ideas: Visual Arts - making a spinner: Develop and apply techniques and processes when making their artworks

Design and Technologies Processes and Production Skills - making a spinner: Generate, develop and communicate design ideas and processes for audiences using appropriate technical terms and graphical representation techniques

Digital Technologies Processes and Production Skills - Plan, create and communicate ideas and information, including collaboratively online, applying agreed ethical, social and technical protocols

HASS - Present ideas, findings, viewpoints and conclusions in a range of texts and modes that incorporate source materials, digital and non-digital representations and discipline-specific terms and conventions

English - Identify and explain how analytical images like figures, tables, diagrams, maps and graphs contribute to our understanding of verbal information in factual and persuasive texts

References

Australian Curriculum. (n.d.). Mathematics: Understanding how Mathematics works. Year 6. Retrieved            from https://www.australiancurriculum.edu.au/f-10-curriculum/mathematics/

Education Services Australia Ltd. (2013). Dice Duels Bike Race. Retrieved from http://www.scootle.edu.au/ec/viewing/L2637/index.html