Introduction
Probability- What is it?
Probability is defined as the likelihood that a certain and/or specific event will occur (Pierce, 2023). For example, in televiswion shows you may sometimes see people placing a bet, and flipping a coin to decide who is the winner. This is know as 50/50 probability, because there are TWO different sides to a coin.
By the end of the following lessons, you will be able to describe the likelihood of possible everyday occurances, as well as conducting your own experiments to help you evaluate probability and chance.
Lets have a look at how probability affects our everyday lives.
A Day at the Beach
Sam and his siblings want to go to the beach this weekend, the love swimming in the cool water and playing on the warm sand. Their mum says that they need to make sure it wont be too hot, too cold, or even rain when they go. How can they plan ahead of time, and make sure that they wont run into any trouble on their beach day? Should they:
1- Go outside and see if it's hot.
2- Leave an egg in a frying pan outside in the sun.
3- Check the weather predicitions on the news or online.
4- Look at the clouds and see if they will rain.
ANSWER: Number Three!
The weather predictions published by news stations are a useful tool for planning outdoor time. They use prior data and scientific behaviour to predict the probability of certain outcomes such as heatwaves, rainfall, snowstorms and more. If sam and his family want to make sure they stay safe this weekend, they better check the weather forecast.
Let's have a look at this website and see what the weather will be like tomorrow.
Perth, Western Australia, Australia Weather Forecast | AccuWeather
Task
Lesson One:
This lesson serves as an introduction to the concepts of probability. We will use this worksheet to learn about common phrases that are used during the prediction, assessment and evaluation proccesses of probability. Use the below definitions to fill out your worksheet.
Likely: May occur, or might be true.
In a sentence: it is likely that we will come to school tomorrow.
Unlikely: Not likely to occur, or might not be true.
In a sentence: It is unlikely that 5 students in the class will all be sick tomorrow.
Certain: Will definently occur, is 100% true.
In a sentence: I am certain that the sky is blue.
Impossible: Will never occur, is 100% untrue.
In a sentence: A unicorn flying through the classroom right now is impossible.
https://www.bing.com/videos/riverview/relatedvideo?q=probability%20yout…
After the lesson we will all discuss our answers. We will then brainstorm our own scenarios, and go around the room and rank them from most likely, to least likely.
Lesson Two:
To begin the lesson, we will be watching an education video on ratios. We will learn what they are, what they are used for, and how they relate to the topic of probability and chance. After the video we will take a few minutes to ask each other any questions that we may have, to make sure everyone has a sound understanding of the task ahead.
https://www.youtube.com/watch?v=xA435umOQuw
Using our knowledge from the last lesson, we will now be conducting our own experiment to assess probability. On each of your desk the supplies have been laid out to be shared between the table group. This includes a drawstring bag, 4 lead pencils, 4 worksheets, and 20 colourful plastic discs of four different colours. Your job is to work as a team to complete the worksheet, however can reach out to the teacher if you require some assistance with any of the questions.
This lesson is intended to help you with developing your ability to analyze mathematical components of experiments, and to assist you with making a prediction in relation to the experiment.
Lesson Three
For this lesson, each student will have access to a website containing free online games in relation to the topic. You have the ability to work through the content at your own pace, feel free to reach out for assistance either to your peers, or to the teacher should you need it. The website contains games with varying levels of skill, so that it is accessible and completion of task is achieveable for everyone. the link for the website is below.
https://free-training-tutorial.com/probability-games.html
Lesson Four
This lesson focuses on solidifying your knowledge in relation to the probability of certain events occuring. It is hoped that by the end of the lesson you can answer the following questions (if you can't, it is absolutely okay, it just means we will have to do some more revision on the topic).
1- What is probability?
2- What are some ways that we can use prediction to assume chance?
3- What are some real life situations when you would have to use probability?
Each student has a worksheet, that they will need to fill out. Based on your preferences you may work individually, in pairs, or in groups. We will start the lesson by rewatching the video from our first lesson, this is to refresh your memories.
https://www.bing.com/videos/riverview/relatedvideo?q=probability%20yout…
Evaluation
|
Skill development |
Excellent/above average |
Good/on track for year level |
Satisfactory/pass |
Incomplete/unsatisfactory |
|
Social |
The student actively sought out participation from their peers, and actively engaged in group conversation during all assigned tasks. The student was able to remain attentive during the lessons despite distraction. |
The student was able to remain engaged with their peers during the majority of lessons. They made an active effort to stay focused on tasks. They participated in almost all activities. |
The student was able to remain engaged during the majority of lessons, they made a sound effort to stay focused on tasks. They participated in most activities. |
The student made little/no effort to participate alongside their peers throughout the unit.
Elaborate: |
|
Lesson 1 |
The student could effectively describe/name instances where the use of probability takes place in everyday life. They completed the worksheet to an excellent standard. |
The student could describe/name instances where the use of probability takes place in everyday life. They completed the worksheet to a good standard. |
The student was able to name a few instances where the use of probability takes place in everyday life. They completed the worksheet to an average/sound standard. |
The student made little /no effort to name a few instances where the use of probability takes place in everyday life. Completion of the worksheet was unsatisfactory.
Elaborate:
|
|
Lesson 2 |
The student took active participation in the group work. They were able to complete the activity with no interruptions, they remained focused and presented accurate data after the experiment. |
The student was able to remain on task and actively participated in the group. They presented accurate data after the experiment. |
The student completed the activity to a sound level. The worksheet presented little mistakes and showed understanding of concepts. |
The student did not complete the activity to a satisfactory standard.
Elaborate: |
|
Lesson 3 |
Not graded. |
|||
|
Lesson 4 |
The student showed full understanding of any concepts presented, they were able to answer any and all questions posed to them. The worksheet was completed to an excellent standard. |
The student showed understanding of any concepts presented. They were to answer the majority of questions posed to them. The worksheet was completed to a good standard. |
The student showed sound understanding of concepts. They were able to answer some questions regarding the topic. The worksheet was completed to a satisfactory standard. |
The student did not complete the activity to a satisfactory standard.
Elaborate: |
Conclusion
The lessons created were based on the learning trajectory presented in Assignment One, wherein the students are expected to gradully gain a deeper understanding of the concepts surrounding probability. They have been created using two learning criteria presented in version 9 of the Australian Curriculum (2023). These being:
-
‘AC9M4P01- Describe possible everyday events and the possible outcomes of chance experiments and order outcomes or events based on their likelihood of occurring; identify independent or dependent events’
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‘AC9M4P02- Conduct repeated chance experiments to observe relationships between outcomes; identify and describe the variation in results’
The lessons factor in contemporary learning pedagogies theorizes by Lev vygotsky (2019), as the students are actively participating in groups, with limited/requested guidance from the educator. This is a common educational pedagogy known as 'social constructivism'. It is in this way, that students are able to explore their own cognitive abilities, as well as gain insight into their individual learning behaviours that affect the way they absorb knowledge.
Credits
ACARA. (2023). Mathematics – Year 4. Australian Curriculum Assessment and Reporting Authority, v.9. https://v9.australiancurriculum.edu.au/f-10-curriculum/learning-areas/m…
Briggs, M. Hansen, A. Hansen, A. (2012). Play-Based Learning in the Primary School. SAGE Publications Limited. https://ebookcentral.proquest.com/lib/cdu/reader.action?docID=880798
Mathantics. (2019, May 16). Math Antics - Basic Probability -->. YouTube. https://www.bing.com/videos/riverview/relatedvideo?q=probability%20yout…
Math With Mr. J. (2020, March 1). Introduction to Ratios (What Are Ratios?) | Ratio Examples and Answers -->. YouTube. https://www.youtube.com/watch?v=xA435umOQuw
National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics.
Pierce, R. (2023). Probability. MathisFun. https://www.mathsisfun.com/citation.php
Vygotsky, L. S. (2019). L. S. Vygotsky's Pedological Works. (1st ed., Vol. 1). Singapore: Springer Singapore. https://link.springer.com/book/10.1007/978-981-15-0528-7