Introduction
In mathematics the term "probability" simply refers to the likelihood of something occurring. We can discuss the probabilities of certain outcomes—how likely they are—when we're unsure about the outcome of an event. The study of events controlled by chance is known as statistics (Kahn Academy, 2022).
What do we know about Chance and Probability?
Chance and probability is all around us and it is likely (there’s that word!) that you have heard it or used it in some form in your every day life. An example is when we look outside at the weather if it is cold, dark clouds above and wind what is the chances of rain? You could say that rain was likely. Another example, what is the chance of you eating lunch today? The answer would be certain as we always have a lunch break at school and there is always food available at school.
Let’s have a think about what we have learnt previously about probability in Year 4 or even earlier this year, can you remember what it was about or the terms used? Let’s watch this short video to refresh our memories on terms used to determine the probability of events occurring. The video will also look at how to use a number line to determine the probability of events occurring and touch on how this is represented as a fraction.
Task
Your mission should you choose to accept it is to design and conduct your own probability experiment. The lessons I've set will assist you in preparing for your final assessment and being able to complete it with confidence.
We Are Learning To (WALT)
By the end of these series of lesson students will be able to describe probabilities using both words and numbers.
What I’m Looking For (WILF)
By the end of this WebQuest students to be able to:
- Order events by likelihood of it occurring
- Describe probabilities using words
- Measure probabilities using numbers, based on equal and likely outcomes
- Predict the likelihood of winning games of chance by considering the number of possible outcomes.
- Use mathematical methods such as tables or graphs to record/display data.
Let's jump into the world of CHANCE and PROBABILITY and have some fun while we are at it!
Process
Five lessons have been developed in this WebQuest using the constructivism theory of providing an opportunity for each student to build upon their previous knowledge and/or experience to “construct” a new theory (Siemon et al., 2011). The structure of the lessons is to assist each and every one of you to progressively increase your knowledge and understanding of chance and probability.
You will begin with LESSON 1 and by LESSON 5 you will apply this learning to conduct your own experiment which will be marked and the results will go towards your final grade.
Each LESSON has two or three tasks for you to complete, providing you with opportunities to play different games to refine and consolidate your understanding prior to the final assessment. Please remember you can always ask your teacher for any help, guidance or further breakdown of a misunderstood concept.
Need some extra help or what some further guidance on what is expected? No problem, included in each lesson is the ‘Let’s Break This Down’ section just for you. If you feel you don’t need this additional help you can skip it and just complete each of the lesson tasks.
Early finishes ‘Extension Activity’ section is just for you. This has been designed to give you an extra challenge.
Lesson 1: What is Chance and Probability?
Let’s have a look at how we are going to build on our previous knowledge and understanding of chance and probability throughout this WebQuest by watching this short clip.
Task 1: Class Discussion
Let’s discuss the probability of events occurring, as well as the vocabulary associated with probability and chance.
Vocabulary: certain, likely, unlikely, impossible
- What will happen? e.g. it is certain we will have a math lesson today.
- What won’t happen? e.g. It is impossible a pig will fly.
- What might happen? e.g. It is unlikely it will rain as there are no dark clouds in the sky.
Helpful HintsIf you are still a bit unsure before you go onto the next task watch this quick clip on the vocabulary of probability to help you understand.
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Task 2: Matching probability and chance words to different events
Thinking about the vocabulary we have learnt thus far in relation to probability we are going to create a table with headings ‘Certain’, ‘Likely’, ‘Unlikely’ and ‘Impossible’ and then write each of these statements under the correct column.
- Magically turning into a giraffe.
- It will rain today.
- I will eat dinner tonight.
- A huge elephant will fit through the classroom door.
- I will learn something today.
- This is a math lesson.
- Pulling a purple marble out of a jar containing 4 purple marbles, 2 pink marbles, 3 yellow marbles and 1 red marble.
Task 3: Quiz Assessing Prior Knowledge
Please take the quick quiz following the link below to demonstrate your understanding of the terms ‘certain’, ‘probable’ (or ‘likely), ‘unlikely’ and ‘impossible’. Remember this is to show me what you already know so I can help you to learn even more!
https://au.ixl.com/maths/year-4/certain-probable-unlikely-and-impossible
Extension ActivityCopy these statements into your workbook and write in the missing word using the vocabulary of probability and chance.
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Lesson 2: Experimental Probability
What is experimental probability?
Experimental probability is documenting the number of times an event/action/outcome occurred when the experiment was conducted and writing it as a fraction based on the total number of times the experiment was conducted.
I can see for some of you this may look harder than what it actually is so let’s watch this short clip which explains experimental probability with diagrams.
Hint: you can refer back to this video anytime throughout these lessons to help you.
Task 1: What does experimental probability look like?
Let’s consider tossing a coin – what is the probability of each outcome? Let’s watch this short clip to break it down for us.
What we have learnt from this clip:
- Probability of an event occurring = number of ways it can happen = total number of outcomes.
- So when a single coin is tossed, there are two possible outcomes: heads or tails.
- Therefore, the probability of any one of them occurring is ½ or 0.5 or 50%. This means that there is an equal chance of tossing a head or a tail.
Example: toss a coin 100 times, how many times will tails come up? Probability says that tails has a ½ a chance, so we can expect 50 tails. But when we actually try it we may get 45 tails or 52 tails… there are endless possibilities, but in most cases the number will be close to 50, this is because there is an equal chance of a head or a tail.
Helpful HintsLet’s watch this video to show how the probability changes as you increase the number of coins tossed.
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Task 2: Let’s do this next task in pairs
Step 1: Now consider tossing two coins:
- What are the possible outcomes?
- Can you write the probability of each outcome as a fraction?
Step 2: Draw and label a two way table like the one below in your workbook to record the results.
| Possible coin combinations | Tally | Frequency | Show it as a fraction |
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Heads, Heads
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Heads, Tails
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Tails, Tails
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Helpful HintsIf you have forgotten how to tally watch this short video.
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Task 3: Possible outcomes and Tallying (Individual)
Step 1: Your task is to toss the three coins together in the air thirty times, tally the results recording it on a clearly labelled two way table.
Step 2: Answer the following questions in your work book:
- Which combination came up most often?
- Which combination came up least often?
- Do you think you would get the same results if you did this again? Yes/No and Why/Why not
Extension ActivityStep 1: Toss four coins twenty times and tally the results on a table Step 2: record the results as a fraction |
Lesson 3: Probability Line – Representing likelihood of events occurring as a fraction
In the previous lessons we have looked at:
- What is probability,
- The vocabulary used to demonstrate the probability of events occurring, and
- How to determine the possible outcomes of an event occurring, participating in the event and recording the outcome in a table.
Probability lines can be used to help us determine the likelihood of an event occurring and using the correct vocabulary.
Here is an example of a probability line:
As you can see the probability line helps us to determinedly the probability of events occurring. It also assists us in going one step further and writing the probability as a fraction.
Helpful HintsHere is a short clip to further explain probability lines and how they are useful when looking at chance and probability. If you think you have got this no need to watch the clip just move on to the task.
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Task 1: writing chance experiments as a fraction
Step 1: Let’s watch this clip on how we can represent chance experiments using fractions.
Step 2: Let's refresh our memories and look back at our previous lesson of tossing coins. When we toss two coins the possible outcomes are: Heads/Heads, Heads/Tails and Tails/Tails.
As there are three possible outcomes there is a 1 in 3 chance when tossing the coins they will both land on heads. This is written as 1/3.
Step 3: In pairs write the probability of the following occurring as a fraction.
- There are 10 marbles (5x blue, 2x pink and 3x green). What is the probability of a pink marble being chosen?
- There are six animals in a barn (2x chickens, 1x cow and 3x sheep). What is the probability that a sheep will escape?
- I have 14 pieces of fruit (4x bananas, 6x apples, 3x oranges and 1 x pear). What is the probability that you will be given an orange to eat?
Task 2: Labelling a two way table to record results
One way to show data of experimental probability is to collate it into a table.
Step 1: Copy the table below into your workbook.
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Colour Spun |
Tally |
Total |
Frequency as a fraction |
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Red |
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Blue |
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Yellow |
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Green |
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Step 2: Let’s use this interactive colour wheel (click the link below) which automatically spins and record the results in the table.
Step 3: Record in your work book the probability of the needle landing on yellow:
- as a fraction?
- using terms such as likely, equal, certain, unlikely or impossible?
Extension ActivityLooking at the picture below answer the following questions:
Image retrieved from https://www.pikpng.com/pngvi/imxoRmR_probability-and-statistics-in-color-marble-jar-clip-art-png-download/ |
Lesson 4: Tying it all together
Task 1: Roll a 6 sided die 50 times.
To make things fun and different instead of using an actual die let’s use the below interactive die.
Step 1: Draw a table in your workbook to record your results.
Step 2: click on the link and press play to roll the die then press pause to stop the die.
Step 3: Tally the results in the table.
Step 4: record the end result of total times each face was rolled as a fraction.
Step 5: Answer the following questions based on your results:
- What number was thrown the most/least?
- Why do you think that is?
- Do you think if you did this challenge again you would get the same result? Why/Why not?
Task 2: What have we learned so far?
Click the links below to complete the following online quiz’s. This will help you to see what areas (if any) you need more help on or to revisit prior to our next lesson which is the final assessment.
https://au.ixl.com/maths/year-5/find-the-probability
https://au.ixl.com/maths/year-5/understanding-probability
Extension Activity
Image retrieved from https://brainly.ph/question/11502529Using the colour wheel above answer the following questions
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Lesson 5:Experiement Assessment
The mathematics behind the popular game of Rock, Paper, Scissors (otherwise known as Jan-Ken-Pon) is investigated in this probability assessment. In pairs students play the game Rock, Paper, Scissors, make a list of possible outcomes, and evaluate theoretical and experimental probabilities. This assessment looks at how well students work with a peer, how they collect data and use this data to answer questions based on their findings.
First, let’s look at how we play Paper, Rock Scissors.
After your teacher has explained the game of Rock, Paper, Scissors, it's up to you to apply all of your understanding of chance and probability from previous lessons to predict which gesture will win the game!
Please remember whilst you are playing this game in pairs the work completed is your own. Each student will need to submit their own work for marking
Helpful Hints
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Task 1: Predict
This is your chance to make an educated guess as to which gesture will be the winner! Remember each gesture has an equal chance in theory, but what is changing that chance?
Task 2: Play and record
- Play the game rock, paper, scissors 100 times with you partner.
- Record the results of each combination played in a table individually (Hint: we have been using a tally to record results in a table).
- Convert the results of each combination played as a fraction.
Task 3: Interpret your results
Answer the following questions independently:
- Which gesture was more likely to arise?
- Which gesture was least likely to arise?
- If you were to play this game again do you think you would get the same results? Yes/no and why/why no
Extension Activity
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Evaluation
Teachers to complete
Assessment Rubic:
Name:___________________
Date:____________________
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Criteria |
All criteria exceeded
Pts 5 |
All criteria achieved
Pts 4 |
Some criteria achieved
Pts 2 |
No criteria met
Pts 0 |
Score |
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Records data of a repeated chance experiment |
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/5 |
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Correctly identifies chance experiment outcome |
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/5 |
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Able to identify the probability of an event occurring using a fraction |
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/5 |
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Can sequence events from most likely to least liekly |
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/5 |
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Able to transfer data collected into a graph and answer questions based on results. |
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/5 |
Overall Grade:
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Excellent Achievement 21 - 25 pts |
High Achievement 16 – 20 pts |
Satisfactory Achievement 10-15 pts |
Limited Achievement 5-10 pts |
Very Low Achievement 0-5 pts |
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Creates successful chance experiments, predicts all possible outcomes and represents the probabilities between 0 to 1 and uses fractions. |
Predicts the outcomes of chance experiments and represents the probabilities between 0 to 1 and uses fractions. |
Lists the outcomes of chance experiments with equally likely outcomes, and states probabilities between 0 and 1. |
List some of the possible outcomes in chance experiments. |
Does not meet the requirements of ‘Limited Achievement’. |
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Credits
ACARA Australian Curriculum Assessment and Reporting Authority. (2018). Foundation to year 10 curriculum. Retrieved from https://www.australiancurriculum.edu.au/f-10-curriculum/mathematics/
SCSA School Curriculum and Standards Authority. Government of Western Australia. (2014). Judging Standards. Retrieved from https://k10outline.scsa.wa.edu.au/home/extranet/login
Siemon, D., Beswick, K., Brady, K., Clark, J., Faragher, R., Warren, E. (2021). Teaching Mathematics Foundations to Middle Years (3 rd ed.). Australia and New Zealand: Oxford University Press.
Website: https://www.youtube.com for all videos and interactive games of chance used throughout this WebQuest.
Images retrieved from:
https://brainly.ph/question/11502529
Teacher Page
Curriculum Strand: Statistics and Probability
Content Descriptor: Chance
Curriculum Descriptor: List outcomes of chance experiments involving equally likely outcomes and represent probabilities of those outcomes using fractions (ACMSP116)
Prior knowledge: In line with the Australian Curriculum students would have been exposed to the following prior knowledge:
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Foundation |
Year 1 |
Year 2 |
Year 3 |
Year 4 |
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Students will answer simple questions (e.g. yes/no) to collect information and make simple inferences (ACMSP011). |
Students identify outcomes of familiar events involving chance, describing them using everyday language such as ‘will happen’, ‘won’t happen’, or ‘might happen’ (ACMSP024). |
Students collect, organise and represent data to make simple inferences and describe outcomes as ‘likely’ or ‘unlikely’ and identify events as ‘certain’ or ‘impossible’ (ACMSP047). |
Students conduct chance experiments, identify and describe possible outcomes and recognise variation in results (ACMSP067) thus enabling them to interpret and compare data displays. |
Students will describe possible events and order the chance of these events occurring (ACMSP092). |
Proficiencies:
Image retrieved from https://www.education.vic.gov.au/school/teachers/teachingresources/discipline/maths/Pages/teaching-practices-and-supports.aspx
| Fluency | Students will be collecting and recording data and apply it to create simple fractions. |
| Reasoning | Students will interpret results of chance experiments, compare the outcomes and communicate this information demonstrating their reasoning ability. |
| Problem Solving | Students will be using estimation ensuring that answers to possible outcomes are realistic. |
| Understanding | Students using fractions to represent the probability of events occurring and using appropriate vocabulary to demonstrate their understanding of chance. |
The source for the curriculum is the Australian Curriculum – Mathematics Foundation to Year 10 scope and sequence. Please clink on the link to access further information on this https://www.australiancurriculum.edu.au/f-10-curriculum/mathematics/