Introduction
What is Probability?
When you listen to weather forecasts, you could hear expressions like these, 'Today there is a 10% chance of rain', 'In the afternoon, there is a possibility of thunder', 'There is a strong likelihood of rain tomorrow'. Because weather forecasts are made by studying charts and weather data to tell us how likely it is. What is the probability of rain in Darwin today?
TODAY’S WEATHER FORECAST
Darwin-Daly for Wednesday Cloudy. Very high chance of showers, most likely during the morning and early afternoon. The chance of a thunderstorm. Winds N 15 to 25 km/h tending NW in the morning then becoming light in the late afternoon.
http://www.bom.gov.au/nt/forecasts/darwin.shtml
As Darwin forecast updated at 1:30pm on Wednesday 23 December 2020, it is partly cloudy but very high (95%) chance of showers.
Let's move onto the next step which is required you to have a look at the clip slides of Probability & Chance and it gives you a clear explanation of the mathematical concepts 'Probability & Chance'!
https://www.slideshare.net/cbsroscommon/probability-chance
Let's try to have a fun game throughout watching a YouTube clip!
https://www.youtube.com/watch?v=IuqK4PPdvPE
Task
- Topic: Probability
- Year level: 4
- Learning goal: Students will develop their understanding of chance by identifying practical activities and events that involve chance and understanding of the mathematical concept; the use of common chance terms such as likely, unlikely, certain, uncertain, possible and impossible by partaking in a variety of hands-on chance activities to investigate data.
- Prior knowledge linked to the topic: To begin with a connection to prior knowledge, I will brainstorm a list of words that could be used to describe the chance of an event occurring such as likely, unlikely, impossible etc. and students will undertake a pre-assessment. This will help me determine how the lesson's learning target fits within the mathematics learning progression of the sequenced math lessons to support students in accessing this topic (Solution Tree Press, 2018).
- Proficiency strands in relation to Probability at Year 4:
'Teaching is for learning, learning is for understanding, understanding is for reasoning and applying and, ultimately problem-solving.'
(Cited in Scholastic Pr1me Mathematics, n.d.)
1. Understanding: To build up a robust understanding of math, I would like you to begin with a fun activity as this recalls the conceptual knowledge of probability using a worksheet of 'possible or impossible' as an introductory of the sequenced lessons.
2. Fluency: To carry out procedural fluency in the lesson, I would like you to focus on solving problems by providing a variety of games and hands-on activities using ICT to access to createwebquest.com.
3. Reasoning: As students love exploring, questioning and reasoning, I believe you would gain a deeper conceptual understanding of mathematics through reasoning.
4. Problem- Solving: The importance of problem-solving in learning mathematics is primarily about reasoning, not memorization (Klerlein & Hervey, n.d.). This allows students to develop their conceptual understanding and problem-solving skills as a result of solving problems (Pennant, 2014). I would also promote you discussion in small groups, encourage you to have "what if?" or "what if not?" questions and provide learning resources to solve problems within the students' zone of proximal development (Vygotsky as cited in Klerlein & Hervey, n.d.).
To check out your prior knowledge linked to the topic, I would like you to watch a YouTube clip, Probability and it tells you to understand the mathematical concepts such as equal, likely, unlikely, certain and impossible.
.gif)
Process
Lesson 1:
Have you heard about the mathematical term Probability? You might have heard some terms of chances such as likely, unlikely, certain and possibly from the weather forecast. To recall your prior knowledge of probability using a worksheet and encourage you to predict the likelihood of a quiz based on the possible outcomes.
Now, it's time for you to take a pre-assessment with me. Are you ready? Once you have completed the assessment paper, please be patient to wait for all your classmates finished. Good job if you complete the worksheet of pre-assessment.
https://easyteaching.net/wp-content/uploads/2017/07/probabilityeventspossibleimpossible.pdf
Here is a quick quiz of Possibly or Possibly not for you to solve the problem.
Organize the statements in order from least likely to most likely.
1. The sun will come up in the morning.
2. It will rain tomorrow.
3. Our school will win the interschool sports carnival this year.
4. My favorite band will perform a concert at our school next week.
https://www.globaleducation.edu.au/teaching-activity/probability-and-pancakes-3-4.html
Here is the link to the answer. After organizing the statements in order, you can share your answer with other classmates.
Lesson 2:
In lesson 2, you will connect to the previous lesson with engaging an activity with a dice in a small group. I set up all resources and materials for this game and when dividing into small groups, differentiation by each student's math capacity will be applied after pre-assessment.
Each group will be given a worksheet and a dice. You need to design a 6-sided dice that has a higher probability of landing on a 3. Once you have completed a worksheet, you need to discuss the question 'How does your dice meet the design challenge?' within the group.
https://easyteaching.net/wp-content/uploads/2017/07/dicechallenge.pdf
*Catering appropriate assessment for diverse learning needs:
For low-level students can undertake a differentiated activity using a worksheet from
https://easyteaching.net/wp-content/uploads/2017/07/probabilityevents4own.pdf
I have also attached a few examples of each probability term along with, so that low-level students can match the statements with each question.
For fast finishers: Students finish earlier can have a turn to match the statements in order using the probability terms and check the answers out independently.
Then, the teacher needs to provide feedback to each student and mark their assessment. This assessment will show teachers in Probability that low-level students are confident in using and understanding, and the mathematical terms such as certain, probable, unlikely or impossible that they can focus on more in the next lesson.
Lesson 3:
To describe the likelihood of everyday events, you will use interactive PowerPoint Presentation by teachstarter.com as a learning resource and provide you 17 problems presented in the paper as when you click the link, there will be only 2 problems coming up without login, therefore, teacher will print out 15 other problems and let you divide into small group with a dice. As you go through all problems together, you can share the results with your partner and will get the answer sheets after investigation.
https://www.teachstarter.com/au/teaching-resource/chance-middle-years-powerpoint/
Because of login issues, I have attached link to 17 questions & answers through Google Drive for you to solve those questions only.
*Catering appropriate assessment for diverse learning needs:
Teachers can divide students into 4 levels to cater for the required differentiation. The lowest group can be leading all those questions by one on one adult assistance and see if they recognize the meaning of terms such as certain, even chance, definite or unlikely, etc. in relation to the understanding of probability. The highest group is working towards understanding probability challenges throughout some worksheets or different games. Dividing students into small groups will help teachers use the assessment information to explicitly teach students having challenges and in which areas in a small group.
Lesson 4:
To use common chance terms and begin to record all the possible outcomes (Australian Mathematical Sciences Institute [AMSI], 2018), you will be provided a chance of a few different experiments and use this information for the variation in results. At the end of the lesson, you will be able to order the term 'chance' in order of likelihood and match the events with each term.
'Head or Tail' game (p.4-5) from education.com
In lesson 4, you will be asked to order events worksheets from AMSI calculate.org.au and you need to place chance terms in order of likelihood such as likely, certain, equal chance, no chance, impossible, unlikely, along the continuum and then match the events to their likelihood of occurring (AMSI, 2018). This following activity is aimed to see if students have any misconceptions regarding the use of common chance terms (AMSI, 2018) and encourage students to understand an event that has happened by chance as a result of the relevant games (Bryant & Nunes, 2012).
https://calculate.org.au/wp-content/uploads/sites/15/2018/12/ordering-events.pdf
*For fast finishers, here is the link to the probability quiz. Once you click it, there are 10 questions coming up. You need to read carefully and click one answer for each question. when you are ready to submit your answers, click on the button 'Send answers' below. You can also check out your wrong answers. Good luck!
http://www.rasmus.is/uk/t/U/st12p01.htm
Lesson 5:
To finalise and assess your knowledge and understanding about probability, you will be given a final assessment task along with smarties. Final lesson consists of the summative assessment and you will be provided to complete the assessment task. Moderate sample work from Australian Curriculum to ensure reliability and moderation with rubric to make reasonable judgement for you and other students (Australian Curriculum, Assessment and Reporting Authority [ACARA], 2014, p. 35-36).
https://docs.acara.edu.au/curriculum/worksamples/Year_4_Mathematics_Portfolio_Satisfactory.pdf
Lesson 5 Summative Assessment Worksheet
Evaluation
| Excellent | Good | Satisfactory | Limited/ incomplete | |
|
Lesson 1 Possible/ Impossible |
Identification of possible and impossible events and ordering of their chances of occurring |
Description of possible and impossible events | Listing of possible and impossible events | Limited understanding of possible and impossible events |
|
Lesson 2 Dice games/ group work |
Demonstrate their prior knowledge of probability and develop their understanding of the topic/ Contributes to each group discussion by providing relevant information and understand the topic clearly |
Demonstrate their prior knowledge of probability appropriately/ Contribute to each group discussion by providing information fairly |
Attempt to use their prior knowledge of probability and try to understand of the topic/ Attempt to share ideas and provide simple information |
Attempt to little effort to understand the topic and show little interest to contribute to the group discussion |
|
Lesson 3 & 4 Problem solving
|
Strong understanding of the question and can predict the likelihood of a specific outcome occurring in chance questions | Are able to predict the likelihood of a specific outcome occurring in chance questions | With some help, student can predict the likelihood of a specific outcome occurring in chance questions | Having some trouble to solve questions and require extra support |
|
Lesson 5 Summative Assessment
|
Student can record answers to show information independently and have a strong understanding of the topic thoroughly | Student can record answers on their own and can explain the topic clearly | With some help, student can record answers and require continued work in order to improve understanding of the topic | Having some trouble to record answers and require differentiation to complete the tasks |
*Please see the link below to the feedback of the student who tested my learning material->
Conclusion
Throughout the hypothetical learning trajectory was used to create hands-on chance games and experiments resources in the form of a webquest to present Assignment 2. This webquest will be used to provide students a variety of learning resources such as quiz and games offering handy and visual tools as well as provide a clear explanation of the language of chance to support diverse learners (Siemon et al., 2015, p.264).
References:
Australian Curriculum Assessment and Reporting Authority [ACARA]. (2014). Foundation to year 10 curriculum: Understand how mathematics works. Retrieved from
https://australiancurriculum.edu.au/f-10-curriculum/mathematics/?year=11755&strand=
Australian Government Bureau of Meteorology. (2020). Darwin Forecast. Retrieved from
http://www.bom.gov.au/nt/forecasts/darwin.shtml
Australian Mathematical Sciences Institute [AMSI]. (2018). Chance Year 3 & 4. Retrieved from
https://calculate.org.au/2018/12/07/chance-year-3-4/
Bryant , P., & Nunes, T. (2012). Children's understanding of probability: A literature review (full report). London: Nuffield Foundation. Retrieved from
https://www.nuffieldfoundation.org/sites/default/files/files/Nuffield_CuP_FULL_REPORTv_FINAL.pdf
CBS Roscommon. (2012). Probability & Chance. Retrieved from
https://www.slideshare.net/cbsroscommon/probability-chance
EasyTeaching.net. (2016). Chance and Probability Worksheets. Retrieved from
https://easyteaching.net/wp-content/uploads/2017/07/probabilityeventspossibleimpossible.pdf
EasyTeaching.net. (2016). Probability Challenge Worksheets. Retrieved from
https://easyteaching.net/wp-content/uploads/2017/07/dicechallenge.pdf
EasyTeaching.net. (2016). Probability Events Worksheets. Retrieved from
https://easyteaching.net/wp-content/uploads/2017/07/probabilityevents4own.pdf
Education.com. (2015). Heads or Tails worksheet: All About Probability (p.4-5). Retrieved from
Gayowksy, A. (2013). Probability Fun. Retrieved from
https://www.youtube.com/watch?v=IuqK4PPdvPE
Global Education. (2012). Probability and pancakes. Retrieved from
https://www.globaleducation.edu.au/teaching-activity/probability-and-pancakes-3-4.html
Hotmath. (2007). Using Probabilities to Make Fair Decisions. Varsity Tutors. Retrieved from
Johnson, L. (2020). How To Calculate Dice Probabilities. Retrieved from
https://sciencing.com/calculate-dice-probabilities-5858157.html
Klerlein, J., & Hervey, S. (n.d.). Mathematics as a Complex Problem-Solving Activity. Generation Ready. Retrieved from
https://www.generationready.com/mathematics-as-a-complex-problem-solving-activity/
Kwon. M. (2021). Lesson 3 Chance Middle Years PowerPoint Slides: 17 Questions & Answers. Retrieved from
Kwon. M. (2021). Lesson 5 Summative Assessment. Retrieved from
https://docs.google.com/document/d/1-IsM8bhDdcAWJsUEKOmfB8hgpFXjBaQ0oD2O7-MJlAg/edit
Kwon, M. (2021). Probability Quiz. Retrieved from
New Path Learning. (2016). Probability. Retrieved from
https://newpathworksheets.com/math/grade-2/probability-5
NSW Department of Education. (2020). Teaching strategies: Stage 4- number- probability. Retrieved from
Pennant, J. (2014). Developing Excellence in Problem Solving with Young Learners. NRICH. Retrieved from
Probability Quiz. (2004). Retrieved from
http://www.rasmus.is/uk/t/U/st12p01.htm
Project Maths. (2009). Teaching & Learning Plans- Plan 1: Introduction to Probability. Junior Certificate Syllabus. Retrieved from
https://www.projectmaths.ie/documents/T&L/IntroductionToProbability.pdf
Scholastic Pr1me Mathematics. (n.d.). Proven to be the world's best practice: Why Pr1me Works. Retrieved from
http://scholasticprimemathematics.com/en/prime-maths-proven-best-practices
Siemon, D., Beswick, K., Brady, K., Clark, J., Faragher, R., & Warren, E. (2015). Teaching Mathematics: Foundation to Middle Years (2nd ed.). Melbourne: VIC: Oxford University Press.
Solution Tree Press. (2018). Prior-Knowledge War-Up Activities: Mathematics Instruction & Tasks In A Pic At Work. Retrieved from
https://www.solutiontree.com/free-resources/mathematicsatwork/mitplcw/
Teachers Pay Teachers. (2016). Smartie Maths- Chance, Probability and Data Activity. Retrieved from
Teach Starter. (2020). Chance Middle Years PowerPoint. Retrieved from
https://www.teachstarter.com/au/teaching-resource/chance-middle-years-powerpoint/
Turtlediary. (2013). Probability- Equal, Likely, Unlikely, Certain, Impossible- Grade 3 Math Lesson. Retrieved from
https://www.youtube.com/watch?v=rlUZXrJGuf8
Washington, B. (2016). Exploring Probability Grade 3-4. Retrieved from
https://slideplayer.com/slide/5289886/
3P Learning. (2013). Mathlectics and the Proficiency Strands. Retrieved from
https://www.3plearning.com/blog/mathleticsproficiencystrandcheatsheet/
Credits
Resources:
* Materials that will be needed to complete all tasks-
- Dices,
- Coins,
- Smarties
- Colour pencils,
- Scissors,
- Glue sticks,
- Mathbooks.
* For group work, students will be divided into small groups (2-3 people) and will be given each worksheet along with the materials. Teacher will use a Smartboard to show students some worksheets by PowerPoint and a few YouTube clips. Students and each group also will be given I-Pad during their group work but under adult's supervision.
* Once students have completed the tasks, they need to grab mathbooks and glue all worksheets on their books. Some games and quizzes may not be provided as a paper, but students still need to record that information on their mathbooks.
Teacher Page
- Curriculum Content Strand (Australian Curriculum and Reporting Authority [ACARA], 2014):
* Describe possible everyday events and order their chances of occurring (ACMSP092)
* Identify everyday events where one cannot happen if the other happens (ACMSP093)
* Identify events where the chance of one will not be affected by the occurrence of the other (ACMSP094)
At the end of the sequenced lessons, students will undertake a summative assessment. This will show teachers the probability they are confident in using and understanding, and the mathematical concept probability that they can focus on more in the future lessons. Students will also complete a few worksheets for probability that includes few YouTube clips which are a guide to probability by helping students solve simple probability problems, encourage them to think of both words and numbers to explain probability as well as construct and discuss in a small group the approach to chance of winning games using dices and other resources (NSW Department of Education, 2020).
Chosen games and activities have been designed linked to the Australian Curriculum and aimed for Year 4 mathematics strands (see above). I strongly believe this webquest can be a useful learning tool for Year 4 mathematics as it can be used to understand for students with the ways in which we talk about uncertainty and adapt it in our everyday situations in which probability arises (Project Maths, 2009). Those chosen games and activities also can help students understand the main ideas of probability by working together in small groups, using the language of the topic probability to improve their communication skills with peers and help them justify their choice whether possible everyday events are likely or unlikely to occur. Furthermore, throughout provided games and activities, students can brainstorm different ways that they can describe the chances of something happening (NSW Department of Education, 2020), and they are clear about what they have been learnt to achieve intended learning outcomes (Siemon et al., 2015, p.53). Using complementary resources in the Maths education settings allows students to build a conceptual understanding of the knowledge and understanding content descriptors which is then evidenced through the achievement standard. Complementary resources such as games through I-Pad and activities give students an opportunity to explore concepts in a hands-on way to build their understanding. These resources can be used to inform teaching and to assess learning against the Australian Curriculum and allow students to use multiple modes of representing their learning.