MATHEMATICS FOR UNDERSTANDING

[Audio] Welcome to the learning activity Statistics and Probability.

[Audio] Big idea is understanding Chance. Dice and pins on a board game.

[Audio] The learning activity is based around Statistics and Probability addressing the Victorina Curriculum and Assessment and Authority. The activity I have designed is A probability game based around the idea of Chance which allows students to experiment situations that involve chance and probability which will steer students in finding outcomes of results..

[Audio] The activity involves students working in groups of two in a game of tossing TWO- DICE. While playing the game students 1 records student 2 roles which will be odd and student 2 records S1 which be even. After multiple trails based on their game students will then go to kept tally and figure out the number of even rolls, odd rolls and total of rolls and if any other factors play apart of the roll. The main purpose of this is to calculate probability in a game involving the toss of two dice. The mathematics behind it is to determine the probability of chance in each outcome in the exploration of the game by rolling the dice, and then calculating the possible sum or amount, and the determining if the information presents are impossible, likely, or certain events of winning the game involving even and odd numbers. Possible questions to aske throughout the game; Q: If we play this game involving odds and even how likely is it we roll an even or an odd? Q: Which odd or even number will occur the most? If so, why do you think this number? After collecting their data students will analyse, interpert and come to conclusions of what the data is representing of likely outcome or certain outcomes of winning the game? At the end bring student all into one group discuss and debrief on the activity and pose pervious questions along with new questions such as; . Q: what would happen if their had 3 dice? Or 4? Q: What I we used different changes of dice with more numbers? Will this be fair game ? Students understanding that the experiment will have a randome outcome..

[Audio] Extending the activity by giving a worksheet to see what students picked upon and their understanding of the studied topic first by discussing indivuldaul, groups and whole class the outcome of the results. IN This activity students need to understand that probability in rolling a dice is just as likely as a event that can occur. Also, figuring out the value is likely 1/6 of a fraction for each roll..

[Audio] The Personal and Social Capability is essential PART OF THE LESSON AS it aids students in understanding themselves and other while working more effectively. Victorian curriculum supports this with further learning of students in evaluating, expressing thoughts and working in groups preparing them for real word issues.

Resources needed. Dice Maths books/ workbook? Sticky notes Pens Paper & Coloured paper Fraction chart Extension activity questions.

[Audio] The framework of this activity focus on using inquiry-based learning as it supports students in critical skills such as creating and sharing information with their peers. According to Kath Murdoch ( 2009) when student's natural curiosity is awakened they develop their own learning and become more engaged in problem-solving and reflect, think critical in solving challenging activities. Therefore, the way we investigate, interact and communicate with our students throughout the activity is a crucial step in steering students with question posing. Allowing student to work together to uncover possible challenges and problems within the activity, this is a clear indication of how they reveal or clarify drawing on prior leaning or new gained knowledge. Supporting students in figuring out more for themselves which gradually exposes their learning. these are some of the things that students are confronted with their thinking in inquiry learning..

[Audio] Range of possibilities The teacher guides students that might have Misconceptions about probability & chance whic . ( Booker 2014, 532, 534) mentions these to be: The language that is used Perception on ideas about possible probability effecting the outcome..

[Audio] These can be addressed by showing students that the event or outcomes are independently to the other roll. Like the first roll is not connected to pervious roll and has a equal roll of probability in new trail. Furthermore, student need to be exposed to chance event game more to break the misconception of chance language and questioned on what likely and unlikely mean in a event when there are more possible outcomes. therefore, making sure students understand key language and meaning of probability terms, such as randomness, variation, intendent and data interpreting by adding real world concepts that students are intrigued by..

[Audio] Encouraging students with what they already now. Low level students will be supported with their predictions with theoretical information and results of the game which they will apply and assess the game with the likely, unlikely event of the dice occurring and guided in describing the language used. At level students will supported by questions of the own and be able to justify their own ideas on rolling dice and answer posed questions. Above level students will supported by asking to use fraction as well as 10 side dice experimenting with higher numbers and large trails. in this activity students need to understand that probability in rolling dice is just as likely as an event can occur and how the value is likely 1/6 of a fraction for each roll with one dice and 1/12 with two dice. Students need to understand for some event the chance of possible outcomes can be predicted. However, the outcome of chance can never be predicted with 1000% confidence..

Mathematics / Level 4 / Statistics and Probability / Chance Describe possible everyday events and order their chances of occurring Elaborations using lists of events familiar to students and ordering them from ‘least likely’ to ‘most likely’ to occur (VCMSP175) Content description Identify everyday events where one cannot happen if the other happens Elaborations using examples such as weather, which cannot be dry and wet at the same time (VCMSP176) Content description Identify events where the chance of one will not be affected by the occurrence of the other Elaborations explaining that the probability of a new baby being either a boy or a girl does not depend on the sex of the previous baby (VCMSP177) Mathematics / Level 6 / Statistics and Probability / Chance Describe probabilities using fractions, decimals and percentages Elaborations investigating games of chance popular in different cultures (VCMSP232) Content description Conduct chance experiments with both small and large numbers of trials using appropriate digital technologies Elaborations conducting repeated trials of chance experiments, identifying the variation between trials and realising that the results tend to the prediction with larger numbers of trials (VCMSP233) Content description Compare observed frequencies across experiments with expected frequencies Elaborations predicting likely outcomes from a run of chance events and distinguishing these from surprising results (VCMSP234).

[Audio] Assessment for this activity, I considered where the learners where at and how respond differently to the activity. As Sullivan 2011 p 5 suggests that all students require questions that are not procedural, but they taught how to problem solve and reasoning in understanding mathematics and choosing relevant context for students learning. I chose to formatively assess students with random questions and annotate work sample from their maths books as well as ending the activity with a worksheet to see how students have extended their thinking and understand chance of probability as well as seeing if student where able to learn from the peers and figure out if it was a fair game. The worksheet aids me in evaluating students understanding and learning. Booker ( 2020) suggests the maths book is a supportive element in keeping track of student's development which I have in cooperated into my lesson to make informed decisions and interact with the students throughout the task using the assessment for, as, of through the lesson..

Probability is an important life skill…. A group of yellow figures and a red figure on the other side.

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