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• VC2M5P01

  list the possible outcomes of chance experiments involving equally likely outcomes and compare to those that are not equally likely

  Elaborations

  • discussing what it means for outcomes to be equally likely and comparing the number of possible and equally likely outcomes of chance events; for example, when drawing a card from a standard deck of cards there are 4 possible outcomes if you are interested in the suit, 2 possible outcomes if you are interested in the colour or 52 outcomes if you are interested in the exact card
  • discussing how chance experiments that have equally likely outcomes can be referred to as random chance events; for example, if all the names of students in a class are placed in a hat and one is drawn at random, each person has an equally likely chance of being drawn
  • commenting on the chance of winning games by considering the number of possible outcomes and the consequent chance of winning
  • investigating why some games are fair and others are not; for example, drawing a track game to resemble a running race and taking it in turns to roll 2 dice, where the first runner moves a square if the difference between the 2 dice is zero, one or 2 and the second runner moves a square if the difference is 3, 4 or 5, and responding to the questions ‘Is this game fair?’, ‘Are some differences more likely to come up than others?’ and ‘How can you work that out?’
  • comparing the chance of a head or a tail when a coin is tossed, whether some numbers on a dice are more likely to be facing up when the dice is rolled, or the chance of getting a 1, 2 or 3 on a spinner with uneven regions for the numbers
  • discussing supermarket promotions such as collecting stickers or objects and whether there is an equal chance of getting each of them

  VC2M5P01 | Mathematics | Mathematics Version 2.0 | Level 5 | Probability

• VC2M5P02

  conduct repeated chance experiments, including those with and without equally likely outcomes, and observe and record the results; use frequency to compare outcomes and estimate their likelihoods

  Elaborations

  • discussing and listing all the possible outcomes of an activity and conducting experiments to estimate the probabilities (for example, using coloured cards in a card game and experimenting with shuffling the deck and turning over one card at a time) and recording and discussing the results
  • conducting experiments, recording the outcomes and the number of times the outcomes occur, and describing the relative frequency of each outcome; for example, using ‘I threw the coin 10 times, and the results were 3 times for a head, so that is 3 out of 10, and 7 times for a tail, so that is 7 out of 10’
  • experimenting with and comparing the outcomes of spinners with equal coloured regions compared to unequal coloured regions; and responding to questions such as ‘How does this spinner differ to one where each of the colours has an equal chance of occurring?’, giving reasons
  • comparing the results of experiments using a fair dice and one that has numbers represented on faces more than once, explaining how this affects the likelihood of outcomes
  • using spreadsheets to record the outcomes of an activity and calculate the total frequencies of different outcomes, representing these as a fraction; for example, using coloured balls in a bag, drawing one out at a time and recording the colour, and replacing them in the bag after each draw
  • investigating Aboriginal and/or Torres Strait Islander children’s instructive games (for example, Diyari koolchee from the Diyari Peoples near Lake Eyre in South Australia), to conduct repeated trials and explore predictable patterns, using digital tools where appropriate

  VC2M5P02 | Mathematics | Mathematics Version 2.0 | Level 5 | Probability

• VC2M5SP02

  construct a grid coordinate system that uses coordinates to locate positions within a space; use coordinates and directional language to describe position and movement

  Elaborations

  • understanding how the numbers on the axes on a grid coordinate system are numbers on a number line and are used to pinpoint locations
  • discussing the conventions of indicating a point in a grid coordinate system; for example, writing the horizontal axis number first and the vertical axis number second, and using brackets and commas
  • comparing a grid reference system to a grid coordinate system (first quadrant only) by using both to play strategy games involving location; for example, in playing the game Quadrant Commander, deducing that in a grid coordinate system the lines are numbered (starting from zero), not the spaces
  • placing a coordinate grid over a contour line, drawing and listing the coordinates of each point in the picture, asking a peer to re-create the drawing using only the list of coordinates, and discussing the reasons for the potential similarities and differences between the 2 drawings

  VC2M5SP02 | Mathematics | Mathematics Version 2.0 | Level 5 | Space

• VCMSP205

  Pose questions and collect categorical or numerical data by observation or survey

  Elaborations

  • posing questions about insect diversity in the playground, collecting data by taping a one-metre-square piece of paper to the playground and observing the type and number of insects on it over time

  VCMSP205 | Mathematics | Level 5 | Statistics and Probability | Data representation and interpretation

• VCMSP207

  Describe and interpret different data sets in context

  Elaborations

  • using and comparing data representations for different data sets to help decision making

  VCMSP207 | Mathematics | Level 5 | Statistics and Probability | Data representation and interpretation

• VCMSP203

  List outcomes of chance experiments involving equally likely outcomes and represent probabilities of those outcomes using fractions

  Elaborations

  • commenting on the likelihood of winning simple games of chance by considering the number of possible outcomes and the consequent chance of winning in simple games of chance such as jan-ken-pon (also known as rock-paper-scissors)

  VCMSP203 | Mathematics | Level 5 | Statistics and Probability | Chance

• VCMSP204

  Recognise that probabilities range from 0 to 1

  Elaborations

  • investigating the probabilities of all outcomes for a simple chance experiment and verifying that their sum equals 1

  VCMSP204 | Mathematics | Level 5 | Statistics and Probability | Chance

• VCMSP206

  Construct displays, including column graphs, dot plots and tables, appropriate for data type, with and without the use of digital technologies

  Elaborations

  • identifying the best methods of presenting data to illustrate the results of investigations and justifying the choice of representations

  VCMSP206 | Mathematics | Level 5 | Statistics and Probability | Data representation and interpretation

• VC2M5SP01

  connect objects to their nets and build objects from their nets using spatial and geometric reasoning

  Elaborations

  • designing and constructing exact nets for packaging particular-shaped items or collections of interest, taking into consideration how the faces will be joined and how the package will be opened
  • visualising folding some possible nets for a range of prisms and pyramids, predicting which will work and which cannot work, and justifying their choices, based on the number, size and position of particular shapes in each diagram
  • sketching nets for a range of prisms and pyramids considering the number, shape and placement of the faces, and testing by cutting and folding
  • investigating objects designed and developed by Aboriginal and/or Torres Strait Islander Peoples, such as those used in fish traps and instructive toys, identifying the shape and relative position of each face to determine the net of the object

  VC2M5SP01 | Mathematics | Mathematics Version 2.0 | Level 5 | Space

• VC2M5SP03

  describe and perform translations, reflections and rotations of shapes, using dynamic geometry software where appropriate; recognise what changes and what remains the same, and identify any symmetries

  Elaborations

  • understanding and explaining that translations, rotations and reflections can change the position and orientation of a shape but not its shape or size
  • using pattern blocks and paper, tracing around a shape and then conducting a series of one-step transformations and tracing each resulting image, and then finally copying the original position and end position on a new sheet of paper
  • demonstrating how different combinations of transformations can produce the same resulting image
  • challenging classmates to select a combination of transformations to move from an original image to the final image, noting the different combinations by using different colours to trace images
  • investigating how animal tracks can be interpreted by Aboriginal and Torres Strait Islander Peoples using the transformation of their shapes, to help determine and understand animal behaviour

  VC2M5SP03 | Mathematics | Mathematics Version 2.0 | Level 5 | Space

• VC2M5ST01

  acquire, validate and represent data for nominal and ordinal categorical and discrete numerical variables to address a question of interest or purpose using software including spreadsheets; discuss and report on data distributions in terms of highest frequency (mode) and shape, in the context of the data

  Elaborations

  • recognising that ordinal data is a form of categorical data even though the data being collected might be numbers, for example, a rating scale using numbers 1–5 to represent the categories people can choose from when asked, ‘What rating would you give this film out of 5?’
  • determining the mode for a set of data and discussing that there may be more than one mode
  • identifying the best methods of presenting data to illustrate the results of investigations and justifying the choice of representations
  • acquiring data through chance experiments, discussing and reporting on the distribution of outcomes and how this relates to equal and unequal outcomes
  • using digital systems to validate data; for example, recognising the difference between numerical, text and date formats in spreadsheets, and setting data types in a spreadsheet to make sure a date is input correctly
  • investigating data relating to the reconciliation process between Aboriginal and Torres Strait Islander Peoples and non-Indigenous Australians, posing questions, discussing and reporting on findings

  VC2M5ST01 | Mathematics | Mathematics Version 2.0 | Level 5 | Statistics

• VC2M5ST03

  plan and conduct statistical investigations by posing questions or identifying a problem and collecting relevant data; choose appropriate displays and interpret the data; communicate findings within the context of the investigation

  Elaborations

  • posing questions about insect diversity in the playground, and collecting data by taping a one-metre-square piece of paper to the playground and observing the type and number of insects on it over time
  • posing a question or identifying a problem of interest; collecting, interpreting and analysing the data; and discussing if the data generated provides the information necessary to answer the question
  • developing survey questions that are objective, without opinion, and have a balanced set of answer choices without bias
  • exploring Aboriginal and/or Torres Strait Islander ranger groups’ and other groups’ biodiversity detection techniques to care for Country/Place, posing investigative questions, and collecting and interpreting related data to represent and communicate findings

  VC2M5ST03 | Mathematics | Mathematics Version 2.0 | Level 5 | Statistics

• VC2M5ST02

  interpret line graphs representing change over time; discuss the relationships that are represented and conclusions that can be made

  Elaborations

  • reading and interpreting different line graphs, discussing how the horizontal axis represents measures of time such as days of the week or times of the day, and the vertical axis represents numerical quantities or ordinal categorical variables such as percentages, money, measurements or ratings such as fire hazard ratings
  • interpreting real-life data represented as a line graph showing how measurements change over a period of time, and make simple inferences
  • matching unlabelled line graphs to the context they represent based on the stories of the different contexts
  • interpreting the data represented in a line graph, making inferences; for example, reading line graphs that show the varying temperatures or ultraviolet (UV) rates over a period of a day and discussing when would be the best time to hold an outdoor assembly

  VC2M5ST02 | Mathematics | Mathematics Version 2.0 | Level 5 | Statistics

• VCNRC035

  Initiate interactions and exchange information with peers, describing feelings and preferences, aspects of daily life, school, friends and hobbies

  Elaborations

  • asking and responding to questions to exchange information about shared interests, hobbies or friends
  • sharing experiences and feelings, such as weekend activities and likes/dislikes using set phrases
  • using communication strategies such as active listening skills, turn-taking cues and requests for clarification or more detail to support the exchange of information
  • comparing routines, interests and hobbies, using language associated with time, sequence and location

  VCNRC035 | Capabilities | Critical and Creative Thinking | Levels 5 and 6 | Communicating | Socialising

• VCNRC045

  Share experiences of learning and using the language being studied, and reflect on the effect of language learning on own identity

  Elaborations

  • preparing a class profile to exchange with students who speak the language being studied, showing language backgrounds and interests represented in the class, using captions and symbols such as flags and words from different languages
  • exploring the idea of stereotypes associated with languages and identities, and discussing how stereotypes affect attitudes and communication and can be inaccurate
  • exploring how their linguistic and cultural background, for example, languages spoken, key relationships and intercultural experiences, influence their sense of who they are
  • connecting various personal experiences of learning the language, and describing how learning the language has influenced own everyday behaviour and language use, for example, using the language outside the language classroom
  • considering whether learning and using the language impacts on their sense of identity either in or out of the classroom

  VCNRC045 | Capabilities | Critical and Creative Thinking | Levels 5 and 6 | Communicating | Reflecting

• VCNRC040

  Listen to, read and view imaginative texts and respond by expressing feelings and opinions about the storyline, themes and characters

  Elaborations

  • responding to stories, myths, fables and films, using modelled language to describe themes, characters and actions
  • producing storyboards to represent key events in different types of imaginative texts, including captions or word bubbles to capture moods or feelings
  • introducing and comparing favourite characters in stories, myths, fables and films, listing associated key words or expressions
  • commenting on elements of humour and drama, and the use of sound effects and facial expressions relating to the characters depicted in stories, myths and fables

  VCNRC040 | Capabilities | Critical and Creative Thinking | Levels 5 and 6 | Communicating | Creating

• VCNRC042

  Translate simple texts from the language being studied to English and vice versa, identifying words and expressions that do not always translate literally and may have more than one meaning

  Elaborations

  • comparing translations of written texts such as advertisements, websites, food packaging and menus, and considering how meanings may be interpreted from a different cultural perspective
  • translating simple sentences, noticing that there is not always word-for-word equivalence
  • recognising that some words cannot be translated into English without losing some of the meaning, or cannot be translated using only one word
  • identifying and explaining expressions and idioms that do not make sense when translated word-for-word
  • explaining to the teacher, peers and family how some words may have many different meanings

  VCNRC042 | Capabilities | Critical and Creative Thinking | Levels 5 and 6 | Communicating | Translating

• VCNRC036

  Collaborate in group tasks and shared experiences which involve planning, making suggestions and completing transactions

  Elaborations

  • planning and organising an event, such as inviting a special guest to speak to the class about celebrations or to share a traditional recipe
  • working with another group, for example, by reading books to younger students, or teaching a skill, such as dyeing eggs, to another class
  • planning and organising an activity such as an excursion or party, using expressions related to place, time and numbers
  • creating displays, presentations or performances for family, friends or the school community to showcase their progress in learning the target language or to promote the learning of the target language and culture

  VCNRC036 | Capabilities | Critical and Creative Thinking | Levels 5 and 6 | Communicating | Socialising

• VCNRC039

  Convey and present information about aspects of personal world, through prepared texts such as diagrams, dialogues and timelines

  Elaborations

  • constructing a visual, digital or narrative profile of the local community for people arriving from overseas, collecting information from public and community texts, such as fliers, newsletters, advertisements and brochures
  • preparing and giving simple oral presentations on personal world, for example, a timeline of growth and change, family celebrations and other special occasions
  • presenting the results of a class survey about aspects of personal world such as daily routines, for example, by creating a poster or digital presentation using diagrams, charts or timelines
  • conveying information to others using descriptive language, for example, producing a simple brochure or an advertisement about a city or tourist attraction in a country where the language is spoken
  • preparing a dialogue with a partner about self
  • using graphic organisers to convey information in particular ways, for example, to show priorities (list/table), to compare statistics or ideas (Venn diagram), or to highlight frequency (graphs)
  • reporting information based on own or group research, and supporting the information with photos, illustrations, captions or diagrams

  VCNRC039 | Capabilities | Critical and Creative Thinking | Levels 5 and 6 | Communicating | Informing

• VCNRC037

  Interact in class activities, using questions, statements and responses to enhance, demonstrate and share understanding

  Elaborations

  • collaborating with peers during individual or group activities
  • checking on progress during learning tasks or activities
  • asking peers politely to do something and responding to requests, for example, giving and receiving things
  • talking about the experience of learning and using the language, comparing what they can and cannot do

  VCNRC037 | Capabilities | Critical and Creative Thinking | Levels 5 and 6 | Communicating | Socialising