Search results

Result list

• VC2M7N10

  use mathematical modelling to solve practical problems involving rational numbers and percentages, including financial contexts such as ‘best buys’; formulate problems, choosing representations and efficient calculation strategies, designing algorithms and using digital tools as appropriate; interpret...

  Elaborations

  • modelling additive situations involving positive and negative quantities; for example, a lift travelling up and down floors in a high-rise apartment where the ground floor is interpreted as zero, or in geography when determining altitude above and below sea level
  • modelling contexts involving proportion, such as the proportion of students attending the school disco, proportion of the bottle cost to the recycling refund, proportion of the school site that is green space, 55% of Year 7 students attended the end of term function or 23% of the school population voted ‘yes’ to a change of school uniform; and interpreting and communicating answers in terms of the context of the situation
  • modelling financial problems involving profit and loss, credits and debits, gains and losses; for example, holding a fundraising sausage sizzle and determining whether the event made a percentage profit or loss
  • finding the sum of a set of consecutive numbers using a loop structure
  • constructing geometric patterns such as a honeycomb, using dynamic geometry functionality
  • using mathematical modelling to investigate the proportion of land mass/area of Aboriginal Peoples’ traditional grain belt compared with Australia’s current grain belt

  VC2M7N10 | Mathematics | Mathematics Version 2.0 | Level 7 | Number

• VC2M9P01

  list all outcomes for two-step chance experiments both with and without replacement, using lists, tree diagrams, tables or arrays; assign probabilities to outcomes and events

  Elaborations

  • discussing two-step chance experiments, such as the game of heads and tails, describing the different outcomes and their related probabilities 
  • using systematic methods such as lists or arrays to record outcomes and assign probabilities, such as drawing the names of students from a bag to appoint 2 team leaders
  • using a tree diagram to represent a three-stage event and assigning probabilities to these events; for example, selecting 3 cards from a deck, assigning the probability of drawing an ace, then a king, then a queen of the same suit, with and without replacing the cards after every draw
  • assigning probabilities to compound events involving the random selection of people from a given population; for example, selecting 2 names at random from all of the students at a high school and assigning the probability that they are both in Year 9

  VC2M9P01 | Mathematics | Mathematics Version 2.0 | Level 9 | Probability

• VC2M4P01

  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

  Elaborations

  • using lists of events familiar to students and ordering them from ‘least likely’ to ‘most likely’ to occur; and considering and discussing why the order of some events might be different for different students
  • predicting the outcome of a coin toss after 5 heads have been tossed in a row, discussing the assertion that because so many heads came up, it is more likely that a tail rather than a head will come up next; and discussing with reasons why this assertion is correct or incorrect
  • predicting how likely it is – from least likely to most likely – that they would select a red ball from a bag containing 10 red balls and 5 white balls, from a bag containing 20 of each, or from a bag that has 25 red balls and 20 white balls, justifying their decision
  • identifying school activities where the chance of them taking place is affected by the chance of other events occurring; for example, given that there is a high chance of a storm on Friday, there is only a small chance that the coastal dune planting project will go ahead
  • listing the outcomes of everyday chance situations and identifying where one cannot happen if the other happens; for example, discussing that it cannot be hot and cold at the same time, or selecting a card from a deck and discussing if it is red it cannot be a spade or a club
  • identifying different dependent events where the chance of one outcome occurring will be affected by the occurrence of other outcomes and different independent events where the chance of one outcome occurring will not be affected by the occurrence of other outcome(s)

  VC2M4P01 | Mathematics | Mathematics Version 2.0 | Level 4 | Probability

• VC2M7M02

  solve problems involving the volume of right prisms including rectangular and triangular prisms, using established formulas and appropriate units

  Elaborations

  • building a rectangular prism out of unit cubes and showing that the measure of volume is the same as would be found by multiplying the 3 edge lengths or by multiplying the area of the base by the height/length
  • developing the connection between the area of the parallel cross-section (base), the height and the volume of a rectangular or triangular prism to other prisms
  • connecting the area of the floor space and the number of floors of a high-rise building to calculate the volume of a building
  • using dynamic geometry software, spatial reasoning and prediction to derive the formula for the volume of prisms

  VC2M7M02 | Mathematics | Mathematics Version 2.0 | Level 7 | Measurement

• VC2MFM01

  identify and compare attributes of objects and events, including length, capacity, mass and duration, use direct comparisons and communicate reasoning

  Elaborations

  • using language to describe the measurement attributes of length, mass, capacity and duration, and connecting the words with the appropriate attribute; for example, using words like ‘tall’, ‘short’, ‘wide’, ‘long’ and ‘high’ to describe the attribute of length
  • directly comparing pairs of objects to say which is longer/shorter, and explaining or demonstrating how they know; for example, standing back-to-back to determine who is taller or choosing to line up the bases of a spoon and fork to decide which is longer and explaining why
  • starting 2 events at the same time to decide which takes longer; for example, putting on a pair of sandals with buckles or Velcro, describing the duration using familiar terms and reasoning, ‘I took a longer time because I’m still learning to do up my buckles’
  • directly comparing pairs of everyday objects from the kitchen pantry to say which is heavier/lighter; for example, hefting a tin of baked beans and a packet of marshmallows or comparing the same pair of objects to say which is longer/shorter and discussing comparisons

  VC2MFM01 | Mathematics | Mathematics Version 2.0 | Foundation Level | Measurement

• VC2M8M04

  solve problems involving time and duration, including using 12- and 24-hour time across multiple time zones

  Elaborations

  • using digital tools to investigate time zones around the world and convert from one zone to another, such as time in Perth, Western Australia, compared to Suva in Fiji or Toronto in Canada
  • recognising the challenges of planning regular virtual meeting times for a company that has both international staff and staff within different states and territories, and the impact daylight savings has due to multiple time zones, explaining the mathematical language used to communicate current time such as Coordinated Universal Time (UTC)+8, Australian Eastern Standard Time (AEST), Australian Central Standard Time (ACST) and Australian Western Standard Time (AWST)
  • planning an international travel itinerary that covers destinations in different time zones across Asia

  VC2M8M04 | Mathematics | Mathematics Version 2.0 | Level 8 | Measurement

• VC2M2M03

  identify the date and determine the number of days between events using calendars

  Elaborations

  • using calendars to locate specific dates and identify what day it is, to determine the date 2 weeks prior to or after a given date
  • creating a class calendar to enter specific dates relevant to the class, for example, students’ birthdays, school assemblies, sports carnivals or class excursions
  • using addition and a calendar to model and solve the problem ‘How many days are left in this year?’ by identifying the number of days left in this month and in each of the remaining months, and using addition to model and solve the problem
  • identifying and locating specific days or dates on a calendar, for example, school holidays, sports days, Anzac Day, Easter, Diwali or Ramadan

  VC2M2M03 | Mathematics | Mathematics Version 2.0 | Level 2 | Measurement

• Mathematics | Mathematics Version 2.0: Learning in Mathematics Version 2.0

  Learning in Mathematics emphasises the importance of providing opportunities for students to develop proficiency in mathematics. This development of proficiency is achieved in how content is explored or developed, that is, how students experience the thinking and doing of mathematics.

  Proficiency...

  Overview material | Mathematics Version 2.0

• VC2M8ST03

  compare variations in distributions and proportions obtained from random samples of the same size drawn from a population and recognise the effect of sample size on this variation

  Elaborations

  • comparing the proportion of students in favour of a proposal for a change in school uniform between different random samples of 50 students from the school population
  • using digital tools to simulate repeated sampling of the same population, such as heights or arm spans of students, recording and comparing means, median and range of data between samples
  • using relative frequencies from historical data to predict proportions and the likely number of outcomes in situations such as weather forecasting or the countries of origin of visitors to tourist attractions
  • investigating the effect that adding or removing data from a data set has on measures of central tendency and spread
  • investigating Aboriginal and/or Torres Strait Islander ranger groups and other groups’ use of sampling techniques to track biodiversity of species

  VC2M8ST03 | Mathematics | Mathematics Version 2.0 | Level 8 | Statistics

• Mathematics | Mathematics Version 2.0: Structure

  Mathematics is presented in 11 levels, from Foundation to Level 10.

  Level 10 also includes Level 10A, which provides opportunities for students to extend their exploration of mathematical notions and further their mathematical studies.

  Strands

  The curriculum is organised into 6 interrelated...

  Overview material | Mathematics Version 2.0

• VC2M2ST01

  acquire data for categorical variables through surveys, observation, experiment and using digital tools; sort data into relevant categories and display data using lists and tables

  Elaborations

  • posing a question of interest about favourite things (for example, asking classmates ‘What are your favourite types of fruit/football teams/days of the week?’), recording responses using a table, and using counting strategies to determine the number of different responses and the most popular and least popular responses
  • investigating questions such as ‘How much rubbish is really rubbish?’ by gathering data about objects in categories (for example, ‘throw away’, ‘recycle’ and ‘re-use’), deciding whether the data answers the question
  • using familiar software to construct a survey to collect class data; sorting and interpreting responses; and considering the questions asked and whether they need to be modified to re-use the survey
  • observing events and using the observations to design a table or list to record data; for example, observing students arriving at school prior to deciding the appropriate data categories for investigating the different ways students get to school
  • exploring the ways Aboriginal and Torres Strait Islander Peoples observe, collect, sort and record data

  VC2M2ST01 | Mathematics | Mathematics Version 2.0 | Level 2 | Statistics

• VC2M6ST03

  plan and conduct statistical investigations by posing and refining questions to collect categorical or numerical data by observation or survey, or identifying a problem and collecting relevant data; analyse and interpret the data and communicate findings within the context of the investigation

  Elaborations

  • selecting and using appropriate peripherals; for example, using a scientific probe to collect data about changing soil moisture for plants, interpreting the data and sharing the results as a digital chart
  • using a spreadsheet to record and analyse data, recognising the difference between cell formats in spreadsheets; for example, changing the default general format to numerical, text or date as needed
  • investigating the daily water usage by a student in the home compared to the World Health Organization claim that between 50 and 100 litres of clean water is needed per person per day
  • collecting sample sets of ‘discrete numerical data’ (for example, the number of cars or pets in a household), where the class is surveyed, then other classes are surveyed, and data is analysed and compared, discussing findings
  • collecting ordinal categorical data through the use of a survey; for example, surveying each member of the class, by asking them to indicate their preference on a five-point scale for a particular graphic and colour combination of a proposed school logo
  • collecting ordinal data for ranking nominees for school captain with respect to several criteria, contrasting the use of a five-point scale compared with using a four-point scale

  VC2M6ST03 | Mathematics | Mathematics Version 2.0 | Level 6 | Statistics

• VC2M7A04

  investigate, interpret and describe relationships between variables represented in graphs of functions developed from authentic data

  Elaborations

  • using graphs to analyse a building’s electricity or gas usage over a period of time, the value of shares on a stock market, or the temperature during a day, interpreting and discussing the relationships they represent
  • using travel graphs to compare the distance travelled to and from school, interpreting and discussing features of travel graphs such as the slope of lines and the meaning of horizontal line segments
  • telling the story behind what is being represented in graphs of functions, for example, graphs representing pouring rates or distance versus time
  • using graphs of evaporation rates to explore and discuss Aboriginal and Torres Strait Islander Peoples’ methods of water resource management

  VC2M7A04 | Mathematics | Mathematics Version 2.0 | Level 7 | Algebra

• VC2MFM02

  sequence days of the week and times of the day, including morning, lunchtime, afternoon and night-time, and connect them to familiar events and actions

  Elaborations

  • ordering images of daily events on a string line across the room, and justifying the placement by referring to morning, lunchtime, afternoon and night-time
  • distinguishing between the days of the school week and weekends, and recognising that the days of the week form a sequence that repeats, with Monday always following on from Sunday
  • sequencing the events from a story in the order in which they occurred, using language like ‘this happened first’ then ‘this happened next’
  • creating, interpreting and discussing classroom rosters, for example, a roster for watering the classroom garden, and asking, ‘Who watered the garden yesterday?’ or ‘Whose turn is it today?’
  • creating a pictorial diary to show the important events that happen on the various days of the week

  VC2MFM02 | Mathematics | Mathematics Version 2.0 | Foundation Level | Measurement

• VC2M1M03

  describe the duration and sequence of events using years, months, weeks, days and hours

  Elaborations

  • naming, listing and using familiar units of time, such as hours, days, weeks and years
  • comparing the number of days in the months of the year and explaining how the months cycle from one year to the next
  • sequencing familiar events, including representing time, on pictorial timelines
  • discussing events and activities and deciding whether they would take closer to an hour, a day, a week, a month or a year; for example, it takes a day for the sun to rise and fall and rise again, but it takes less than an hour for me to walk to school
  • investigating durations of time represented in Aboriginal and/or Torres Strait Islander seasonal calendars

  VC2M1M03 | Mathematics | Mathematics Version 2.0 | Level 1 | Measurement

• VC2M10M01

  solve problems involving the surface area and volume of composite objects using appropriate units

  Elaborations

  • determining the volumes and surface areas of composite solids, formed from a range of right prisms and cylinders, by considering the individual solids from which they are constructed
  • estimating the surface area and volume of composite objects in practical contexts
  • using mathematical modelling to provide solutions to problems involving surface area and volume; for example, ascertaining the rainfall that can be saved from a rooftop and the optimal shape and dimensions for rainwater storage based on where it will be located on a property, or determining whether to hire extra freezer space for the amount of ice cream required at a fundraising event for the school or community

  VC2M10M01 | Mathematics | Mathematics Version 2.0 | Level 10 | Measurement

• VC2M2M05

  identify, describe and demonstrate quarter, half, three-quarter and full measures of turn in everyday situations

  Elaborations

  • identifying things that turn in the school environment, for example, the handle on a tap or a door, or the dial or switch on a piece of equipment; and identifying a half turn and a full turn, drawing a diagram and labelling it with arrows to show the direction and amount of turn
  • giving and following instructions to move during an activity; for example, demonstrating and describing half, quarter and full turns in a choreographed dance
  • investigating hands turning on a clock and relating quarter, half and full hours to angles and the language of clockwise or anticlockwise
  • giving or following directions to locate an object in the room or to provide a pathway through a grid, such as programming a robot, referring to quarter, half, three-quarter and full turns

  VC2M2M05 | Mathematics | Mathematics Version 2.0 | Level 2 | Measurement

• VC2M10ST03

  construct two-way tables and discuss possible relationship between categorical variables

  Elaborations

  • using two-way tables to investigate and comparing the survey responses to questions involving five-point Likert scale against 2 different categories of respondents, for example, junior students’ responses compared to senior students’ responses to a survey question
  • recording data in two-way tables and using percentages and proportions to identify patterns and associations in the data
  • conducting a litter survey around the school, considering the relationship between different categorical variables such as the day of the week (as canteen specials might lead to different types of litter) or the weather (due to hot days leading to more icy poles and cold drinks being sold)

  VC2M10ST03 | Mathematics | Mathematics Version 2.0 | Level 10 | Statistics

• VC2M3N06

  estimate the quantity of objects in collections and make estimates when solving problems to determine the reasonableness of calculations

  Elaborations

  • estimating how much space a grid paper representation of a large number such as 20 200 will take up on the wall and how much paper will be required
  • estimating the number of people in a large gathering (for example, a school assembly) using known numbers (such as how many students per class)
  • choosing which place value they would estimate to for different situations; for example, choosing to estimate to the nearest ten when estimating how many dots on a ladybird or choosing to estimate to the nearest thousand when estimating crowd sizes at a venue
  • checking the reasonableness of an addition calculation by using two- and three-digit numbers to the nearest ten or hundred to estimate; for example, using 200 + 400 = 600 to estimate and check the solution to the calculation 219 + 385

  VC2M3N06 | Mathematics | Mathematics Version 2.0 | Level 3 | Number

• VC2M6N04

  apply knowledge of place value to add and subtract decimals, using digital tools where appropriate; use estimation and rounding to check the reasonableness of answers

  Elaborations

  • applying estimation strategies to addition and subtraction of decimals to at least thousandths before calculating answers or when a situation requires just an estimation
  • applying whole-number strategies; for example, using basic facts, place value, partitioning and the inverse relationship between addition and subtraction, and properties of operations to develop meaningful mental strategies for addition and subtraction of decimal numbers to at least hundredths
  • working additively with linear measurements expressed as decimals up to 2 and 3 decimal places; for example, calculating how far off the world record the athletes were at the last Olympic Games in the women’s long jump or shot-put and comparing school records to the Olympic records
  • deciding to use a calculator as a calculation strategy for solving additive problems involving decimals that vary in their number of decimal places beyond hundredths; for example, 1.0 − 0.0035 or 2.345 + 1.4999

  VC2M6N04 | Mathematics | Mathematics Version 2.0 | Level 6 | Number