List outcomes of chance experiments involving equally likely outcomes and represent probabilities of those outcomes using fractions Recognise that probabilities range from 0 to 1 Achievement standard (excerpt in bold) Level 4 Level 5 Level 6 Students describe different methods Students pose questions to gather Students interpret and compare a for data collection and data and construct various displays variety of data displays, including representation, and evaluate their appropriate for the data, with and displays for two categorical variables. effectiveness. They construct data without the use of digital technology. They analyse and evaluate data from displays from given or collected data, They compare and interpret different secondary sources. Students with and without the use of digital data sets. Students list outcomes compare observed and expected technology. Students list the of chance experiments with frequencies of events, including probabilities of everyday events. equally likely outcomes and those where outcomes of trials are They identify dependent and assign probabilities as a number generated with the use of digital independent events. from 0 to 1. technology. They specify, list and communicate probabilities of events using simple ratios, fractions, decimals and percentages. Activities Proficiencies Quantify the chance of an event occurring Fluency in listing possible outcomes from a chance experiment as fractions Investigate all the possible outcomes of an event and describing the chance of each outcome occurring Understanding through using fractions to represent probabilities Conduct fair tests or experiments including adequate sample sizes and controlling variables Problem solving by investigating chance through experiments Link chance to fractions and using the language of probability such as “blue has a one in three chance of being selected” Reasoning through interpreting results of chance experiments Investigate the probabilities of all outcomes for a simple chance experiment and verifying that their sum equals 1 Considering different levels Level 4 Students who are working at this level could: Describe possible everyday events and order their chances of occurring. Level 6 Students who are working at this level could: Compare observed frequencies across experiments with expected frequencies (e.g. coin tosses). Assessment ideas Students: Are given a bag of coloured lollies or counters and asked to write the fraction expressing the chance of each colour being drawn out; students are then asked to make a coloured spinner that simulates this same chance. Resources
List outcomes of chance experiments involving equally likely outcomes and represent probabilities of those outcomes using fractions Recognise that probabilities range from 0 to 1 Achievement standard (excerpt in bold) Level 4 Level 5 Level 6 Students describe different methods for data collection and representation, and evaluate their effectiveness. They construct data displays from given or collected data, with and without the use of digital technology. Students list the probabilities of everyday events. They identify dependent and independent events. Students pose questions to gather data and construct various displays appropriate for the data, with and without the use of digital technology. They compare and interpret different data sets. Students list outcomes of chance experiments with equally likely outcomes and assign probabilities as a number from 0 to 1. Students interpret and compare a variety of data displays, including displays for two categorical variables. They analyse and evaluate data from secondary sources. Students compare observed and expected frequencies of events, including those where outcomes of trials are generated with the use of digital technology. They specify, list and communicate probabilities of events using simple ratios, fractions, decimals and percentages. Activities Proficiencies Quantify the chance of an event occurring Investigate all the possible outcomes of an event and describing the chance of each outcome occurring Conduct fair tests or experiments including adequate sample sizes and controlling variables Link chance to fractions and using the language of probability such as “blue has a one in three chance of being selected” Investigate the probabilities of all outcomes for a simple chance experiment and verifying that their sum equals 1 Fluency in listing possible outcomes from a chance experiment as fractions Understanding through using fractions to represent probabilities Problem solving by investigating chance through experiments Reasoning through interpreting results of chance experiments Considering different levels Level 4 Students who are working at this level could: Describe possible everyday events and order their chances of occurring. Level 6 Students who are working at this level could: Compare observed frequencies across experiments with expected frequencies (e.g. coin tosses). Assessment ideas Students: Are given a bag of coloured lollies or counters and asked to write the fraction expressing the chance of each colour being drawn out; students are then asked to make a coloured spinner that simulates this same chance. Resources