Chance
Data
Embedded Files
Definition
Definition
The language of chance is used to describe events such as certain, likely, equally likely (or even chance), unlikely and impossible. The probability of an event is a number between 0 and 1 that indicates the chance of something happening. (NSW Mathematics K-10 Syllabus)
The probability of something happening is generally written as a fraction. However, answers can also be written as percentages and decimals.
Teaching and learning activities
Teaching and learning activities
The resources below provide targeted teaching strategies to support student improvement in this skill.
Each downloadable lesson activity includes:
learning intentions
a list of required resources
a step-by-step lesson sequence
printable classroom materials
Select the download all icon to download all available activities or select each activity separately.
Understanding chanceUse the language of chance to describe the probability of an event occurring, including determining their numerical values as fractions, decimals and percentages.
Popular birthdaysStudents interpret unique birthdays chart to investigate probability of events occurring, including using their own data.
Download all (ZIP)Download the resource pack containing all activities.
PLAN2 Areas of focus
PLAN2 Areas of focus
An Areas of focus template has been created in PLAN2 to support targeted teaching of Text structure in your learning area.
Search for the DoE template titled ‘DoE HSCMinStd Writing: Text structure’ in the Areas of focus template library tab within the Plan menu, and customise it for your students’ needs.
For more information about using PLAN2 Areas of focus templates with this resource, visit the Using this resource with PLAN2 page. .
Relevance to the numeracy test marking
Relevance to the numeracy test marking
The feedback for a Level 3 performance in the HSC minimum standard online numeracy test states:
Individuals performing at this level typically “select appropriate strategies from a variety of everyday mathematical processes in familiar and some less familiar contexts. They interpret and comprehend mathematical information in written material, diagrams, charts and tables, and common chance events.”
Students are able to describe, compare and interpret the likelihood of everyday chance events.
Connections with ACSF Level 3 descriptors
Connections with ACSF Level 3 descriptors
The relevant Level 3 ACSF descriptors for numeracy are shown here to demonstrate how determining outcomes of common chance events are assessed in the HSC minimum standard online test. The performance features identified show what a student is able to do in order to achieve at this level and are provided to support teachers to understand what is required to achieve a Level 3 in this skill.
Numeracy Indicator 3.09: Selects and interprets mathematical information that may be partly embedded in a range of familiar, and some less familiar, tasks and texts
Focus area: Complexity of mathematical information
Level 3 performance features:
interprets and comprehends familiar and routine common chance events
Numeracy Indicator 3.10: Selects from and uses a variety of developing mathematical and problem solving strategies in a range of familiar and some less familiar contexts
Focus area: Mathematical knowledge and skills: statistics and probability
Level 3 performance features:
describes, compares and interprets the likelihood of everyday chance events (e.g. rolling a six on a dice or the chance of rain) using qualitative terms such as certain, likely, impossible and relates these to everyday or routine fractions, decimals or percentages
Numeracy Indicator 3.11: Uses a combination of both informal and formal oral and written mathematical language and representation to communicate mathematically
Focus area: Oral mathematical language
Level 3 performance features:
uses a combination of both informal and formal oral mathematical and general language to present and discuss the mathematical and problem solving process and result
Connections with Numeracy Learning Progression:
Connections with Numeracy Learning Progression:
The progressions describe a typical developmental sequence of literacy and numeracy learning. The numeracy progression sub-elements, levels and indicators relevant to chance are provided here to assist teachers to identify students’ capabilities and needs to support targeted teaching.
Element: Statistics and probability
Sub-element: Understanding chance (UnC)
UnC2 — Comparing chance
UnC2 — Comparing chance
describes and orders the likelihood of events in non-quantitative terms such as certain, likely, highly likely, unlikely, impossible (e.g. if there are more blue than red marbles in a bag, blue is more likely to be selected; I am certain that I won’t win the competition because I didn’t enter)
records outcomes of chance experiments in tables and charts
demonstrates that outcomes of chance experiments may differ from expected results (e.g. we will not get the same results every time we roll a dice)
UnC3 — Fairness
UnC3 — Fairness
identifies all possible outcomes of one-step experiments and records outcomes in tables and charts
explains why outcomes of chance experiments may differ from expected results (e.g. just because there are six numbers on a dice doesn’t mean you are going to roll a 6 every six rolls, you may not roll a 6 in the entire game)
explains that the probabilities of all chance events are either ‘impossible’, ‘certain to happen’ or lie somewhere in between
UnC4 — Probabilities
UnC4 — Probabilities
expresses the theoretical probability of an event as the number of ways an event can happen out of the total number of possibilities
identifies a range of chance events that have a probability from 0 – 1 (e.g. you have zero probability of rolling a 7 with one roll of a standard 6-sided dice; the probability that tomorrow is Wednesday given today is Tuesday is 1)
describes probabilities as fractions of one (e.g. the probability of an even number when rolling a dice is 3/6 )
expresses probabilities as fractions, decimals, percentages and ratios recognising that all probabilities lie on a measurement scale of 0 to 1 (e.g. uses numerical representations such as 75% chance of rain or 4 out of 5 people liked the story; explains why you can’t have a probability less than zero)
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