Mathematics
Scope and Sequence
Statistics and Probability Foundation to Level
10
Introduction
What is a Scope and Sequence?
scope

The breadth and depth of
content to be covered in a curriculum at any one time (e.g. week, term, year,
over a student’s school life.) All that you do in a given period.

sequence

The order in which content
is presented to learners over time. The order in which you do it.

Together a scope and
sequence of learning bring order to the delivery of content, supporting the
maximising of student learning and offering sustained opportunities for
learning. Without a considered scope and sequence there is the risk of ad hoc
content delivery and the missing of significant learning.
http://activated.act.edu.au/ectl/design/scope_and_sequence.htm

Why does a school need a scope and sequence?
An agreed Scope and Sequence for a Learning
Area, provides a sound basis for a school being able to offer a guaranteed and viable curriculum by
addressing gaps in students’ leaning and eliminating unnecessary repetition. A shared Scope and Sequence within a
school enables teachers to have clarity about the knowledge, skills and
dispositions that students will acquire in their learning and what they need to
learn next. A Scope and Sequence supports teachers with effective unit and
lesson planning and enables teachers to maintain a developmental focus on
student learning as students progress through the school.
The Mathematics Scope and Sequence developed
by WMR
This document has been developed to support schools
with the transition to AusVELS Mathematics for 2013. While it provides examples
of yearly overviews and learning sequences based on the content descriptors in
the Australian Curriculum, it is not a complete curriculum. Each individual
school can use the documents as a basis for developing a guaranteed and viable curriculum that caters for the needs of
their school community.
Levels Foundation to 10A each include a set of
learning goals/ intentions for each content substrand intended to provide a
user friendly guide to the essential learnings around which teachers and teams
could base their unit and lesson development.
Proficiency strands are listed next to each learning
goal / intention as a guide only and teachers / teams are encouraged to
consider all proficiencies equally whilst planning units and lessons. Where a
particular proficiency is not listed for a content substrand teachers and
teams should endeavour to contextualise the learning goals to address these
proficiencies. Please note the following:
Sequence of teaching
The
learning goals/intentions are listed adjacent to the content descriptions to
assist teachers when developing a teaching program. They are not necessarily in
the order to be taught – teachers /teams will make their own decisions
regarding this. The third column has been included to assist teams to develop
ideas for unit planning.
A
sample Scope and Sequence Overview is also provided for each of the year levels
from F to 10A. The number of weeks given to each unit in the overview acts as a
guide and the total number of weeks allows for the many interruptions in a
typical school year.
Links between the Learning
Goals/Intentions and the proficiency strands
(a) The Learning Goals/Intentions have
been identified to relate most closely to one of the four proficiency strands
(shown in 3 below). This identification is shown in brackets at the end of each
Learning Goal/Intention:
·
Understanding
is identified by (U)
·
Fluency
is identified by (F)
·
Problem
Solving is identified by (PS)
·
Reasoning
is identified by (R)
(b) In this document there are less
Problem Solving and Reasoning proficiency strands identified than those for
Understanding and Fluency. Should teachers wish to include more of these
proficiencies in their curriculum, they are encouraged to emphasise them when
teaching, and to develop appropriate learning tasks.
Proficiency strands
The
proficiency strands describe the actions in which students can engage when
learning and using the content. While not all proficiency strands apply to
every content description, they indicate the breadth of mathematical actions
that teachers can emphasise. The proficiencies listed next to each learning
goal / intention are examples of how students might achieve the goal or what
they have demonstrated by achieving the goal but are dependent on the context
in which the learning takes place.
Understanding
Students
build a robust knowledge of adaptable and transferable mathematical concepts.
They make connections between related concepts and progressively apply the
familiar to develop new ideas. They develop an understanding of the
relationship between the ‘why’ and the ‘how’ of mathematics. Students build
understanding when they connect related ideas, when they represent concepts in
different ways, when they identify commonalities and differences between
aspects of content, when they describe their thinking mathematically and when
they interpret mathematical information.
Fluency
Students
develop skills in choosing appropriate procedures, carrying out procedures
flexibly, accurately, efficiently and appropriately, and recalling factual
knowledge and concepts readily. Students are fluent when they calculate answers
efficiently, when they recognise robust ways of answering questions, when they
choose appropriate methods and approximations, when they recall definitions and
regularly use facts, and when they can manipulate expressions and equations to
find solutions.
Problem
Solving
Students
develop the ability to make choices, interpret, formulate, model and
investigate problem situations, and communicate solutions effectively. Students
formulate and solve problems when they use mathematics to represent unfamiliar
or meaningful situations, when they design investigations and plan their
approaches, when they apply their existing strategies to seek solutions, and
when they verify that their answers are reasonable.
Reasoning
Students
develop an increasingly sophisticated capacity for logical thought and actions,
such as analysing, proving, evaluating, explaining, inferring, justifying and
generalising. Students are reasoning mathematically when they explain their
thinking, when they deduce and justify strategies used and conclusions reached,
when they adapt the known to the unknown, when they transfer learning from one
context to another, when they prove that something is true or false and when
they compare and contrast related ideas and explain their choices.
Useful
references for teams
and teachers to use when planning units of work and lessons include the
following:
·
Ultranet
Design Space – DEECD Big Ideas in Number Maps  128428217
·
Ultranet
design Space – Mathematics eBookboxes  66512121
·
Teaching Mathematics Foundations to Middle Years
Dianne Siemon, Kim Beswick, Kathy
Brady, Julie Clark, Rhonda Faragher and Elizabeth Warren
·
Mathematics Domain Page DEECD
·
Building Numeracy – George Booker
·
Teaching Primary
Mathematics George Booker, Denise Bond, Len Sparrow, Paul Swan
·
What We Know About
Mathematics Teaching and Learning MCREL
·
WMR Numeracy Design Space
106126201
·
Acara Scope and Sequence
Documents http://www.australiancurriculum.edu.au/Download
·
VCAA – resources http://www.vcaa.vic.edu.au/Pages/foundation10/curriculum/index.aspx
Please note: Teachers will be required to join
each Ultranet design space before being able to access the resource. The number
associated with each space should be entered into the search box in ‘available
design spaces’ in order to find the space.
Foundation
Level
Statistics and
Probability
AusVELS
Content Descriptors

Learning
Goals/ Intentions and Proficiencies
Essential
Learning

Unit
Development Ideas
How is the essential learning developed into units
of work? How do students make connections between the learning goals and
those included in other content strands or substrands? How do we ensure
students become proficient in fluency, understanding, reasoning and problem
solving?

Data representation and interpretation
·
Answer yes/no
questions to collect information (ACMSP011)

Students will:
·
pose questions about
themselves and familiar objects and events (U)
·
represent responses to
questions using simple displays (PS)
·
use data displays to
answer simple questions (R)
·
Problem Solve through modelling authentic problems, using
familiar counting sequences to solve unfamiliar problems, and discussing the
reasonableness of the answer (PS)
 Reason
by explaining comparisons of quantities (R)


Achievement Standard: Students answer simple questions to collect
information.
Level 1
Statistics
and Probability
AusVELS
Content Descriptors

Learning
Goals/ Intentions and Proficiencies
Essential
Learning

Unit
Development Ideas
How is the essential learning developed into units
of work? How do students make connections between the learning goals and
those included in other content strands or substrands? How do we ensure
students become proficient in fluency, understanding, reasoning and problem
solving?

Chance
·
Identify outcomes of familiar events
involving chance anddescribe them using everyday language such as ‘will
happen’, ‘won’t happen’ or ‘might happen’ (ACMSP024)
Data
representation and interpretation
·
Choose simple questions and gather
responses (ACMSP262)
·
Represent data with objects and drawings
where one object or drawing represents one data value. Describe the displays
(ACMSP263)

Students
will:
·
pose questions about
themselves and familiar objects and events (U)
·
identify outcomes of
familiar events involving chance, describing them using everyday language (R)
·
represent responses to
questions using simple displays such as a probability line (F)
·
Problem Solve through
modelling authentic problems, using familiar counting sequences to solve
unfamiliar problems, and discussing the reasonableness of the answer (PS)
·
Reason by explaining comparisons of
quantities (R)
·
use data displays to
answer simple questions, developing the language of least, most, same amount
(U)
·
Use tally marks to
record (F)
·
determinine
which questions will gather appropriate responses for a simple investigation
(R)
·
Problem Solve through
modelling authentic problems, using familiar counting sequences to solve
unfamiliar problems, and discussing the reasonableness of the answer (PS)
·
Reason by explaining comparisons of
quantities (R)
·
Understand that one
object or drawing represents on data value (U)
·
Explain the display
and what it tells us about the data (U)
Compares categories using language such as greatest or least (R


Achievement Standard: Students describe data displays. Students classify
outcomes of simple familiar events. They collect data by asking questions and
draw simple data displays.
Level 2
Statistics
and Probability
AusVELS
Content Descriptors

Learning
Goals/ Intentions and Proficiencies
Essential
Learning

Unit
Development Ideas
How is the essential learning developed into units
of work? How do students make connections between the learning goals and
those included in other content strands or substrands? How do we ensure
students become proficient in fluency, understanding, reasoning and problem
solving?

Chance
·
Identify practical activities and everyday
events that involve chance. Describe outcomes as ‘likely’ or ‘unlikely’ and
identify some events as ‘certain’ or ‘impossible’ (ACMSP047)
Data
representation and interpretation
·
Identify a question of interest based on
one categorical variable. (ACMSP048)
·
Collect, check and classify data (ACMSP049)
·
Create displays of data using lists, table
and picture graphs and interpret them (ACMSP050)

Students will:
·
Create a probability meter to place
everyday events to match the language of chance (R)
·
Identify practical activities and everyday
events that involve chance. (U)
·
Describe outcomes as ‘likely’ or ‘unlikely’
and identify some events as ‘certain’ or ‘impossible’ (U)
·
classify a list of everyday events
according to how likely they are to happen, using the language of chance, and
explaining reasoning
·
Make conjectures about chance events and
test these (PS)
·
Show fluency
through listing possible outcomes of chance events (F)
·
Formulate problems from authentic
situations, (PS)
·
determine questions for gathering data (R)
·
determine methods for gathering and
recording data – including a table (F)
·
Gather data relevant to the question (F)
·
recognise the usefulness of tally marks (F)
·
identifying categories of data and using
them to sort data (R)
·
check and classify data (F)
·
create picture graphs to represent data
using one to one correspondence (PS)
·
create displays of data using lists, table
and picture graphs (PS)
·
compare the usefulness of different data
displays (R)
·
show reasoning
by creating and interpreting simple representations of data (R)


Achievement
Standard: Students make sense
of collected information. They describe
outcomes for everyday events. Students collect data from relevant questions
to create lists, tables and picture
graphs.
Level 3
Statistics
and Probability
AusVELS Content
Descriptors

Learning
Goals/ Intentions and Proficiencies
Essential
Learning

Unit
Development Ideas
How is the essential learning developed into units
of work? How do students make connections between the learning goals and
those included in other content strands or substrands? How do we ensure
students become proficient in fluency, understanding, reasoning and problem
solving?

Chance
·
Conduct chance experiments, identify and describe
possible outcomes and recognise variation in results (ACMSP067)
Data
representation and interpretation
·
Identify questions or issues for categorical
variables. Identify data sources and plan methods of data collection and
recording (ACMSP068)
·
Collect data, organise into categories and create
displays using lists, tables, picture graphs and simple column graphs, with
and without the use of digital technologies (ACMSP069)
·
Interpret and compare data displays (ACMSP070)

Students
will:
·
Conduct repeated trials of chance
experiments such as tossing a coin or drawing a ball from a bag and
identifying the variations between trials.
(F,R)
·
Collect and record
categorical data to answer an identified question. (R)
·
Identify efficient ways to record
data, and representing and reporting the results of investigations including using digital technologies. (P)
·
Compare and contrast between
displays of data and make appropriate conclusions. (U)


Achievement Standard: By the end of Level 3, students interpret
and compare data displays.Students conduct chance experiments and list possible
outcomes. They carry out simple data investigations for categorical variables.
Level 4
Statistics
and Probability
AusVELS Content
Descriptors

Learning
Goals/ Intentions and Proficiencies
Essential
Learning

Unit
Development Ideas
How is the essential learning developed into units
of work? How do students make connections between the learning goals and
those included in other content strands or substrands? How do we ensure
students become proficient in fluency, understanding, reasoning and problem
solving?

Chance
·
Describe possible everyday events and order their
chances of occurring (ACMSP092)
·
Identify everyday events where one cannot happen if
the other happens (ACMSP093)
·
Identify events where the chance of one will not be
affected by the occurrence of the other (ACMSP094)
Data
representation and interpretation
 Select and trial methods for
data collection, including survey questions and recording sheets (ACMSP095)
 Construct suitable data
displays, with and without the use of digital technologies, from given
or collected data. Include tables, column graphs and picture graphs
where one picture can represent many data values (ACMSP096)
 Evaluate the effectiveness of
different displays in illustrating data features including variability(ACMSP097)

Students will:
Discuss and apply
probabilities to everyday situations ranging from Impossible (0) to
Certain(1). (R)
·
Apply an understanding of
mutually exclusive events such as tossing a coin once,
which can result in either heads or tails, but not both. (R)
·
Apply an understanding of
independent events such as the outcome in rolling a die cannot affect the
outcome in tossing a coin. (R)
·
Choose an effective
way to collect and record data for a given investigation. (P)
·
Choose appropriate
representations for different types of data for interpretation, especially
using digital technologies. (P)
·
Compare and contrast different
displays of data and make appropriate conclusions. (U)


Achievement Standard: By the end of Level 4, students
identify dependent and independent events. They describe different methods for
data collection and representation, and evaluate their effectiveness. Students list the
probabilities of everyday events. They construct data displays from given or
collected data.
Level 5
Statistics
and Probability
AusVELS Content
Descriptors

Learning
Goals/ Intentions and Proficiencies
Essential
Learning

Unit
Development Ideas
How is the essential learning developed into units
of work? How do students make connections between the learning goals and
those included in other content strands or substrands? How do we ensure
students become proficient in fluency, understanding, reasoning and problem
solving?

Chance
·
List outcomes of chance experiments involving equally likely outcomes and represent probabilities of those outcomes
using fractions (ACMSP116)
·
Recognise that probabilities range from 0 to 1(ACMSP117)
Data
representation and interpretation
1.
·
Pose questions and collect categorical or numerical data by
observation or survey (ACMSP118)
·
Construct displays, including column graphs, dot
plots and tables, appropriate for data type,
with and without the use of digital technologies(ACMSP119)
·
Describe and interpret different data sets
in context (ACMSP120)

Students
will:
·
Understand the likelihood of
winning simple games of chance by considering the number of possible
outcomes. (U)
·
Represent the likelihood of winning
simple games of chance in fractional form. (F)
·
Discuss and apply probabilities to
everyday situations ranging from 0 to 1. (R)
·
Pose questions regarding and
collect and interpret both numerical and categorical data. (R,P)
·
Choose appropriate
representations for different types of data for interpretation, especially
using digital technologies. (R)
·
Compare and contrast
different sets of data and make appropriate conclusions. (U)


Achievement Standard: By the end of Level 5, students
compare and interpret different data sets. Students list outcomes of chance
experiments with equally likely outcomes and assign probabilities between 0 and
1. Students pose questions to gather data, and construct data displays
appropriate for the data.
Level 6
Statistics and Probability
AusVELS Content
Descriptors

Learning Goals/
Intentions and Proficiencies
Essential Learning

Unit Development Ideas
How
is the essential learning developed into units of work? How do students make
connections between the learning goals and those included in other content
strands or substrands? How do we ensure students become proficient in
fluency, understanding, reasoning and problem solving?

Chance
·
Describe probabilities using fractions, decimals and
percentages (ACMSP144)
·
Conduct chance experiments with both small and large
numbers of trials using appropriate digital technologies (ACMSP145)
·
Compare observed frequencies across
experiments with expected frequencies(ACMSP146)
Data
representation and interpretation
·
Interpret and compare a range of data displays,
including sidebyside column graphs for two categorical variables (ACMSP147)
·
Interpret secondary data presented
in digital media and elsewhere (ACMSP148)

Students
will:
·
Understand use and convert between probabilities
using fractions, decimals and percentages. (U,F)
·
Conduct trials of chance and
identify the variation between trials. (U,F)
·
Understand why larger
numbers of trials result in more accurate probabilities. (U)
·
Compare observed and
expected probabilities. (R)
·
Select and use a range of
appropriate data representations for comparison between sets of similar data.
(U,F)
·
Discuss and interpret data
found in everyday situations. (R)


Achievement Standard: By the end of Level 6, students
compare observed and expected frequencies. They interpret and compare a variety
of data displays including those displays for two categorical variables. They
evaluate secondary data displayed in the media. Students list and communicate
probabilities using simple fractions, decimals and percentages.
Level 7 Statistics and Probability
Data Representation and Interpretation and Chance
AusVELS
Content Descriptors

Learning
Goals/ Intentions and Proficiencies
Essential
Learning

Unit
Development Ideas
How is the essential learning developed into units
of work? How do students make connections between the learning goals and
those included in other content strands or substrands? How do we ensure
students become proficient in fluency, understanding, reasoning and problem
solving?

Data
Representation and Interpretation
·
Identify and
investigate issues involving numerical data collected from primary and secondary sources (ACMSP169)
· Construct and compare a range of data displays
including stemandleaf plots and dot plots (ACMSP170)
· Calculate mean, median, mode and range
for sets of data. Interpret
these statistics in the context of data (ACMSP171)
· Describe and interpret data displays
using median, mean and range (ACMSP172)
Chance
· Construct sample spaces for
singlestep experiments with equally likely outcomes (ACMSP167)
· Assign probabilities to the outcomes of events and
determine probabilities for events (ACMSP168)

Students will:
· Describe the difference between primary and secondary
data. (U)
· Collect, organise and describe numerical data collected
from primary sources. (PS)
· Analyse numerical data collected from secondary sources.
(PS)
· Explain why some data representations are more appropriate
than others for particular data sets. (U)
· Construct and compare data displays including ordered stem
and leaf plots, and dot plots. (F)
· Calculate the mean, median, mode and range for sets of
data. (F)
· Explain and interpret data, including referring to the
mean, median, mode and range of the data. (R)
· Compare data sets from real life, including using the
location of the mean and median on graphs. (R)
· Describe how outliers may affect the comparison of data
sets when the mean, median and range are used.(U)
· Define key terms, including probability, sample space,
favourable outcomes, trial, events and experiments. (U)
· Identify equally likely outcomes and outcomes that are not
equally likely.(F)
· Construct sample spaces for singlestep experiments with equally
likely outcomes. (U)
· Calculate the probability of an event as a decimal,
fraction or percentage. (F)


Achievement Standard:
By the end of Level 7, students determine
the sample space for simple experiments with equally likely outcomes and assign
probabilities to those outcomes. They calculate mean, mode, median and range
for data sets. They construct stem and leaf plots and dot plots.
Level 8 Statistics and Probability
Chance and Data
Representations
AusVELS
Content Descriptors

Learning Goals/
Intentions and Proficiencies
Essential Learning

Unit Development Ideas
How is the essential learning developed into units
of work? How do students make connections between the learning goals and
those included in other content strands or substrands? How do we ensure
students become proficient in fluency, understanding, reasoning and problem
solving?

Chance
 Identify complementary events and use the
sum of probabilities to solve problems. (ACMSP204)
 Describe events using language of 'at
least', exclusive 'or' (A or B but not both), inclusive 'or' (A or B or
both) and 'and'. (ACMSP205)
 Represent events in twoway tables and Venn
diagrams and solve related problems. (ACMSP292)
Data Representations
 Investigate techniques for collecting data,
including census, sampling and observation(ACMSP284)
 Explore the practicalities and implications
of obtaining data through sampling using a variety of investigative
processes. (ACMSP206)
 Explore the variation of means and
proportions of random samples drawn from the same population. (ACMSP293)
 Investigate the effect of individual data
values, including outliers, on the mean and median. (ACMSP207)

Students
will:
·
Demonstrate that probabilities range between 0 to 1
by convention and that calculating the probability of an event allows the
probability of its complement to be identified. (R)
·
Identify the
complement of familiar events (eg the complement of getting a head on a coin
is getting a tail, the complement of winning a game is not winning the game).
(R)
·
Calculate probabilities for sample spaces for
singlestep experiments (eg drawing a marble from a bag with 2 black and 3
white marbles with replacement. (F)
·
Pose ‘and’, ‘or’, ‘not’ probability questions about
objects or people. (R)
·
Show that
representing data in Venn diagrams or twoway tables facilitates the
calculation of probabilities. (U)
·
Use Venn diagrams and twoway tables to calculate
probabilities for events satisfying ‘and’, ‘or’, ‘given’ and ‘not’
conditions. (R)
·
Collect data to answer the questions using Venn
diagrams or twoway tables. (P)
·
Know the difference
between a sample and a census and when each might be appropriate. (U)
·
Be able to create,
implement and interpret survey data through sampling techniques. (P,R)
·
Use sample properties
(for example mean, median, range) to predict characteristics of the
population acknowledging uncertainty. (U)
·
Use displays of data to
explore and investigate effects. (R)


Achievement Standard:
By the end of Year 8, students choose appropriate
language to describe events and experiments. Students model authentic
situations with twoway tables and Venn diagrams. They explain issues related
to the collection of data and the effect of outliers on means and medians in
that data.
Level 9
Statistics and Probability
Chance and Data
Representations
AusVELS Content Descriptors

Learning Goals/
Intentions and Proficiencies
Essential Learning

Unit Development Ideas
How
is the essential learning developed into units of work? How do students make
connections between the learning goals and those included in other content
strands or substrands? How do we ensure students become proficient in fluency,
understanding, reasoning and problem solving?

Data Representations
·
Investigate reports of
surveys in digital media and elsewhere for information on how data were
obtained to estimate population means and medians (ACMSP227)
·
Identify everyday
questions and issues involving at least one numerical and at least one
categorical variable, and collect data directly from secondary sources (ACMSP228)
·
Construct backtoback
stemandleaf plots and histograms and describe data, using terms including
‘skewed’, ‘symmetric’ and ‘bi modal’ (ACMSP282)
·
Compare data displays
using mean, median and range to describe and interpret numerical data sets in
terms of location (centre) and spread (ACMSP283)
Chance
·
List all outcomes for
twostep chance experiments, both with and without replacement using tree
diagrams or arrays. Assign probabilities to outcomes and determine
probabilities for events (ACMSP225)
·
Calculate relative
frequencies from given or collected data to estimate probabilities of events
involving 'and' or 'or' (ACMSP226)

Students
will:
·
develop a question that will aid the comparison of
two or more sets of data. (U)
·
use appropriate investigative techniques to collect
data. (PS)
·
choose appropriate secondary data (F)
·
identify everyday
questions and issues involving at least one numerical and at least one
categorical variable (R)
·
display comparative data, such as backtoback
stemandleaf plots and histograms. (F)
·
explain comparative data, such as backtoback stemandleaf
plots and histograms. (R)
·
describe data , using spread, mean, medium,
outliers, skewed, symmetric . (U)
·
explain the data and draw conclusions. (R)
·
evaluate media reports
and use statistical knowledge to draw conclusions (U)
·
list all the outcomes for a two step chance
experiment using a tree diagram. (F)
·
assign probabilities, using the tree diagram. (F)
·
use the tree diagram to solve problems, including and, or and not. (F)
·
solve probability questions, using a tree diagram
for events ( without replacement). (F)
·
use Venn Diagrams to solve problems with ‘and’,
‘or’, and ‘not’. (PS)


Achievement Standard:
By the
end of Level 9, students compare techniques for collecting data in primary and
secondary sources. They make sense of the position of the mean and median in
skewed, symmetric and bimodal displays to describe and interpret data.
Students calculate relative frequencies to estimate probabilities, list
outcomes for twostep experiments and assign probabilities for those outcomes.
They construct histograms and backtoback stemandleaf plots.
Level 10 Statistics and Probability
Data representation and Interpretation
AusVELS Content
Descriptors

Learning Goals/ Intentions and Proficiencies
Essential
Learning

Unit Development Ideas
How is the essential learning developed
into units of work? How do students make connections between the learning
goals and those included in other content strands or substrands? How do we
ensure students become proficient in fluency, understanding, reasoning and
problem solving?

·
Determine quartiles and interquartile range (ACMSP248)
·
Construct and interpret box plots and use them to
compare data sets (ACMSP249)
·
Compare shapes of box plots to corresponding histograms
and dot plots (ACMSP250)
·
Use scatter plots to investigate and comment on
relationships between two continuous variables (ACMSP251)
·
Investigate and describe bivariate numerical data where
the independent variable is time (ACMSP252)
·
Evaluate
statistical reports in the media and other places by linking claims to
displays, statistics and representative data (ACMSP253)

Students will:
·
determine the minimum and maximum
values in a set of data (F)
·
determine the range in a set of data (F)
·
determine the median in a set of data
(F)
·
determine the upper and lower
quartiles in a set of data (F)
·
determine the interquartile range in a
set of data (F)
·
compare data sets numerically (U) (R)
·
represent data by constructing a box
plot (F)
·
compare data sets visually using box
plots (U) (R) e.g. the distribution of Aboriginal and Torres Strait Islander
people by age with that of the Australian population as a whole
·
understanding that box plots are an
efficient and common way of representing and summarising data and can
facilitate comparisons between data sets
·
represent the same set of data
visually in various ways such as box plots, histograms and dot plots(U)
·
compare the various visual
representations of a set of data and explain their features (U)
·
represent data sets as scatter plots (F)
·
use authentic data to construct
scatter plots, make comparisons and draw conclusions (R)
·
comment on relationships between continuous variables
using their scatter plots
·
investigate and describe relationships between
variables (F) (U)
·
construct and interpret data displays
representing bivariate data over time (F) (U) (R)
·
investigate and describe bivariate data where the
independent variable is time (F) (U)
·
Use real life data to explain and evaluate statistical
reports presented in the media (F) (U) (R)
·
Investigate data in different ways to make comparisons
and draw conclusions (R) (PS) (U) (F)


Achievement Standard:
Students
compare data sets by referring to the shapes of the various data displays. They
describe bivariate data where the independent variable is time. Students
describe statistical relationships between two continuous variables. They
evaluate statistical reports. They calculate quartiles and interquartile
ranges.
Level 10A Statistics and Probability
Chance
AusVELS Content
Descriptors

Learning
Goals/ Intentions and Proficiencies
Essential
Learning

Unit
Development Ideas
How is the
essential learning developed into units of work? How do students make
connections between the learning goals and those included in other content
strands or substrands? How do we ensure students become proficient in
fluency, understanding, reasoning and problem solving?

·
Investigate reports of studies in digital media and
elsewhere for information on the planning and implementation of such studies,
and the reporting of variability (ACMSP277)

Students will:
·
Evaluate media reports that refer to data from a
range of contexts (R)
·
Evaluate the visual representation of data in media
reports (R)
·
Evaluate the size and type of samples used for data
collection in a variety of contexts (R)
·
Discuss appropriate methods of sampling for data
collection (U)
·
Generate data by posing appropriate questions and
making decisions about sampling a population (U)(R)


Level 10A Statistics and Probability
Data Representation and Interpretation
AusVELS Content
Descriptors

Learning
Goals/ Intentions and Proficiencies
Essential
Learning

Unit
Development Ideas
How is the
essential learning developed into units of work? How do students make
connections between the learning goals and those included in other content
strands or substrands? How do we ensure students become proficient in
fluency, understanding, reasoning and problem solving?

·
Calculate and interpret the mean and standard
deviation of data and use these to compare data sets (ACMSP278)
·
Use information technologies to investigate
bivariate numerical data sets. Where appropriate use a straight line to
describe the relationship allowing for variation (ACMSP279)

Students will:
·
Calculate the mean for a data set (F)
·
Calculate the standard deviation for a data set (F)
·
Compare data sets using their standard deviations
and mean values (R) (U)
·
Discuss data sets by interpreting their mean and
standard deviations (R) (U)
·
Represent bivariate numerical data sets graphically
using digital technologies (F)
·
Use straight lines (line of best fit) to represent
scatter plots and to describe the relationships between variables (F) (U)

