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Mathematics
Scope and Sequence
Manunda Terrace Primary School
Year 5:
Number and Algebra…………………... 3 - 9
Measurement and Geometry….….10 – 15
Statistics and Probability……………16 - 18
Key:
Red text:
Identifies achievement standards and strand connections
Blue text:
T-9 Literacy and Numeracy Net
Australian Curriculum NT
School
Year 5 -
1 of 21
Manunda Terrace Primary
Foreword
In 2011, Manunda Terrace Primary School was the focus of three major projects.
Firstly, it was selected to be a Pilot School to trial the Australian Mathematics Curriculum.
Secondly, Manunda Terrace Primary School received funding through the National
Partnership Smarter Schools Project, Maximising Improvement in Literacy and Numeracy,
to support improved numeracy learning outcomes.
Thirdly, Manunda Terrace Primary was extremely fortunate to have a Numeracy Coach
from the Department of Education Darwin Regional Curriculum Team, Carolyn Clark,
based part time on-site for the first half of 2011 to support changed mathematical
pedagogy.
After familiarisation with the Australian Mathematics Curriculum, teachers determined the
need to unpack the specific content of the Australian Curriculum content descriptions.
Small teams of teachers researched various documents, including the Northern Territory
Curriculum Framework and T-9 Literacy and Numeracy Net. They also examined various
resources including Count Me in Too and First Steps to extrapolate and make explicit
content knowledge, aligned with quality pedagogical practice. This exercise has resulted
in the publication of the Manunda Terrace Primary School Mathematics Scope and
Sequence. Parallel to this process, staff engaged in developing mathematics resources,
participated in various professional learning experiences, and applied this knowledge to
writing units of work using the Australian Curriculum mathematics learning area with
improved teaching practice.
We wish to acknowledge and thank:
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The hard work of Manunda Terrace Primary School teaching staff of 2011
Carolyn Clark’s outstanding support and contribution (Numeracy Coach, Darwin
Regional Curriculum Team)
Department of Education and Training support through the Darwin Regional
Curriculum Team
National Partnership Project funding, through Maximising Improvements in Literacy
and Numeracy
Curriculum Teaching and Phases of Learning Australian Curriculum pilot
We believe that our own staff will continue to develop and improve pedagogy, through
the use of this document to ensure best learning outcomes for our students. We hope
that this document will be useful for other schools as a starting point for their own
journey in pedagogy, curriculum and assessment in mathematics teaching.
Sally Winch
Principal
Australian Curriculum NT
School
Lisa Hirschausen
Assistant Principal
Year 5 -
2 of 21
Manunda Terrace Primary
Mathematics Scope and Sequence
Number and Algebra
Achievement Standards
Proficiency Strands
Understandings: By the end of Year 5, students solve simple problems involving
the four operations using a range of strategies. They check the reasonableness
of answers using estimation and rounding. Students identify and describe factors
and multiples. They explain plans for simple budgets. Students connect threedimensional objects with their two-dimensional representations. They describe
transformations of two-dimensional shapes and identify line and rotational
symmetry. Students compare and interpret different data sets.
Skills: Students order decimals and unit fractions and locate them on number
lines. They add and subtract fractions with the same denominator. Students
continue patterns by adding and subtracting fractions and decimals. They find
unknown quantities in number sentences. They use appropriate units of
measurement for length, area, volume, capacity and mass, and calculate
perimeter and area of rectangles. They convert between 12 and 24 hour time.
Students use a grid reference system to locate landmarks. They measure and
construct different angles. Students list outcomes of chance experiments with
equally likely outcomes as probabilities between 0 and 1. Students pose
questions to gather data, and construct data displays appropriate for the data.
Understanding includes making connections
between representations of numbers, using fractions
to represent probabilities, comparing and ordering
fractions and decimals and representing them in
various ways, describing transformations and
identifying line and rotational symmetry
Fluency includes choosing appropriate units of
measurement for calculation of perimeter and area,
using estimation to check the reasonableness of
answers to calculations and using instruments to
measure angles
Problem Solving includes formulating and solving
authentic problems using whole numbers and
measurements, and creating financial plans
Reasoning includes investigating strategies to
perform calculations efficiently, continuing patterns
involving fractions and decimals , interpreting results
of chance experiments, posing appropriate
questions for data investigations and interpreting
data sets
Achievement Standard Work Samples
http://www.australiancurriculum.edu.au/Mathematics/Curriculum/F-10
Number and Place Value
AC Content Descriptor
AC Elaborations
Identify and describe
factors and multiples
of whole numbers
and use them
to solve problems
 Use estimation
and rounding to
check the
reasonableness
of answers to
calculations
So learning will include

Year 5 – Number and Algebra
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
Using models investigate factors in multiplication, eg manipulate arrays to find
out how many different arrays can be made with a given product, and record
and explain reasoning as to how many ways the arrays can be described? eg
o for product 24 outlined or cut out arrays could be: 2 x 12 array, 12 x 2 array,
6 x 4 array, 1 x 24 array ... (Leading to identifying and understanding factors
for a given product),
o Online factors and arrays activity
http://illuminations.nctm.org/ActivityDetail.aspx?id=64
Investigate ways of recording factors of products using, eg factor trees
http://nzmaths.co.nz/resource/factor-trees , hundred charts
Predict what a sequence ‘down the line’ might be in investigating multiplicative
patterns products (multiples); find the missing part/s of multiple sequence and
justify and explain outcomes; investigate and record patterns made, using 100
charts
Use multiple and factor knowledge to estimate and check reasonableness of
answers when solving problems
Investigate ways of compare and displaying factors of multiples to find common
ones, eg
o factors of 2 2 4 6 8
or
o factors of 2 2 4 6 8 10 12 14
o factors of 4 4
8 12
o factors of 3 3
6
9 12
15
o factors of 8 8
First Steps Number: Book 2: RNP – KU6
Use estimation and
rounding to check the
reasonableness of
answers to calculations
 Recognising the
usefulness of
estimation to
check
calculations
 Applying mental
strategies to
estimate the
result of
calculations,
such as
estimating the
cost of a
supermarket
trolley load
Australian Curriculum NT
School
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Estimate money totals using strategies such as inverse operations and
rounding, eg estimate cost of five children’s movie tickets then two adult tickets
to determine whether $100 will be enough, and if the sellers ‘change’ is correct.
Continue to develop efficient mental strategies (as listed in Year 4 strategies find the face
) for solving real context problems but with larger numbers, and
o use estimation and rounding to check reasonableness of answers; fluently
round numbers to nearest 10, 100, 1000
First Steps Number: Book 2: Cal – KU8, KU10
Year 5 -
3 of 21
Manunda Terrace Primary
AC Elaborations
Solve problems involving
multiplication of large
numbers by one or two-digit
numbers using efficient
mental, written strategies
and appropriate digital
technologies
 Exploring
techniques for
multiplication
such as the area
model, the Italian
lattice method or
partitioning of
numbers
Year 5 – Number and Algebra
AC Content Descriptor
 Applying the
distributive law
using arrays to
model
multiplication and
explain
calculation
strategies
Number and Place Value
So learning will include
 Investigate and solve real context large numbers by 1 and 2 digit, multiplication
problems, using a variety of techniques including area models (First Steps
Number, names model as Multiplication Grids), Italian lattice methods, and
partitioning with base ten columns in tradition multiplication algorithms
 Investigate the ‘distributive property of multiplication over addition’ using real
context larger number scenarios eg model to visually show on an array, 4 x 587
= (4 x 500) + (4 x 80) + (4 x 7)
 Solve real context problems, using a variety of problem solving methods, and
use models to explain what they did and why it makes sense, eg think boards
that could include, words, pictures, diagrams, numbers including algorithms
Investigate different problem types, eg
o Equal grouping problems: with ‘repeated addition’ or rate type problems (eg
cost, measurement, length) for multiplication. Problems exploring both ‘how
many groups?’ and ‘how many in each group?’, eg If chocolate frogs cost 75
cents each, how much did Jeff pay for a bag of 25 frogs?
o Comparison type problems: where the product is unknown, (multiplication),
eg Ali picked 26 oranges; Sally picked 16 times as many as Ali. How many
did she pick?
o Combination type problems: where problems involve counting the number of
possible pairings that can be made between two sets, eg buying 3 tops and 5
shorts and investigating how many different combinations could be made, eg
models for investigations could be arrays, tree diagrams
o Product of Measure problems: eg the area of a rectangle is 95cm² and has
one side that is 20cm long. How long is the adjacent side?
(Refer: First Steps Number: Book 2 page 90)
 Investigate how multiplication models equate to different algorithm processes;
explain and justify the choice of approach for particular scenarios
 Determine the relationship between pairs of values in a table and predict values
not represented by generalising, eg predict the revenue from a class enterprise
selling friendship bands from a table, find the cost of ? bands
Number
of Bands
Money
5
10
$
1
0
$20
15
20
25
o Display data from a table of values in a graph and investigate the ‘shape of
the graph’; make conjectures about why it has this type of shape; construct
other multiple type values tables (as in example above) and investigate their
graph ‘shapes’. Discuss and explain similarities and differences in terms of
the multiples of numbers used
Italian lattice multiplication - link
http://www.education.vic.gov.au/studentlearning/teachingresources/maths/mathsco
ntinuum/number/N40002ma.htm
Area model multiplication -link
http://www.education.vic.gov.au/studentlearning/teachingresources/maths/mathsco
ntinuum/number/N40002P.htm
First Steps Number: Book 2: Cal – KU1, KU3, KU4, KU5, KU6; RNP – KU4, KU5
Australian Curriculum NT
School
Year 5 -
4 of 21
Manunda Terrace Primary
Number and Place Value
AC Content Descriptor
Year 5 – Number and Algebra
Solve problems involving
division by a one-digit
number, including those
that result in a remainder
AC Elaborations
So learning will include
 Using the fact
 Estimate simple problems requiring division by one digit numbers using known
that equivalent
facts, eg 9 people share $300 so they’ll get $30 each since 300 ÷ 10 = 30
division
 Solve real context word problems by dividing; use larger numbers by 1 digit with
calculations result
remainders; eg use models to explain what they did and why it makes sense
if both numbers
such as think boards; could include, words, pictures, diagrams, numbers and
are divided by the
algorithms
same factor
 Include problem types such as, eg
o Equal grouping problems: with ‘fair sharing or rate type problems (cost ,
 Interpreting and
measurement, length) for partitioning division , eg ‘How many groups? and
representing the
‘How many in each group?
remainder in
o Comparison type problems: where the group size is unknown, (partition
division
division) or measurement division, eg Mia has 17 shells; how many times as
calculations
many shells does Tegan have, if she has 95?
sensibly for the
o Combination type problems: eg there are three types of ice-cream cones and
context
various ice cream flavours. If 18 different ice creams can be made, how
many different flavours are there?
(Refer: First Steps Number Number: Book 2 pg 90)
 Solve real scenario problems to investigate how remainders can be expressed
in different ways; explain why that way of expressing remainder has been
chosen. Remainder types include;
o ‘left over’ remainder, eg 24 lollies equally shared between 7 friends
o remainder partitioned as a fraction, eg each can holds 200mls. If the jug
holds 1L and 300mL, how many cans would that be? (6 ½ cans)
o remainder is discarded, eg if a skipping rope is 25m long, how many 3m
length ropes can be made? ( 8 )
o forced to next whole number, eg a boat can hold 6 people. How many trips
needed to carry 21 people across a river? (4)
o remainder is rounded to give an approximate result, eg a family of 6 share a
packet of 40 snakes. About how many snakes do they get each? (about 7)
First Steps Number: Book 2: Cal – KU1, KU3, KU4, KU5; RNP – KU4, KU5
Use efficient mental and
written strategies and
apply appropriate digital
technologies to solve
problems
 Using calculators
to check the
reasonableness
of answers
 Applying known
facts and
strategies
 Continue to develop efficient mental and written strategies (refer Year 4 listed
strategies ) for solving real context problems that require the use of all four
operations
 Read, say, write in words and digits, compare and order whole numbers to
hundred millions and enter these numbers into a calculator for practical
purposes, eg make comparisons of populations of different cities or states
 Use efficient mental, written and calculator strategies to add, subtract, multiply
and divide (including decimal numbers) to solve multi step word problems, eg
add costs of items and then work out change from a defined amount
 Use place value knowledge to partition numbers mental in order to simplify
computation, eg to multiply 23 x 4 think 2 tens and 3 ones multiplied by 4, = 8
tens and 12 ones = 9 tens and 2 = 92; or thinks, 23 x 4 = 11 x 4 doubled + 4; or
25 x 4 – 8
First Steps Number: Book 2: Cal – KU1, KU3, KU4, KU5; RNP – KU4, KU5
Australian Curriculum NT
School
Year 5 -
5 of 21
Manunda Terrace Primary
Patterns and Algebra
Year 5 – Number and Algebra
AC Content Descriptor
Describe, continue
and create patterns with
fractions,
decimals and whole
numbers resulting
from addition and
subtraction
AC Elaborations
 Using the number
line to create
patterns involving
fractions or
decimals
So learning will include
 Know and explain the repeated pattern of hundreds, tens and ones across the
place value ‘groups’ of ones, thousands and millions, eg 657 432 156 = 657
million, 432 thousand and 156 ones
 Use models to investigate patterns by copying, creating, extending and
determining them when adding or subtracting decimal and fractional notion, eg
use marked or empty number lines, use table of values (as illustrated in
Number and Place Value substrand above), pattern making using matchsticks,
popsticks, straws
 Use models to investigate the patterns that eventuate from adding or
subtracting a given amount, such as ½ to or from ½, ¼, 1/8, 1/3, 1/6 sequences,
and describe and record the patterns formed; identify and explain the pattern
rule eg use marked number line, fraction walls, value tables
 Investigate the relationship in patterns between fractions and decimals; explain
patterns created and record findings, eg use models such as fraction walls and
100 x 100 grids, fraction circles and hundredth discs
First Steps Number: Book 2: RNP – KU1, KU3, KU4, KU5, KU6
Hundredth disc BLM 28:
http://wps.ablongman.com/ab_vandewalle_math_6/0,12312,3547876-,00.html
Use equivalent number
sentences involving
multiplication & division to
find unknown quantities
 Using relevant
problems to
develop number
sentences
 Use a variety of problem types to make equivalent multi step multiplication and
division number sentences and justify reasoning as to why they are equivalent
or not. Use symbols to show the relationship of operations on either side of an
equal sign, eg
o Investigate given multiplication and division number sentences in terms of
equivalence using’ true or false’ statements, and justify decision choice, eg
3 x 46 = 6 x 23 or 52 ÷ 12 = 26 ÷ 6 (problem should challenge and
encourage the move towards relational thinking instead of computation; for
example above numbers have been doubled or halved)
o Solve’ open sentences’ multiplication and division problems using
partitioning and combining (part part whole relationships), eg 20 x 48 = ∆ =
24 ; use models such as number lines to justify reasoning, leading to
discussions on relational thinking
First Steps Number: Book 2: UO – KU7, KU8; Cal – KU1, KU3, KU4, KU5, KU6;
RNP – KU3, KU4
Australian Curriculum NT
School
Year 5 -
6 of 21
Manunda Terrace Primary
Year 5 – Number and Algebra
Fractions and Decimals
AC Content Descriptor
AC Elaborations
So learning will include
Compare and order
common unit fractions and
locate and represent them
on a number line
 Recognising the
connection
between the order
of unit fractions
and their
denominator
 Count in fractions indicating the different names and representations, eg one
third, two thirds, three thirds or one; four thirds or one and a third; five thirds or
one and 2 thirds..., place each fraction 1/2, ¼ , 1/8, 1/3 and 1/6 on marked or
empty 0 – 1 number lines
 Investigate and compare different sized models (including measurement
attributes of mass and volume) to find fractions that are relative to that particular
whole, eg explain that one quarter of the family size pizza is more than half of
the small pizza; ½ the weight of the bag of marbles is more than ¾ the weight of
the shoe box of foam bricks
 State what the numerator and denominator mean in numerical representation of
fractions, eg ‘ the bottom number says how many parts in the whole, the top
number says how many of those parts we have’ (vinculum: the horizontal line
placed over the top of denominator indicates that it’s to be considered as a
group)
 Estimate the shaded fraction on geometric shapes, and order and record the
fractions on a number line marked 0-1
 Order familiar unit fractions and explain why they are larger or smaller, eg use
models to verify and justify which is bigger and why
 Use a 0-2 number line (with random points marked on it) and write the fraction
indicated by each point. Justify why fraction representation has been chosen, in
particular noting the choice of denominator. Note equivalent fractions
First Steps Number: Book 1: UFN- KU5
Investigate strategies to
solve problems involving
addition and subtraction of
fractions with the same
denominator
 Modelling and
solving addition
and subtraction
problems involving
fractions by using
jumps on a
number line, or
making diagrams
of fractions as
parts of shapes
 Using different strategies, investigate everyday occurrences of adding and
subtracting fractions and consider the relevance of equally divided and shared
parts and the relevance of size of the whole; record using models, proving and
justifying outcomes, eg
o share 3 pancakes between 4 people
o eating family sized pizzas in comparison to mega sized pizzas to feed the
family. Add together everyone’s shares; or subtract for the number of pieces
eaten by each member from the whole number of pizzas bought; prove and
justify what is the best sized pizza for value, for the family needs
 Investigate strategies to solve fraction addition and subtraction problems, and
justify the strategies used eg
o Use models to add and subtract simple fractions with the same denominator,
eg
 use jumps on marked or empty number lines to verify order sequence and
explain outcomes
 investigate addition and subtraction scenarios using, eg fraction walls
First Steps Number: Book 1: UFN – KU5; Book 2: Cal – KU7
Recognise that the place
value system can be
extended beyond
hundredths
 Use knowledge of
place value and
division by 10 to
extend the number
system to
thousandths and
beyond
 Recognising the
equivalence of one
thousandth and
0.001
Australian Curriculum NT
School
 Count, read, write, say and order sequences of decimal numbers to
thousandths
 Count number sequences forwards and backwards by decimal numbers, and
read and say numbers with two decimal places correctly, eg say ‘point three
two’, or ‘thirty two hundredths’, NOT ‘point thirty two’, read and say 9.263 as
nine point two six three, not nine point two hundred and sixty three
(understanding that the cyclic pattern of ones, tens, and hundreds used in
saying whole numbers, does not apply to decimals)
 Investigate where and why decimals to the thousandths and beyond are found
in real contexts, eg timing in sports statistics, measuring, science connections
 Relate decimals usage to everyday experiences, eg
o investigate decimals using real context measurement scenarios with length,
mass, area, volume, capacity and money; comparing similarities and
differences, and explaining the relationships of measurement unit
conversions to decimal numbers, eg mm to cm to m
 Use real context scenarios to investigate multiplication and division by 10, to
connect understandings that numbers both sides of the decimal point have a 10
to 1 ratio, and thousandths is equivalent to 0.001, eg
o using measuring metric system conversions with length, mass, area, volume,
capacity and money
Year 5 -
7 of 21
Manunda Terrace Primary
Fractions and Decimals
Year 5 – Number and Algebra
AC Content Descriptor
AC Elaborations
So learning will include
 Understand that base ten place value knowledge extends to even smaller
values of thousandths and beyond as part of the numbers less than one; use
models such as explaining the relationship between tens, ones and tenths
using objects such as a bundle of 10 straws where one straw is 1, eg show 14.2
using one bundle of 10 straws, 4 single straws and 2 pieces of a straw cut into
10 equal pieces; take examples (such as above) through to thousandths
understandings using technology models
 Use the constant function on a calculator to investigate counting by hundredths
and thousandths, eg
o press 0.01 =, = … Predict what will happen next after 0.09 and justify by
proving outcome using other models. Investigate, record and compare how
many presses it takes to get from one whole number to the next with tenths,
hundredths and thousandths
 Round decimals up or down to the nearest tenth and hundredth to estimate
numbers for calculating and check reasonableness of calculations and can say
which two whole numbers the answer will be between, eg 4.1 x 4.5 will be
between 15 and 17 because 4 x 4 is less than 4 x 5
First Steps Number: Book 1: UWDN – KU3, KU7, KU8 ; UFN – KU6
Compare, order and
represent decimals
 Locating decimals
on a number line
 Compare and order numbers up to two decimal places knowing that the number
of decimal places or length does not reflect the value of the number, eg
explains why 0.4 is greater than 0.32
 Connect decimal, fraction and word representations, eg know 0.2 and 2/10 both
represent two tenths, write decimals to thousandths in expanded form
 Use models to compare order and represent decimal places to thousandths
such as using marked, empty or broken number lines (also CMIT washing line),
eg
o to place a decimal between an identified pair of decimal numbers, eg 4
4.2
x?
4.8
5
o to identify the closest whole number to a given decimal
o to place given decimals (eg 0.007 and 0.7) on the correct/best estimate
points of a marked number line 0 to 1
o to decide which decimals are smaller or bigger (4.3, 4.07, 4.301)
o to place decimals that have ‘friendly fractions’ (halves, fifths, fourths and
eighths that more easily connect conceptually to decimal equivalents) on an
unlabelled but fractionally segmented number line (fourths, fifths) and
provide the fraction equivalent for each placed decimal; investigate and
discuss similarities and differences in the way both decimals and fractions
are written
First Steps Number: Book 1: UWDN – KU3, KU7, KU8 ; UFN – KU6
Australian Curriculum NT
School
Year 5 -
8 of 21
Manunda Terrace Primary
Money and Financial Matters
Year 5 – Number and Algebra
AC Content Descriptor
Create simple financial
plans
Australian Curriculum NT
School
AC Elaborations
So learning will include
 Creating a simple
budget for a class
fundraising event
 Use real scenarios to investigate the concepts of calculating, predicting and
manipulating ingoing and outgoing money in order to effectively finance a real
or simulated event, and make conjectures about how personal or group
decisions made influence the end result
 Use calculators to enter, read and calculate money transactions and know that
a display of 5.3 means $5.30
 Understand that the GST (Goods and Services Tax) is a 10% government tax
included in the purchase price of many goods and services, and investigate it’s
prevalence, eg collect shopping brochures, newspapers, magazine
advertisements
 Investigate the interrelatedness of the term ‘percent’ and the term ‘hundredth’,
understanding that percent is a new notation not a new concept, and is
represented by the symbol %
 Calculate 50%, 25% and 75% by mentally using fractional equivalents, eg finds
25% by halving and halving again (Year 6 Australian Curriculum content
descriptor) and identify the 10% GST component of collected invoices and
receipts
 Identifying the
GST component
of invoices and
receipts
Teaching Financial Literacy link
http://www.teaching.financialliteracy.gov.au/home.html
Year 5 -
9 of 21
Manunda Terrace Primary
Resources
Year 5 – Number and Algebra
Maths manipulatives resources– Manunda PS library
Scootle - Learning Objects http://www.scootle.edu.au/ec/p/home
First Steps Number Number: Book 1: UWDNT – Understand Whole
and Decimal Numbers; UFN – Understand Fractional Numbers;
Book 2: UO – Understand Operations; Cal – Calculate; RNP –
Reason about Number Patterns
Teaching Financial Literacy link
http://www.teaching.financialliteracy.gov.au/home.html
Number lines: marked ( with sequenced numbers), empty (no
numbers ), broken (a segment that is marked but doesn’t begin at
zero, eg __15__________________56_)
Number expanders
http://www.education.vic.gov.au/studentlearning/teachingresources/
maths/mathscontinuum/number/numberexpander.htm
National Library of Virtual Manipulatives http://nlvm.usu.edu/
http://wps.ablongman.com/ab_vandewalle_math_6/0,12312,354787
6-,00.html
Gay West resource file
Maths 300 Username:
(check administration for username and
password)
Collections: include any items that can be handled, from
commercially made maths resources (eg counters, link blocks, geo
shapes, small objects collections - mini people / teddy bears / fruit),
to environmentally collected items (eg leaves, shells), to art items
(eg popsticks, coloured papers, beads, pipe cleaners)
Model: has been used to describe actions using manipulatives,
games and strategies to show a process of understanding
Problem Solving Strategies
Making a table
Drawing a graph
Pictorial representation
Use of algorithms
Guess and check
Act out problem
(Further information on Problem Solving)
Key Mathematical Language (EAL/D)
Number and Place Value
Rounding, estimating, increasing, decreasing, divide, addition, sum, total, difference, difference between, compare, ascending order,
descending order, differences, lower, higher
Patterns and Algebra
Sequence, position, number, array, multiples, vertical, horizontal, row, column, double, increase, decrease, sum, difference
Fractions and Decimals
Percent, denominator, numerator, equal, tenths, hundredths, the fraction equivalent, constant function on a calculator
Money and Financial Matters
Goods and Services Tax as GST, budget, income, payment, the symbol %, interest, bank account, wage, salary, deposit, withdrawal,
borrow, loan
Australian Curriculum NT
School
Year 5 -
10 of 21
Manunda Terrace Primary
Mathematics Scope and Sequence
Measurement and Geometry
Achievement Standards
Proficiency Strands
Understandings: By the end of Year 5, students solve simple
problems involving the four operations using a range of strategies.
They check the reasonableness of answers using estimation and
rounding. Students identify and describe factors and multiples.
They explain plans for simple budgets. Students connect threedimensional objects with their two-dimensional representations.
They describe transformations of two-dimensional shapes and
identify line and rotational symmetry. Students compare and
interpret different data sets.
Skills: Students order decimals and unit fractions and locate them
on number lines. They add and subtract fractions with the same
denominator. Students continue patterns by adding and
subtracting fractions and decimals. They find unknown quantities
in number sentences. They use appropriate units of measurement
for length, area, volume, capacity and mass, and calculate
perimeter and area of rectangles. They convert between 12 and
24 hour time. Students use a grid reference system to locate
landmarks. They measure and construct different angles.
Students list outcomes of chance experiments with equally likely
outcomes as probabilities between 0 and 1. Students pose
questions to gather data, and construct data displays appropriate
for the data.
Understandings: By the end of Year 5, students solve simple
problems involving the four operations using a range of strategies.
They check the reasonableness of answers using estimation and
rounding. Students identify and describe factors and multiples.
They explain plans for simple budgets. Students connect threedimensional objects with their two-dimensional representations.
They describe transformations of two-dimensional shapes and
identify line and rotational symmetry. Students compare and
interpret different data sets.
Skills: Students order decimals and unit fractions and locate them
on number lines. They add and subtract fractions with the same
denominator. Students continue patterns by adding and
subtracting fractions and decimals. They find unknown quantities
in number sentences. They use appropriate units of measurement
for length, area, volume, capacity and mass, and calculate
perimeter and area of rectangles. They convert between 12 and
24 hour time. Students use a grid reference system to locate
landmarks. They measure and construct different angles.
Students list outcomes of chance experiments with equally likely
outcomes as probabilities between 0 and 1. Students pose
questions to gather data, and construct data displays appropriate
for the data.
Achievement Standard Work Samples
Achievement Standard Work Samples
http://www.australiancurriculum.edu.au/Mathematics/Curriculum/F-10
http://www.australiancurriculum.edu.au/Mathematics/Curriculum/F-10
Year 5 - Measurement and Geometry
Using Units of Measurement
AC Content Descriptor
AC Elaborations
So learning will include
Choose appropriate units of
measurement for length,
area, volume, capacity and
mass
 Investigating
alternative measures
of scale to
demonstrate that
these vary between
countries and change
over time, eg
temperature
measurement in
Australia, Indonesia,
Japan and USA
 Know that some tasks require measuring different attributes (length, area,
volume, mass and temperature) and more accurate measurement than
others, eg more accuracy required when measuring water for cooking
bread than for making cordial
 Know the relationships between km, m, cm, and mm and use visualisation
of each unit in order to estimate length at a glance
 Measure mass accurately to the nearest graduation in kg, g, by first
choosing an appropriate measuring instrument that allows for the level of
precision needed for the purpose, eg chooses bathroom scales to weigh
their luggage before travelling on a plane
 Investigate the relationship of the size of ‘measurement units’ in length,
area, volume, capacity and mass, to the object/area being measured,
and use and justify choice of measuring units eg
o for measuring with accuracy or for approximation purposes
o when measuring very small to very large objects/spaces, eg using mm
for measuring insects, km for distances between places
 In real context scenarios understand and use standard metric
measurement symbols when recording measurements
o square metres – 1m2 = 10 000 square cm
o square centimetres 1cm2 = 100 square mm
o cubic metre – 1m3 = 100cm x 100cm x 100cm
o cubic centimetres – 1cm3 = 10mm x 10mm x 10mm
o Kilometres – 1km = 1 000m
o Hectares – 1ha = 10 000 square metres ( 100m x 100m)
o Investigate imperial measurement units, the geographical locations
where these are used, or historically have been used, and compare
and contrast these to the metric system of measurement, eg knows
historical relationships between inches and centimetres, feet and yards
to metres, acres and hectares
 Recognising that
some units of
measurement are
better suited for some
tasks than others, eg
kilometres rather than
metres to measure
the distance between
two towns
First Steps Measurement: Book 1: UU – KU2, KU5, KU6, KU7, KU8; DM –
KU4, KU5
Australian Curriculum NT
School
Year 5 -
11 of 21
Manunda Terrace Primary
Using Units of Measurement
AC Content Descriptor
AC Elaborations
Calculate the perimeter and  Exploring efficient
area of rectangles using
ways of calculating
familiar metric units
the perimeters of
rectangles such as
adding the length and
width together and
doubling the result
Year 5 - Measurement and Geometry
 Exploring efficient
ways of finding the
areas of rectangles
So learning will include
 Understand the concept/meaning of perimeter, area and volume writing a
description of each and giving examples of where measuring these
attributes might be needed, eg water in a fish tank, distance around the
school boundary fence, size of cloth needed to fully cover a table or bird
cage
 Investigate measuring a rectangular area by placing identical square units
in rows or columns over the surface without overlays or gaps,
investigating the relationship of these units to the concept of a
multiplication array (leading to understand a row of squares (determined
by the length of the side) can be seen as a single row unit that can be
replicated by multiplication/repeated addition; (how many times being
determined by the length (number of units) of the other side- or Width of
the rectangle)
 Investigate and describe ways of calculating the area of a rectangle using
the array concept and explain reasoning as to which description is the
most efficient eg Area = column of 8 + column of 8 + column of 8; Area =
columns of 8 (length) x rows of 3 (width); A = L x W
 Devise a method to calculate the approximate area of a large region; use,
verify, and justify its efficiency, recognising the need for larger units of
area; hectare and square kilometre
 Investigate and identify areas that are less than, about the same as and
larger than a square metre and understand that a square metre area can
be various shapes, eg a rectangle
 Investigate and describe ways of calculating perimeter and explain
reasoning as to which description is the most efficient, including strategies
to measure curved boundaries eg Perimeter = side 1+side 2 + side 3 +
side 4; Perimeter = (L x 2) + (W x 2); Perimeter = L + W x 2
First Steps Measurement: Book 1: UU – KU2, KU5, KU6, KU7, KU8; DM KU4, KU5
Compare 12 and 24 hour
time systems and convert
between them
 Investigating the ways
time was and is
measured in different
Aboriginal Country
such as using tidal
change
 Using units hours,
minutes and seconds
 Investigate and make generalisations about where and why 12 or 24 hour
representations of time occur in the environment, eg find example in
newspapers, TV schedules, tide times, plane timetables
 Write , draw and explain scenarios that show a need to understand the
use of 12 and 24 hour time notation, eg catching a plane
 Use real context scenarios to investigate the relationships between 12
and 24 hour and am and pm understandings; eg
o convert between 12 and 24 hour representations of time that use
hours, minutes and seconds when reading and interpreting 12 and 24
hour timetables to work out travel plans (bus and train timetables –
schedule or online)
 Research ways different indigenous groups across Australia measure
time
 Calculate elapsed time from a timetable, eg reads a bus timetable and
says the next bus will come in 25 minutes and takes 30 minutes to get
into town, its 3pm now, so I’ll get there at 3:55 if I catch it and can identify
assumptions such as bus on time, and bus won’t break down
 Investigate different strategies when using clock faces or timelines to
calculate time durations, eg use the ‘jump’ method to find time from 8:15
to 10:50. to do this, eg set as a table - 8.15 to 9.00 is 45mins, 9.00 to
10.00 is 60mins, 10.00 to 10.50 is 50 mins, so add mins and convert
(Note: 24 hour time is written 0525 or 1418, not 05:25; no colon)
First Steps Measurement: Book 1: DM – KU6
Australian Curriculum NT
School
Year 5 -
12 of 21
Manunda Terrace Primary
Shape
AC Elaborations
So learning will include
Connect three-dimensional
objects with their nets and
other two-dimensional
representations
 Identifying the shape
and relative position
of each face of a solid
to determine the net
of the solid, including
prisms and pyramids
 Using models investigate how key property features of cubes, cylinders,
cones, and rectangular prisms relate to each object, particularly noting
the placement and 2D shape of faces; and recording findings, eg
o constructing and deconstructing the nets (flat 2D pattern) of shapes eg
by cutting open a variety of shaped boxes; using geo shapes,
polydrons, cardboard/paper, isometric and grid paper
o investigate how many different nets can be made for a ‘given’ shape,
predicting, constructing and justifying findings, eg Maths 300 #116
cube nets
o investigate the nets of various sized, but same 3D objects, and predict
and make generalisations about the key features, eg investigate
different sized rectangular prisms noting whether size of length, width
or height changes the 2D shapes in the nets
o identify and record by drawing different views and representations of
3D objects including
 nets
 perspective drawings (showing length, width and height
representation),
 isometric drawings – 3D shapes drawn on isometric grids (shows a
90º angle drawn as a 30ºangle)
 orthogonal views, eg build simple 3D shapes with cubes, then
represent the top, front, back and side views as 2D shape drawings,
eg http://nzmaths.co.nz/resource/winning-ways, use card matching
sets
 cross sections, eg oblique cut cross section of a cylinder shows an
oval
 Use card sets to match 3D objects with different 2 D representations, eg
using cards set of photos of regular and irregular 3D objects from different
view points, and card sets of related 2D representations such as isometric
drawings, orthogonal views, perspective drawings and nets; and justify
matching of cards checking on a real 3D model
 Predict and test which pentomino nets can be folded to make an open
box and which are symmetrical
 Make tessellations with pentominos and explain strategy used
Year 5 - Measurement and Geometry
AC Content Descriptor
 Representing twodimensional shapes
such as photographs,
sketches and images
created by digital
technologies
First Steps Measurement: Book 2: RS – KU1, KU2, KU3
Australian Curriculum NT
School
Year 5 -
13 of 21
Manunda Terrace Primary
Location and Transformation
AC Content Descriptor
Use a grid reference
system to describe
locations. Describe routes
using landmarks and
directional language
AC Elaborations
 Comparing aerial
views of Country,
desert paintings and
maps with grid
references
Year 5 - Measurement and Geometry
 Creating a grid
reference system for
the classroom and
using it to locate
objects and describe
routes from one
object to another
So learning will include
 Interpret and use simple scales, eg one grid square length equals ten km,
coordinates, eg 2B and keys on maps and plans (such as a street
directory or map of their town) when locating features or giving directions
 Match photographs of a scene to the positions , shown on a plan, from
which the photographs were taken
 Play coordinate grid games eg Hurkle
http://www.aimsedu.org/aimskids/ipuzzles/hurkle/index.html
 Construct a map or plan of a familiar location that includes a key of
significant items and a simple coordinate grid
 Give or follow instructions to move involving turning through a given
rotation clockwise or anticlockwise or moving a given number of steps
N,S, E, W (with compass points shown)
 Use a coordinate grid system on a local street map to identify/record
specific items or places given the coordinates
 Interpret and create maps and plans involving positive coordinates and
intermediate compass points
 Calculate the distance between two locations or coordinates on a map
given a simple scale. Investigate ‘Google Earth’ site
First Steps Measurement: Book 2: RL KU1, KU2, KU3
Describe translations,
reflections and rotations of
two-dimensional shapes.
Identify line and rotational
symmetry
 Identifying and
describing the line
and rotational
symmetry of a range
of two-dimensional
shapes, by manually
cutting, folding and
turning shapes and by
using digital
technologies
 Identifying the effects
of transformations by
manually flipping,
sliding and turning
two-dimensional
shapes and by using
digital technologies
 Using models investigate and compare by predicting outcomes, then
manipulating 2D shapes to find and explore, if and how many points of
rotational symmetry they have, (ie the 2D shape or ‘footprint’ rotated
about a point (without flipping it over) lands in a position exactly matching
the footprint. The ‘order of rotational symmetry’ is the number of times the
shape matches the footprint in a full turn); explain and record results, eg
an equilateral triangle has a rotational symmetry of order 3, (3 points)
 Use models of 2D shapes to investigate the relationship of symmetry and
rotational symmetry properties, eg a parallelogram has no lines of
symmetry but two points of rotational symmetry; create words having line
or rotational symmetry using uppercase letters that exhibit symmetry
 Classify triangles and quadrilaterals according to side length, shape and
symmetry
 Use dynamic geometry software to create tessellation patterns where 2D
shapes are manipulated through line and rotational symmetry, eg
o describe the Tetris shapes and how they fit together
o GeoGebra http://www.geogebra.org/cms/
 Investigate the angle properties of tessellating 2D shapes
First Steps Measurement: Book 2: RT – KU1, KU2, KU3, KU4; RG – KU1
Apply the enlargement
transformation to familiar
two-dimensional shapes
and explore the properties
of the resulting image
compared with the original
 Using digital
technologies to
enlarge shapes
 Using a grid system
to enlarge a favourite
image or cartoon
 Investigate the connections between proportional reasoning and the
geometric concept of similarity by enlarging and reducing dimensions of
2D shapes, eg take photos of everyday objects in the classroom; print
photo and work out the scale of the photo to the object
 use a variety of grid papers such as 1cm or 2cm to create or use given
ratios, (eg 1cm square = to 3cm squares, or 1:3) when drawing 2D
shapes, comparing original drawing with the transformed (enlarged or
reduced) drawing
 informally use 1 point perspective over a grid to create enlarged and
reduced transformations
 use dynamic geometry software to explore the idea of ratio, eg GeoGebra
http://www.geogebra.org/cms/
First Steps Measurement: Book 2: RT – KU1, KU2, KU3, KU4; RG – KU1
Australian Curriculum NT
School
Year 5 -
14 of 21
Manunda Terrace Primary
Geometric Reasoning
Year 5 - Measurement and Geometry
AC Content Descriptor
Estimate, measure and
compare angles using
degrees. Construct angles
using a protractor
Australian Curriculum NT
School
AC Elaborations
So learning will include
 Measuring and
constructing angles
using both 180° and
360° protractors
recognising that
angles have arms and
a vertex, and that size
is the amount of turn
required for one arm
to coincide with the
other
 Draw and accurately measure angles to the nearest degree using a
variety of tools to measure real context and on-screen angles, eg using
protractors and electronic protractors, cardboard angle wheels (100th disc
/ 2 spliced circles together)
 Understand and use ‘degree’ º notation to label measurements
 Investigate angles properties of polygons by direct measurement and
through the use of dynamic geometric software, eg sum of interior angles
of a rectangle
 Explore angle size by cutting up shapes and putting corners (angles)
together
 Name angle type, use standard geometrical marks to identify equal sides
of shapes, equal angles and right angles
 Classify angles using terms, acute, right, obtuse, straight, reflex and mark
on a full circle
 Understand and use 180º and 360º protractors to make comparative
measures of different angles and relate amount of turn to degrees, eg 90º,
180º, 270º and 360º, eg labelling a protractor drawing with greater than
and less than angles named and marked around the circle; use interactive
sites such as the Banana Game
 Make creative patterns and designs using 2D shapes; explain the shape
and angles in your design
Year 5 -
15 of 21
Manunda Terrace Primary
Year 5 - Measurement and Geometry
Resources
First Steps Measurement: Book 1: UU – Understand Units; DM –
Direct Measure; Book 2: IM – Indirect Measure; E – Estimate; RL
– Represent Location; RS – Represent Shape; RT – Represent
Transformation; RG – Reason Geometrically
http://www.brainpop.com/ (check administration for username
and password)
http://nrich.maths.org/public/
http://www.amathsdictionaryforkids.com/dictionary.html maths
dictionary
National Library of Virtual Manipulatives http://nlvm.usu.edu/
Collections: include any items that can be handled, from
commercially made maths resources (eg counters, link blocks,
geo shapes, small objects collections - mini people / teddy bears
/ fruit), to environmentally collected items (eg leaves, shells), to
art items (eg popsticks, coloured papers, beads, pipe cleaners)
Model: has been used to describe actions using manipulatives,
games and strategies to show a process of understanding
Problem Solving Strategies
Guess and check
Create an organized list
Looking for a pattern
(further information on problem solving)
Key Mathematical Language (EAL/D)
Using Units of Measurement
conversion, convert, area, columns, rows, array, surface region, perimeter, square metres, square centimetres, square kilometres,
hectares, length, width, breadth, cubic centimetre, volume, litre, millimetre, millilitres, metric, kilogram, grams, half a kilogram, quarter
of a kilogram, second, analogue, digital, timetable, am, pm,
Shape
vertex/vertices, front, top, side views, depth, cross-section, apex, cuboid, regular shape, irregular shape, decagon, heptagon,
pentominoes, right angle, perpendicular lines, parallel lines, intersecting lines, tetromino, tetrix
Location and Transformation
degree, clockwise, half turn, quarter turn, anticlockwise, tessellation, cross-section, route, North, South, East, West, boundary
Geometric Reasoning
right angle, perpendicular lines, parallel lines, acute, right, obtuse, straight, reflex angles
Australian Curriculum NT
School
Year 5 -
16 of 21
Manunda Terrace Primary
Mathematics Scope and Sequence
Statistics and Probability
Achievement Standards
Proficiency Strands
Understandings: By the end of Year 5, students solve simple problems
involving the four operations using a range of strategies. They check
the reasonableness of answers using estimation and rounding.
Students identify and describe factors and multiples. They explain
plans for simple budgets. Students connect three-dimensional objects
with their two-dimensional representations. They describe
transformations of two-dimensional shapes and identify line and
rotational symmetry. Students compare and interpret different data
sets.
Skills: Students order decimals and unit fractions and locate them on
number lines. They add and subtract fractions with the same
denominator. Students continue patterns by adding and subtracting
fractions and decimals. They find unknown quantities in number
sentences. They use appropriate units of measurement for length,
area, volume, capacity and mass, and calculate perimeter and area of
rectangles. They convert between 12 and 24 hour time. Students use a
grid reference system to locate landmarks. They measure and
construct different angles. Students list outcomes of chance
experiments with equally likely outcomes as probabilities between 0
and 1. Students pose questions to gather data, and construct data
displays appropriate for the data.
Achievement Standard Work Samples
http://www.australiancurriculum.edu.au/Mathematics/Curriculum/F-10
Understanding includes making connections between
representations of numbers, using fractions to represent
probabilities, comparing and ordering fractions and decimals
and representing them in various ways, describing
transformations and identifying line and rotational symmetry
Fluency includes choosing appropriate units of
measurement for calculation of perimeter and area, using
estimation to check the reasonableness of answers to
calculations and using instruments to measure angles
Problem Solving includes formulating and solving authentic
problems using whole numbers and measurements, and
creating financial plans
Reasoning includes investigating strategies to perform
calculations efficiently, continuing patterns involving fractions
and decimals, interpreting results of chance experiments,
posing appropriate questions for data investigations and
interpreting data sets
Year 5 – Statistics and Probability
Chance
AC Content Descriptor
AC Elaborations
So learning will include
List outcomes of chance
experiments involving
equally likely outcomes and
represent probabilities of
those outcomes using
fractions
 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 (rockpaper-scissors)
 Use in context, understand, calculate and explain that in chance
experiments probability can be express as the number of successful trials
(one action in an experiment) divided by the total number of the trials, eg
5 tails in 20 flips of the coin, 5 divided by 20
 Use and devise games or models to investigate chance events where the
likely hood of occurrences is known (theoretical probability) and compare,
discuss and explain what happens in trials using fractional
representations; record outcomes of the trials, and analyse data to make
conjectures about winning strategies eg
o Predict, play, discuss, record and analyse outcomes in ‘equal chance’
games, eg a spinner with two colours on each half has a 50 – 50
chance or ½ a chance of coming up; using one coin to toss heads or
tails; the winner of a race between two children of equal ability
o Devise and conduct repeated trials to investigate the relationships
between numerical ‘randomness’ of criteria and the likelihood of
chance event, eg, 6 has more chance of coming up when tossing a 6
sided dice (1 in 6 chance), than if you tossed a 20 sided dice (1 in 20
chance); on a ¾ blue and ¼ red spinner, blue is more likely to be spun
because it covers ¾ of the spinner
o Play and analyse outcomes of games such as Greedy pig or Heads
and Tails as described in Year 4, and use this to make conjectures
about probability of chance - expressed as fractions, and about
winning strategies; explain reasoning
 Rank discrete events from most likely to least likely based on the
numerical probability involved, eg drawing cards at random from a 52
pack of cards, an ace has a less likely chance at 1 in13 (1/13 of being
picked than a red card, at an equal chance or ½ chance
 Says which events have more chance, equal chance or less chance by
reading and understanding the context, eg knows that the more raffle
tickets they buy in a raffle the more chance they have of winning or
getting a prize and can relate this to the number of tickets sold says: I
have one chance in 5 thousand of winning which is better than one
chance in a million
(For some events the exact probability can be determined by an analysis
of the event itself, eg six sided dice toss – 1 in 6 chance. A probability
determined in this manner is call a theoretical probability)
First Steps Chance and Data: UC – KU4, KU5
Australian Curriculum NT
School
Year 5 -
17 of 21
Manunda Terrace Primary
Chance
AC Content Descriptor
AC Elaborations
Recognise that probabilities  Investigating the
range from 0 to 1
probabilities of all
outcomes for a simple
chance experiment and
verifying that their sum
equals 1
So learning will include
 Use models to investigate and understand that probability is expressed as
a numerical value, where ‘impossibility’ indicates 0 and certainty indicates
1, eg on a 0 – 1 number line, eg given an event such as ‘there will be a
crocodile story on the cover of NT News this month’, mark a point on the
number line to indicate how likely the event will be
 Investigate and understand the numerical value of probability, 0 and 1,
also relates to common fractions and percentage, eg a spinner with two
colours one on each half has an even or 50 – 50 chance, or ½ a chance,
or a 50% chance; a one coloured blue spinner has a zero chance of
spinning red, so 0 – impossible or 0%; and an all red spinner will spin red,
so is a ‘certain chance ’ or 1, or 100%
 Use common percentages to describe likelihood of real context
investigation outcomes, eg 50%, 25%, 75%, 100% chance
 Utilises graphic organisers, eg tree diagrams, to identify possible
outcomes
 Investigate, predicts and records possible outcomes of an event using the
numerical value 0 to 1, a fractional value, and percentage, eg describe
the likelihood of outcomes, eg 1 in 4 chance so ¼ or 25% chance
First Steps Chance and Data: UC – KU4, KU5
Australian Curriculum NT
School
Year 5 -
18 of 21
Manunda Terrace Primary
Data representation and interpretation
AC Content Descriptor
Year 5 – Statistics and Probability
Pose questions and collect
categorical or numerical
data by observation or
survey
AC Elaborations
So learning will include
 Posing questions about
insect diversity in the
playground, collecting
data by taping a onemetre-square piece of
paper to the
playground and
observing the type and
number of insects on it
over time
 Investigate, design (including using IT) and effectively choose and use
data collection methods that best suit the context eg questionnaires,
surveys, sampling techniques, tables, lists, observations, experiments,
simulations
 Using given or chosen contexts, pose questions that will elicit numerical
and categorical data about element/s of that context; design collection
strategies; justify which are the most effective and efficient in eliciting and
collecting data, eg
o for life in the playground, collect categorical (types of insects) and
numerical (number of insects in each type group) data on insect
diversity in the playground using a sampling over time strategy
o pose a question in response to a localised issue, such as information
needed to take to School Council about playground facilities such as,
‘Does our school playground meet every child’s needs?’
 observe and collect data on the density (numerical data), of children
over time in various parts of the playground (categorical data)
 survey to find out age of children using specific spaces in the
playground using snapshot over time approach, (categorical data)
 survey children by Year level (numerical and categorical data) to
find out their preferred space (categorical data)
Consider questions such as what variables need to be considered
when designing data collection strategies and why? eg, time of data
collection and possible impact on results
 Investigate posing ‘What is the likelihood of................?’ or ‘How many
items could you draw out......? type questions and design simple
experiments using the most effective data collection strategy to answer
questions, eg
o How many blue marbles are you likely to draw out of a container
holding the same number of green and blue marbles in ten draws?
Design a sampling technique that is based on long trial understandings
and explain reasoning in choosing that data collection strategy
 Collect data to answer a question in their own context, eg what sort of litter
do students at the school leave behind? What proportion of students in the
school are from different cultural groups/ by first deciding what data they
need and how they might collect it
First Steps Chance and Data: CPDA – KU1, KU2
Construct displays,
including column graphs,
dot plots and tables,
appropriate for data type,
with and without the use of
digital technologies
 Identifying the best
methods of presenting
data to illustrate the
results of
investigations and
justifying the choice of
representations
 Construct data displays, investigating the effect that the choice of display
type (hand and technology generated) has on the ease of interpreting
data, to answer a focus question; explain reasoning, represent collected
data on a suitable graph (including using technology) and justify the choice
of graph, eg
o use a variety of data displays such as column and bar graphs and
histographs
o simple line graph (A graph that uses points connected by lines to
show how something changes in value as time goes by or as something
else happens, eg temperature over time in degrees)
o dot plots (similar to a bar chart, with the bars replaced by a series of
dots each one representing a fixed number of elements. For continuous
data, the dot plot is similar to a histogram, with the rectangles replaced
by dots. A dot plot can also help detect any unusual observations
(outliers), or any gaps in the data set.), eg activities such as
http://nzmaths.co.nz/resource/fridge-pickers
http://nzmaths.co.nz/resource/winning-dots
o diagrams and tables, eg Venn diagrams and Carroll diagrams (two
way tables)
Year 1’s
Year 4’s
Bike to school
3
14
Car to school
15
5
o Investigate situations and the data displays involving permutations,
(ordered arrangements of a set of objects/symbols) and describe
discoveries, eg How many different combinations can you make from 4
different flavoured ice creams and 3 different types on cones
o Resource: Choosing appropriate graphical displays
http://www.education.vic.gov.au/studentlearning/teachingresources/mat
hs/mathscontinuum/mcd/M37508P.htm#a3
 Understand and uses key features of data displays, eg labels, titles, and x
and y axis and scales
First Steps Chance and Data: CPDB – KU1, KU2, Ku3, KU4, KU5
Australian Curriculum NT
School
Year 5 -
19 of 21
Manunda Terrace Primary
Data representation and interpretation
AC Content Descriptor
Year 5 – Statistics and Probability
Describe and interpret
different data sets in context
AC Elaborations
 Using and comparing
data representations
for different data sets
to help decision
making
So learning will include
(Graphs and charts tell about information; and different types of
representations tell different things about the same data)
 Investigate ways of analysing displays of data to generate inferences
about the focus question, i.e. the reason for the data collection, focussing
on the variability of the data, the centre of the data (clustering) and the
‘shape’ of the data, (how spread out or clustered the data is, using
questions (☻) like, eg
o What do the numbers tell us about...?
o If we asked another ‘group’ how would our data look? What if we asked
a larger group, how would it look then?
o How do the numbers in this graph (about a group) compare to another
groups’ graph?
o Where is the data ‘clustering’? How much of the data is or is not in the
cluster?
o What kinds of variability might need to be considered in interpreting this
data?
o Would this data be different if ...? (change of sample, group or setting)
o What does the graph not tell us? What might we infer?
o What new questions could come out of this data?
(J A Van De Walle, K S Karp, J M Bay-Williams; 2004, pg 453)
 Investigate ways of analysing and comparing data and displays; make
statements and predictions about the information using data displays to
support their arguments, eg
o interpret sampling data to predict fairly accurately the height of a new
child joining their class next week
o sketch the shape of data in a graph (without using any specific data) by
matching the sketch to a written or orally described situation; match a
data display from a selection of different types, to match a written or
orally described situation
o read and use data shown in published tables to help make decisions,
eg reads a menu or price list or compare tables in mobile phone plans
to help make a choice of which one to buy
o interpret expected or unexpected variations in data displays and reason
as to the cause and the effect eg variation in data showing how many
children line up at the canteen as soon as the lunch bell goes, or at later
times during lunch; on Tuesday, 16 children from the class bought their
lunch at the canteen
 Understand, identify and compare variability shown in and across data
displays, and investigate the most effective data display to show the
variability of data for a particular context, eg
o Variability within and between groups (detailed in Year 4)
o Sampling variability, eg collect data from a coin tossed 10 times that
might show 5 heads and 5 tails, or many other combinations (variables)
 Understand and use different data sources to interpret and compare
information, eg
o real-life applications like graphs and tables found in newspapers or
online
o advertising information sheets
 Interpret data displays and make statements, predictions and conclusions
from it including about the mode if appropriate, eg says paper is the most
common rubbish that we leave behind, and concludes most of the trees in
the school ground are eucalypts
First Steps Chance and Data: ID – KU1, KU2, KU3
Australian Curriculum NT
School
Year 5 -
20 of 21
Manunda Terrace Primary
Year 5 – Statistics and Probability
Resources
First Steps: UC – Understand Chance; CPDA – Collect and
Process Data Part A; CPDB – Collect and Process Data Part B;
ID - Interpret Data
Spinners: Spinners can be easily designed using colours
segments or number ranges, and have multiple uses in maths
across all strands. They can be made from a spinner printout, a
pen and a paperclip. They do not require assembly. ‘Talking
Namba – Scaffolded foundational numeracy approach’ – has a
short video clip at this link, showing how a spinner is made and
used. http://ourcourses.ntschools.net/course/view.php?id=271
National Library of Virtual Manipulatives http://nlvm.usu.edu
http://www.amathsdictionaryforkids.com/dictionary.html maths
dictionary
Collections: include any items that can be handled, from
commercially made maths resources (eg counters, link blocks,
geo shapes, small objects collections - mini people / teddy bears
/ fruit), to environmentally collected items (eg leaves, shells), to
art items (eg popsticks, coloured papers, beads, pipe cleaners)
Model: has been used to describe actions using manipulatives,
games and strategies to show a process of understanding
Problem Solving Strategies
Guess and check
Create an organized list
Looking for a pattern
(more information on problem solving)
Key Mathematical Language (EAL/D)
Chance
most likely, least likely, experimental data, occurrence, prediction, investigations, judgements, possible, impossible, certain, fair,
odds-on, favourite, perhaps, 50-50, outcomes, equally likely, chance, even chance, equal chance, combinations, frequency, table,
random, never, possibility, analyse, predict, order, probability, tally, experiment, probable, event, trial.
Data representation and interpretation
tally, bar graph, column graph, axis, heading, labels (graph), table
Australian Curriculum NT
School
Year 5 -
21 of 21
Manunda Terrace Primary