Download Year Level Plan

DEPARTMENT OF EDUCATION
C2C
Year Level Plan
Mathematics
Year 6
Year level description
Curriculum intent
The proficiency strands Understanding, Fluency, Problem Solving and Reasoning are an integral
part of mathematics content across the three strands: Number and Algebra, Measurement and
Geometry, and Statistics and Probability. The proficiencies reinforce the significance of working
mathematically within the content and describe how the content is explored or developed. They
provide the language to build in the developmental aspects of the learning of mathematics.
At this year level:
Understanding includes describing properties of different sets of numbers, using fractions and
decimals to describe probabilities, representing fractions and decimals in various ways and describing
connections between them, and making reasonable estimations
Fluency includes representing integers on a number line, calculating simple percentages, using
brackets appropriately, converting between fractions and decimals, using operations with fractions,
decimals and percentages, measuring using metric units, and interpreting timetables
Problem Solving includes formulating and solving authentic problems using fractions, decimals,
percentages and measurements, interpreting secondary data displays, and finding the size of
unknown angles
Reasoning includes explaining mental strategies for performing calculations, describing results for
continuing number sequences, explaining the transformation of one shape into another, explaining
why the actual results of chance experiments may differ from expected results
Achievement standard
By the end of Year 6, students recognise the properties of prime, composite, square and triangular
numbers. They describe the use of integers in everyday contexts. They solve problems involving all
four operations with whole numbers. Students connect fractions, decimals and percentages as
different representations of the same number. They solve problems involving the addition and
subtraction of related fractions. Students make connections between the powers of 10 and the
multiplication and division of decimals. They describe rules used in sequences involving whole
numbers, fractions and decimals. Students connect decimal representations to the metric system and
choose appropriate units of measurement to perform a calculation. They make connections between
capacity and volume. They solve problems involving length and area. They interpret timetables.
Students describe combinations of transformations. They solve problems using the properties of
angles. 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 locate fractions and integers on a number line. They calculate a simple fraction of a quantity.
They add, subtract and multiply decimals and divide decimals where the result is rational. Students
calculate common percentage discounts on sale items. They write correct number sentences using
brackets and order of operations. Students locate an ordered pair in any one of the four quadrants on
the Cartesian plane. They construct simple prisms and pyramids. Students list and communicate
probabilities using simple fractions, decimals and percentages.
C2C adapted with permission by NT DoE © The State of Queensland
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Unit outline Semester 1
Sequencing the teaching and learning
Term 1
Unit 1
Students have opportunities to develop
understandings of:
 Properties of numbers: factors,
multiples, prime and composite
numbers
 Fractions: related denominators,
comparing, adding, subtracting
 Measurement: metric system,
connection to decimals, length,
mass and capacity
 3 dimensional objects: prisms,
pyramids, geometric features,
nets, constructing.
Term 2
Unit 2
Students have opportunities to develop
understandings of:
 Properties of numbers: identify
properties of square, triangular,
prime and composite numbers
 Fractions and decimals: add and
subtract decimals to thousandths,
use estimation and rounding to
check reasonableness of answers
 Data: collect, display and interpret.
Unit 3
Students have opportunities to develop
understandings of:
 Integers: properties of numbers,
investigating positive and negative
numbers
 Fractions, decimals and
percentages: calculating
equivalent fractions, decimals and
percentages
 Decimals and the metric system:
units of measurement, identifying
relationships between metric units
 Time: interpreting and using
timetables
Unit 4
Students have opportunities to develop
understandings of:
 Data interpretation: interpreting a
variety of data displays, including
unfamiliar display types
 Addition and subtraction (whole
numbers and decimals): applying
appropriate mental and written
strategies and digital technologies
to solve problems involving
addition and subtraction and
solving problems involving
decimals to thousandths using a
variety of mental and written
strategies
 Addition and subtraction
(fractions): adding and subtracting
fractions with the same and related
denominators
 Chance: representing probability
as a fraction, decimal or
percentage between 0 and 1
 Order of operations: exploring the
order of operations in problems
and in equations.
General capabilities and Cross-curriculum priorities
Opportunities to engage with:
C2C adapted with permission by NT DoE © The State of Queensland
Opportunities to engage with:
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Unit outline Semester 2
Sequencing the teaching and learning
Term 3
Term 4
Unit 5
Students have opportunities to develop
understandings of:
 Properties of numbers: exploring
the properties of prime, composite,
square and triangular numbers and
using prime factors to identify
greatest common factors and
lowest common multiples
 Four operations: adding and
subtracting whole numbers and
decimals, multiplying by two digit
whole numbers and decimals and
dividing by two digit whole
numbers and decimals with
terminating remainders
 Patterns: creating and continuing
number patterns involving whole
numbers, fractions and decimals
and using a table of values to write
a rule to describe the pattern
 3 dimensional shapes: drawing
nets of prisms and pyramids and
constructing 3D objects using
concrete materials and nets.
Unit 6
Students have opportunities to develop
understandings of:
 Chance: expressing probability as
a fraction, decimal and/or
percentage and comparing
observed frequencies with
expected frequencies
 Patterns and algebra: applying the
order of operations to complete
multiple operations within the same
number sentence
 Fractions and money: making
connections between equivalent
representations of the same
number, finding fractions of a
quantity and calculating
percentage discounts
 Data representation and
interpretation: investigating
representations of data in the
media, influences on data and
misleading data.
Unit 7
Students have opportunities to develop
understandings of:
 Transformations: combining
transformations to create shapes
and tessellations
 Angles: classifying and measuring
angles and establishing
generalisations about vertically
opposite angles, adjacent angles
on a straight line and angles at a
point
 Measurement: converting between
equivalent units of measure and
exploring the relationship between
the length of the sides and the
area of the rectangles
 Volume and capacity: exploring
volume and capacity and the
relationship between the two and
measuring and estimating volume
and capacity.
Unit 8
Students have opportunities to develop
understandings of:
 Cartesian coordinate system:
introducing the four quadrants of a
Cartesian plane, plotting coordinates
on the Cartesian plane, designing and
evaluating a game involving plotting
coordinates on the Cartesian plane
 Chance: describing probabilities on a
scale from 0 to 1, comparing expected
and observed frequencies and
exploring the effect of the number of
trials (in a chance experiment) on the
outcomes
 Fractions, decimals and percentages:
revising the connections between
fractions, decimals and percentages,
adding and subtracting fractions and
decimals and finding a percentage
discount
 Operations: revising strategies to
estimate, add, multiply and divide
when operating with whole numbers,
and choosing and using the most
appropriate operations to solve
problems.
General capabilities and Cross-curriculum priorities
Opportunities to engage with:
Opportunities to engage with:
Key to General capabilities and Cross-curriculum priorities
Literacy
Numeracy
Personal and social
Intercultural understanding
competence
C2C adapted with permission by NT DoE © The State of Queensland
ICT competence
Critical and creative thinking
Ethical behaviour
Aboriginal and Torres Strait
Asia and Australia’s
Sustainability
Islander histories and cultures
engagement with Asia
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Assessment Semester 1
Teachers and children organise evidence of learning in individual folios. The individual folio is constructed jointly by a teacher, a child, parents/carers and other
partners. It becomes a dynamic record of examples of a child’s learning and development.
Term 1
Term 2
Unit 2: Identifying properties of whole
numbers
Short answer questions
Students identify, describe and
sequence whole numbers according to
their properties.
Unit 3: Sporting skills
Assignment/Project
Unit 4: Data decoder
Short answer questions
Students perform a number of tasks,
recording their scores for each task.
Students convert these scores to
equivalent fractions and decimals to
demonstrate their understanding of the
relationship between the three
representations of the same number.
Students make decisions informed by
interpreting and comparing a range of
data displays.
Unit 3: Rodeo round-up
Short answer questions
Students use and interpret more than
one transport timetable when organising
a trip to a rodeo. Students use
available information to make informed
decisions about the suitability of each
transport option.
Making consistent judgements / Feedback
Curriculum leaders will randomly sample student work to check for consistency of Teachers will moderate to identify A-E samples before marking practical
demonstration tasks. They will participate in on-going moderation conversations
teacher judgments.
to achieve consensus and consistency of judgments.
Teachers will co-mark the assignment/project to achieve consensus and
consistency of judgments.
Curriculum leaders will randomly sample student work to check for consistency of
teacher judgments.
C2C adapted with permission by NT DoE © The State of Queensland
4 of 8
www.det.nt.gov.au
Assessment Semester 2
Teachers and children organise evidence of learning in individual folios. The individual folio is constructed jointly by a teacher, a child, parents/carers and other
partners. It becomes a dynamic record of examples of a child’s learning and development.
Term 3
Unit 5: Year 6 mathematics QCAT
Written
Term 4
Unit 6: Is it fair?
Written
Unit 7: Transformations and
tessellations
Assignment/Project
The QCAT gathers evidence about how Students apply knowledge of chance
well students apply the proficiency
events, variation and bias to develop
strands to:
arguments and improve game fairness.
 identify and describe the properties
of special numbers
 create sequences of whole
numbers and describe the rules
used to create them
use mathematical reasoning to solve
simple and multi-step problems
involving nets and all four operations
with whole numbers and decimals.
Students use a combination of
transformations to create a shape that
can be used in a tessellating pattern.
Making consistent judgments/ Feedback
Teachers will co-mark the QCAT to achieve consensus and consistency of
judgments.
Year level teachers will moderate the QCATs to identify A-E samples to take to
cluster moderation in Term 4.
C2C adapted with permission by NT DoE © The State of Queensland
Teachers will moderate to identify A-E samples before marking design and
practical demonstration tasks. They will participate in on-going moderation
conversations to achieve consensus and consistency of judgments.
Curriculum leaders will randomly sample student work to check for teacher
consistency of judgments.
Year level teachers will participate in cluster moderation of the QCATs.
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Balance and coverage of content descriptions
Year 6
Number and Algebra
Term
Number and place value
1
Identify and describe properties of
prime, composite, square and
triangular numbers.
1
2
3
Term
Measurement and Geometry
4
5
Using units of measurement
1
2
Connect decimal representations
to the metric system.
1
3
Statistics and Probability
4
Chance
3
7
2
3
4
Describe probabilities using
fractions, decimals and
percentages.
4
6
8
3
7
Conduct chance experiments with
both small and large numbers of
trials using appropriate digital
technologies.
4
6
8
Solve problems involving the
comparison of lengths and areas
using appropriate units.
7
Compare observed frequencies
across experiments with
expected frequencies.
4
6
8
Connect volume and capacity
and their units of measurement.
7
2
Select and apply efficient mental
and written strategies and
appropriate digital technologies to
solve problems involving all four
operations with whole numbers.
4
Investigate everyday situations
that use positive and negative
whole numbers and zero. Locate
and represent these numbers on
a number line.
3
5
8
Convert between common metric
units of length, mass and
capacity.
Interpret and use timetables.
Fractions and decimals

Compare fractions with related
denominators and locate and
represent them on a number line.
1
Solve problems involving addition
and subtraction of fractions with
the same or related
denominators.
1

Shape

Construct simple prisms and
pyramids.
1
C2C adapted with permission by NT DoE © The State of Queensland
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1
3

5
2
4
Term

Data representation and
interpretation

Interpret and compare a range of
data displays, including side-byside column graphs for two
categorical variables.
2
Interpret secondary data
presented in digital media and
elsewhere.

4
6
www.det.nt.gov.au
Balance and coverage of content descriptions
Year 6
Number and Algebra
Fractions and decimals cont.
Term
1
Find a simple fraction of a
quantity where the result is a
whole number, with and without
digital technologies.
Add and subtract decimals, with
and without digital technologies,
and use estimation and rounding
to check the reasonableness of
answers.
2
2
3
3
6
4
Multiply decimals by whole
numbers and perform divisions
that result in terminating
decimals, with and without digital
technologies.
Term
Measurement and Geometry
Statistics and Probability
Term
4
8
5
Multiply and divide decimals by
powers of 10.
3
5
Make connections between
equivalent fractions, decimals and
percentages.
3
6
Money and financial
mathematics


Investigate and calculate
percentage discounts of 10%,
25% and 50% on sale items, with
and without digital technologies.

 6


C2C adapted with permission by NT DoE © The State of Queensland
8
8
4


7


8
Location and transformation
1
2
Investigate combinations of
translations, reflections and
rotations, with and without the
use of digital technologies.

Introduce the Cartesian
coordinate system using all four
quadrants.

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3
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Balance and coverage of content descriptions
Year 6
Number and Algebra
Term
Patterns and algebra
1
Continue and create sequences
involving whole numbers,
fractions and decimals. Describe
the rule used to create the
sequence.
1
Explore the use of brackets and
order of operations to write
number sentences.
2
3
5
2
4
Term
Measurement and Geometry
4
Geometric reasoning
1
2
Investigate, with and without
digital technologies, angles on a
straight line, angles at a point and
vertically opposite angles. Use
results to find unknown angles.




6
3
Statistics and Probability
Term
4

7


References
http://www.australiancurriculum.edu.au/ Australian Curriculum Version 3.0 dated 23 January 2012
Copyright © The State of Queensland (represented by the Department of Education and Training)
Copyright in this work is owned by or licensed to the State of Queensland (acting through the Department of Education and Training), PO Box 15033 City East QLD
4002 Australia and is reproduced with its permission. No part may be further reproduced in hardcopy form by anyone outside the Northern Territory Department of
Education without the express permission of the Queensland Department of Education and Training.
C2C adapted with permission by NT DoE © The State of Queensland
8 of 8
www.det.nt.gov.au