DEPARTMENT OF EDUCATION
Year 10 Mathematics/Numeracy
Learning Area
Mathematics
Length
60 hours per semester
120 hours per year
Background
The Australian Curriculum states that “Teachers use the Australian Curriculum content and achievement
standards first to identify current levels of learning and achievement and then to select the most
appropriate content (possibly from across several year levels) to teach individual students and/or groups of
students. This takes into account that in each class there may be students with a range of prior
achievement (below, at, and above the year level expectations) and that teachers plan to build on current
learning”.
The development of the Northern Territory Mathematics and Numeracy courses employs these principles
to ensure students have access to successful pathways at Stage 1.
Purpose
This document provides a strategy for aligning the learning requirements of the Australian Curriculum (AC)
and the assessment requirements of the Northern Territory Certificate of Education and Training (NTCET).
The AC provides the content descriptors and achievement standards for Year 10 Mathematics. The NTCET
through assessment design criteria and performance standards provides a common standard for student
achievement at Stage 1 and Stage 2. To cater for a diversity of student needs at Year 10, two courses have
been developed; Mathematics and Numeracy, with a common set of Performance Standards within which
the AC Achievement Standards are embedded.
www.education.nt.gov.au
DEPARTMENT OF EDUCATION
Mathematics Courses and Senior Secondary Pathways
At Year 10, students can undertake a course which caters for their learning requirements and will enable
them to proceed to appropriate Stage 1 Mathematics. The arrows below do not depict the only options.
Year 10
Mathematics
Year 11 – Stage 1
Year 12 – Stage 2
Mathematics
Specialist Mathematics
Mathematical Applications
Mathematical Studies
Mathematical Pathways
Mathematical Methods
Mathematical Applications
Mathematical Pathways
Mathematical Applications
Mathematical Applications
Mathematical Pathways
Mathematical Pathways
Numeracy
Numeracy for Work and
Community Life
Achievement Standards
The Achievement Standards of the AC as outlined below are embedded in common Performance Standard
for Mathematics and Numeracy. The Performance Standards are to be used for the assessment of student
learning.
Achievement standards
By the end of Year 10, students recognise the connection between simple and compound interest. They
solve problems involving linear equations and inequalities. They make the connections between algebraic
and graphical representations of relations. Students solve surface area and volume problems relating to
composite solids. They recognise the relationships between parallel and perpendicular lines. Students
apply deductive reasoning to proofs and numerical exercises involving plane shapes. They 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.
Students expand binomial expressions and factorise monic quadratic expressions. They find unknown
values after substitution into formulas. They perform the four operations with simple algebraic fractions.
Students solve simple quadratic equations and pairs of simultaneous equations. They use triangle and
angle properties to prove congruence and similarity. Students use trigonometry to calculate unknown
angles in right-angled triangles. Students list outcomes for multi-step chance experiments and assign
probabilities for these experiments. They calculate quartiles and inter-quartile range.
www.education.nt.gov.au
DEPARTMENT OF EDUCATION
Content Descriptors
Content descriptors are organised under three strands: Number and Algebra, Measurement and Geometry,
Statistics and Probability. Teachers should use the content descriptors of the AC to develop a program for
their students. There are twenty-five content descriptors for Year 10 and sixteen for 10A Mathematics. All
content descriptors for Year 10 Mathematics are to be covered over a whole year. 10A Mathematics is
extension content for potential candidates of Stage 2 Mathematical Studies and Specialist Mathematics.
Content Descriptions
Number and Algebra
Money and financial mathematics
1.
Connect the compound interest formula to repeated applications of simple interest using appropriate digital
technologies (ACMNA229)
Real numbers
2.
Define rational and irrational numbers and perform operations with surds and fractional indices (ACMNA264)
3.
Use the definition of a logarithm to establish and apply the laws of logarithms (ACMNA265)
Patterns and algebra
4.
Factorise algebraic expressions by taking out a common algebraic factor (ACMNA230)
5.
Simplify algebraic products and quotients using index laws (ACMNA231)
6.
Apply the four operations to simple algebraic fractions with numerical denominators (ACMNA232)
7.
Expand binomial products and factorise monic quadratic expressions using a variety of strategies (ACMNA233)
8.
Substitute values into formulas to determine an unknown (ACMNA234)
9.
Investigate the concept of a polynomial and apply the factor and remainder theorems to solve problems
(ACMNA266)
Linear and non-linear relationships
10. Solve problems involving linear equations, including those derived from formulas (ACMNA235)
11. Solve linear inequalities and graph their solutions on a number line (ACMNA236)
12. Solve linear simultaneous equations, using algebraic and graphical techniques including using digital technology
(ACMNA237)
13. Solve problems involving parallel and perpendicular lines (ACMNA238)
14. Explore the connection between algebraic and graphical representations of relations such as simple quadratics,
circles and exponentials using digital technology as appropriate (ACMNA239)
15. Solve linear equations involving simple algebraic fractions (ACMNA240)
16. Solve simple quadratic equations using a range of strategies (ACMNA241)
17. Describe, interpret and sketch parabolas, hyperbolas, circles and exponential functions and their transformations
18. Solve simple exponential equations
19. Apply understanding of polynomials to sketch a range of curves and describe the features of these curves from
their equation
20. Factorise monic and non-monic quadratic expressions and solve a wide range of quadratic equations derived from
a variety of contexts
www.education.nt.gov.au
DEPARTMENT OF EDUCATION
Measurement and Geometry
Using units of measurement
21. Solve problems involving surface area and volume for a range of prisms, cylinders and composite solids
(ACMMG242)
22. Solve problems involving surface area and volume of right pyramids, right cones, spheres and related composite
solids (ACMMG271
Geometric reasoning
23. Formulate proofs involving congruent triangles and angle properties (ACMMG243)
24. Apply logical reasoning, including the use of congruence and similarity, to proofs and numerical exercises
involving plane shapes (ACMMG244)
25. Prove and apply angle and chord properties of circles (ACMMG272)
Pythagoras and trigonometry
26. Solve right-angled triangle problems including those involving direction and angles of elevation and depression
(ACMMG245)
27. Establish the sine, cosine and area rules for any triangle and solve related problems (ACMMG273)
28. Use the unit circle to define trigonometric functions, and graph them with and without the use of digital
technologies (ACMMG274)
29. Solve simple trigonometric equations (ACMMG275)
30. Apply Pythagoras’ theorem and trigonometry to solving three-dimensional problems in right-angled triangles
(ACMMG276)
Statistics and Probability
Chance
31. Describe the results of two- and three-step chance experiments, both with and without replacements, assign
probabilities to outcomes and determine probabilities of events. Investigate the concept of independence
(ACMSP246)
32. Use the language of ‘if ....then, ‘given’, ‘of’, ‘knowing that’ to investigate conditional statements and identify
common mistakes in interpreting such language (ACMSP247)
33. Investigate reports of studies in digital media and elsewhere for information on their planning and
implementation (ACMSP277)
Data Representation and interpretation
34. Determine quartiles and interquartile range (ACMSP248)
35. Construct and interpret box plots and use them to compare data sets (ACMSP249)
36. Compare shapes of box plots to corresponding histograms and dot plots (ACMSP250)
37. Use scatter plots to investigate and comment on relationships between two numerical variables (ACMSP251)
38. Investigate and describe bivariate numerical data where the independent variable is time (ACMSP252)
39. Evaluate statistical reports in the media and other places by linking claims to displays, statistics and
representative data (ACMSP253)
40. Calculate and interpret the mean and standard deviation of data and use these to compare data sets (ACMSP278)
41. Use information technologies to investigate bivariate numerical data sets. Where appropriate use a straight line
to describe the relationship allowing for variation (ACMSP279)
www.education.nt.gov.au
DEPARTMENT OF EDUCATION
EVIDENCE OF LEARNING
Students need to demonstrate evidence of learning in Mathematics or Numeracy through the following
assessment types
Assessment Type 1: Skills and Applications Tasks (60%– 80%)

at least three tasks
Assessment Type 2: Folio (20%-40%)

at least one investigation.
Students are to provide evidence of learning in four to six assessments tasks.
The same performance standards are used to assess both Year 10 Mathematics and Year 10 Numeracy.
YEAR 10 MATHEMATICS/NUMERACY OVERVIEW
Year 10 Course
Australian
Curriculum Content
Strands and
Descriptors
Mathematics
Year 10
for students at a
standard to
achieve success
at Year 10 AC
Number and
Algebra
1-20
Measurement and
Geometry
21 - 30
Statistics and
Probability
31-41
Assessment Types, Tasks and Weighting
Mathematics and
Numeracy
Assessment Types:
1. SATs 60% - 80%
at least three skills and applications
tasks per semester
2. FOLIO 20% - 40%
at least one investigation for the folio
per semester
Numeracy
for students
below the
standard required
for success at
Year 10 AC
From relevant year
levels
Number and
Algebra
Measurement and
Geometry
Statistics and
Probability
Performance
Standards for
Assessment
For a semester long Mathematics or
Numeracy subject, it is recommended that
students provide evidence of their learning
through four to six assessment tasks
Mathematical
knowledge and skills
and their application
1-3
Mathematical
modelling and
problem-solving
1-2
Communication of
mathematical
information
1-2
www.education.nt.gov.au
PERFORMANCE STANDARDS FOR YEAR 10 MATHEMATICS AND NUMERACY
Mathematical knowledge and skills and their
application

A



B



C



D 


E


Extensive knowledge of content and
understanding of concepts.
Efficient application of mathematical ideas
and processes in solving complex
problems.
Consistent demonstrations of accuracy and
detail in complex problem solutions.
Considerable knowledge of content and
understanding of concepts.
Relevant application of mathematical ideas
and processes in solving complex
problems.
Demonstration of accuracy and detail in
complex problem solutions.
Sound knowledge of content and
understanding of concepts.
Appropriate application of mathematical
ideas and processes in solving routine
problems.
Demonstration of accuracy and some detail
in routine problem solutions.
Limited knowledge of the content and
understanding of concepts.
Limited application of mathematical ideas
and processes in solving routine problems
Demonstration of some accuracy and
limited detail in routine problem solutions.
Very limited knowledge of the content and
understanding of concepts.
Very limited application of mathematical
ideas and processes in solving routine
problems.
Demonstration of some limited accuracy or
detail.
Communication of mathematical
information
Mathematical modelling and problem-solving








In-depth interpretation of the mathematical results in the context
of the problem.
In-depth understanding of the reasonableness and possible
limitations or extensions of the interpreted results and recognition
of assumptions made.

Complete interpretation of the mathematical results in the context
of the problem.
Some depth of understanding of the reasonableness and
possible limitations or extensions of the interpreted results, and
recognition of assumptions made

Appropriate interpretation of the mathematical results in the
context of the problem.
Sound understanding of the reasonableness and possible
limitations or extensions of the interpreted results and some
recognition of assumptions made.

Limited interpretation of the mathematical results in the context of
the problem.
Limited awareness of the reasonableness and possible
limitations or extensions of the interpreted results.








Very limited attempt at interpretation of the mathematical results
in the context of the problem.
Very limited awareness of the reasonableness and possible
limitations or extensions of the results.

Proficient communication of
mathematical concepts used to develop
logical arguments
Proficient use of correct notation,
representations and terminology.
Effective communication of mathematical
concepts used to develop logical
arguments
Effective use of correct notation,
representations, and terminology.
Appropriate communication of
mathematical concepts used to develop
logical arguments
Appropriate use of correct notation,
representations, and terminology.
Limited communication of mathematical
concepts used to develop logical
arguments
Limited attempt to use correct notation,
representations, and terminology.
Very limited communication of
mathematical concepts used to develop
logical arguments
Very limited attempt to use correct
notation, representations, and
terminology.
DEPARTMENT OF EDUCATION
YEAR 10 MATHEMATICS
LEARNING AND ASSESSMENT PLAN 20___
School ____________________________
Subject Mathematics / Numeracy
Teacher ___________________________
Semester ________________________
Cohort
Describe your students and their learning needs regarding content strands and descriptors
Learning Program Design
Describe:



how the learning program has been designed to engage the range of students in the cohort described above
topics selected to cater for the cohort
the intended delivery of the learning program (eg students will undertake elements of the program off-campus, programs
delivered over ten weeks)
Content Strands and Descriptors (tick as appropriate)
Number and Algebra
Measurement and Geometry
Statistics and Probability
1
2
3
4
5
21
22
23
24
25
31
32
33
34
35
6
7
8
9
10
26
27
28
29
30
36
37
38
39
40
11
12
13
14
15
16
17
18
19
20
Other Content Descriptors for
Numeracy
41
Other Content Descriptors for
Numeracy
Other Content Descriptors for
Numeracy
Capabilities to be developed (tick as appropriate)
Literacy
Numeracy
ICT capabilities
Critical and creative thinking
Personal and social capabilities
Ethical behaviour
Intercultural understanding
Cross-curriculum Priorities (tick as appropriate)
Aboriginal and Torres Strait Islander histories and cultures
Asia and Australia
Sustainability
Assessment
Type
Weighting
Year 10 Assessment Descriptions per Semester
Performance Standards
Activities and descriptions of Assessment Tasks
For a semester long Mathematics / Numeracy subject, it is recommended that students
provide evidence of their learning through four to six assessment tasks;
MKSA 1-3
MMPS 1-2
SATs
at least three skills
and applications
tasks per semester
60%-80%
Folio
at least one
investigation for the
folio per semester
20%-40%
Head of Faculty _________________________ Date: __________________
Consultant _________________________ Approved / Not Approved
Expiry Date _________________________ Accession Number: ______________
CMI 1-2
Assessment
Conditions
e.g. task type, word
length, time allocated,
supervision