Years 7–10 Numeracy Indicators
In Year 7, students:
In Year 8, students:
CE 7
i.
Calculating and estimating
Numeracy
square roots of perfect squares, e.g.
9,
i.
CE 9
CE 10
Interpret and use:
positive and negative numbers
index notation, e.g. positive integral indices and zero index
irrational numbers, e.g. 
i.
Select and combine strategies and procedures using mental and
written strategies, with or without technologies, to carry out
operations with rational numbers and integers to solve complex
problems. Explain the method/s
ii.
Combine strategies and procedures to calculate solutions,
recording values using representations, including scientific
notation and negative indices in complex contexts. Explain
the method/s
i.
Identify preferred mental and written strategies, select and use
definitions, rules, representations and estimates, with or without
technologies in calculations involving complex data and contexts.
Explain the method/s
iii.
Identify various ways to solve problems involving complex
data or situations and estimate a range of solutions
ii.
Interpret, clarify, and analyse the mathematical features and
conditions of a situation. Use a range of strategies such as using
models, rules or formulas to solve problems. Explain possible
solutions
•
•
•
Apply knowledge of index laws to simplify expressions that
include indices and perform calculations involving positive
and negative indices,
e.g. recognising that 5 -1 and 1 are equivalent expressions
5
64
ii.
In Year 10, students:
Students continue to apply knowledge of real numbers, indices,
scientific notation and irrational numbers from previous year
levels
ii.
Select or combine strategies including the application of the
associative, commutative and distributive laws to aid mental
and written computation to calculate solution/s
iii.
Identify relevant information, sort problems by concept,
iii.
strategies or procedures, such as matching a relationship to an
informal rule and estimating a range of solutions
Identify various ways to solve problems, including using factors,
applying a rule and estimating a range of solutions
iv.
Check the reasonableness of solutions, using strategies
including applying order of operations
iv.
Check the reasonableness of solutions, using strategies including iv.
approximations of very large and very small numbers
Check the reasonableness of solutions, including significant
figures. Review the selection of rules and solutions against
estimates
iii.
Check the reasonableness of solutions and review assumptions
and methods of working
v.
Create financial plans, determine the best buys and calculate
the unit costs of products, with or without technologies
v.
Create financial plans to solve problems involving profit and loss,
with or without technologies. Compare and evaluate fees linked
to consumer products
Create financial plans to solve problems involving simple
interest. Determine an amount (budget) to meet monthly or
yearly needs
iv.
Apply simple interest formula to calculate compound interest and
solve related problems
v.
Create financial plans, analyse the impact of debt and identify
strategies for debt management
v.
PR 7
PR 8
PR 9
i.
i.
i.
ii.
Recognising and using patterns and relationships
CE 8
Compare, order and position:
positive and negative numbers, including fractions
numbers given in index notation
whole numbers as products of powers of prime numbers
•
•
•
•
In Year 9, students:
iii.
Use letters to represent variables and write algebraic
expressions for real-life situations
Solve problems involving variables by:
•
Create and evaluate algebraic expressions by substituting a
given value for each variable
•
Apply arithmetic laws to algebraic expressions, e.g. order of
operation applies to patterns written in algebraic form
•
PR 10
Solve problems and make predictions involving application of i.
patterns and algebraic expressions, using:
simplifying (recognising groupings of like terms)
e.g. 7x + 3x + 2y = 10x + 2y
•
factorising (writing equivalent equations when integers in the
expression have a common factor)
e.g. 9y + 6x = 3(3y + 2x)
index laws (powers of a variable can be simplified)
e.g. y2 × y3 = y × y × y × y × y = y 5
•
distributive law (expanding by collecting like terms)
e.g. calculating areas of a shape
Make predictions and solve algebraic problems involving:
simplifying using index laws
factorising using common algebraic factors
algebraic fractions with a common denominator
substituting values into formulas
•
•
•
•
expanding grouped representations
e.g. 3(2x + 5y) = 6x +15y
Verify solutions
Verify solutions
iv.
Describe, extend, create and predict number and linear
patterns. Interpret and analyse graphs representing linear
relationships including interpolation and extrapolation
ii.
iii.
Plot linear equations and non-rule based data on a Cartesian
plane, with or without technologies
ii.
Solve linear equations using algebraic and graphical techniques,
strategies including guess and check, and verifying solutions by
substitution
iii.
February 2012 Page 1 of 3
Find the distance between two points on a Cartesian plane
using a range of strategies, with or without technologies
ii.
Use graphs to solve equations involving:
simple non-linear relations
linear graphs using the coordinates of two points
iii.
•
•
Solve, with or without technologies, problems involving:
line of best fit
linear equations including simple algebraic fractions and those
derived from formulas
• linear inequalities, including graphing solutions on a number
line
• linear simultaneous solutions
• simple quadratic equations
•
•
Use graphs and equations to analyse and illustrate relations
involving:
• parallel and perpendicular lines
• simple quadratics
• circles
• exponentials
In Year 7, students:
FDPR 7
i.
In Year 9, students:
In Year 10, students:
FDPR 8
FDPR 9
FDPR 10
i.
i.
i.
•
Using fractions, decimals,
percentages, ratios and rates
Using spatial reasoning
Numeracy
Solve problems involving:
finding a common denominator in operations with a range
of fractions, including those with unrelated denominators
and mixed numbers
• finding percentages of quantities
• expressing one quantity as a fraction or percentage of
another
• converting between equivalent representations of
percentages, fractions and decimals,
e.g. 20% is equivalent to 1 and 0.2
In Year 8, students:
Solve problems using:
percentage increases and decreases, e.g. population
growth
• terminating and recurring decimals, choosing the
appropriate representation
• rates and ratios using fractions and percentages
•
Identify relationships between graphs and equations
corresponding to simple rate problems
Use graphs and equations to analyse and illustrate proportional
relationships
5
•
•
simple ratios
rounding decimals to a specified number of decimal
places
SR 7
SR 8
SR 9
i.
Draw different views of prisms and solids using combinations
of prisms and analyse their positions in the environment
i.
Identify properties for congruence of triangles and confirm
congruence using transformations
i
Use the properties of similarity and ratio to solve problems
involving enlargement and transformation
i.
Use congruence, similarity and angle properties to solve
problems involving plane shapes
ii.
Classify triangles according to their side and angle properties
and describe quadrilaterals
ii.
Identify properties of quadrilaterals using congruent triangles
and angle properties, e.g. side lengths, parallelism, angles,
diagonals and symmetry
ii.
Identify the relationship between the corresponding sides of
similar right-angled triangles
ii.
Solve problems involving right-angled triangles, e.g. angles of
elevation and depression, and direction
iii.
Prove that the sum of the angles of a triangle is 180° and
make connections to the sum of the angles of a quadrilateral
iv.
Identify angle relationships when two straight lines are
crossed by a transversal, e.g. corresponding, alternate and
co-interior angles
iii.
Create and interpret complex spatial information from maps and
grids
iii.
Use the relationship between areas of similar figures and
the ratio of the corresponding sides to solve problems
v.
Plot tables of values or ordered pairs, and find values for a
point on a Cartesian plane
iv.
Apply trigonometry and Pythagoras’ Theorem to solve
problems involving right-angled triangles
vi.
Identify line and rotational symmetries. Describe translations,
reflections in an axis, and rotations of multiples of 90° on a
Cartesian plane using coordinates
Years 7–10 Numeracy Indicators Australian Curriculum v.3
SR 10
Queensland Studies Authority August 2012 Page 2 of 3
Interpreting and drawing conclusions from statistical information
Numeracy
In Year 7, students:
In Year 8, students:
In Year 9, students:
In Year 10, students:
SI 7
SI 8
SI 9
SI 10
i.
Construct sample spaces for single-step experiments with
equally likely outcomes
i.
Identify complementary events (the sum of all probabilities for
an event will equal 1) and use sum of probabilities to solve
problems
i.
List all outcomes of two-step chance experiments, both with
and without replacement using tree diagrams or arrays, and
determine probabilities for events
i.
Use the language of probability, e.g. if … then, given, of,
knowing that, to investigate conditional statements. Identify
common mistakes in interpreting such language and describe
the concept of independence
ii.
Assign probabilities to the outcomes of events. Explain the
difference between empirical data (everyday experimental
probability) and theoretical (expected) probability
ii.
Describe events using numerical representations and use
language:
• at least
• exclusive (A or B but not both)
• inclusive (A or B or both)
• and (both A and B)
ii.
Calculate relative frequencies to estimate probabilities of
events involving “and” or “or” statements
ii.
Describe the results of two- and three-step chance
experiments, both with and without replacements, assign
probabilities to outcomes and determine probabilities of events
iii.
Represent and interpret chance events in two-way tables and
Venn diagrams
iii.
Identify issues involving numerical data from both primary
and secondary sources, e.g. reliability, variation, sample size
iv.
Analyse the practicalities and implications of obtaining data
through sampling using a variety of investigative processes
iii.
Identify everyday questions and issues involving at least one
numerical and at least one categorical variable. Identify
techniques for collecting primary data for specific purposes,
including census and sampling
iii.
Identify questions and issues involving a number of variables,
and interpret data from secondary sources
iv.
Collect, represent and summarise sets of data and calculate
mean, median and range. Identify the mode
v.
Describe the effect of individual data values, including outliers,
on measures of central tendency (mean, median, mode)
iv.
Collect data directly from secondary sources, including reports
of surveys in digital media. Estimate means and medians from
data
iv.
Analyse techniques for collecting data, including census,
sampling and observation, to evaluate the effectiveness of
collection strategies and identify refinements
v.
Construct and compare a range of data displays including
stem-and-leaf plots and dot plots
vi.
Interpret a range of data displays including tables, histograms,
sector graphs, divided bar graphs and time series
v.
Construct data displays including back-to-back stem-and-leaf
plots and histograms. Make comparisons using terms including
“skewed”, “symmetric” and “bimodal”
v.
vi.
Describe and interpret data displays using mean, median
and range. Analyse and interpret different types of data,
including grouped data
vi.
Compare data displays using measures of central tendency
and range. Review sample sizes and the reliability of the data
vi.
Using measurement
M7
M8
Describe trends in:
numerical data where the independent variable is time
box plots to compare data sets
scatter plots to comment on relationships between two
continuous variables
• graphs and equations to illustrate proportional relationships
• 5 number summaries to numerically and visually compare
the centre and spread of data sets
•
•
•
Evaluate statistical reports by linking claims to displays,
statistics and representative data
M9
M 10
i.
Evaluate the reasonableness of an estimate by comparing
to known measurement units
i.
Convert volume or area units to another, e.g. cm2 → mm2.
Choose measuring instruments and methods based on the
level of accuracy required
Students continue to apply knowledge of units measurements
from previous year levels
Students continue to apply knowledge of units of
measurements from previous year levels
ii.
Calculate the area of rectangles, triangles and
parallelograms and the volume of rectangular prisms, using
established formulas and appropriate units of measure
ii.
Identify the relationship between features of circles, e.g.
circumference, area, radius and diameter. Use formulas to find
circumference and area
i.
Calculate the areas of composite shapes, the surface area and
volume of cylinders and right prisms
i.
Calculate the surface area and volume for spheres, a range of
prisms and composite solids, e.g. pyramids, cones and
cylinders
iii.
Find perimeters and areas of parallelograms, trapeziums,
rhombuses and kites. Use formulas to find the volume of
triangular and other prisms
iv.
Use 12- and 24-hour time to solve problems within a single
time zone
ii.
Use 12- and 24-hour time to solve problems across time zones
ii.
Use very small and large time scales and intervals to solve
problems
iii.
Create schedules for authentic situations, estimating duration
of events and including transition periods
Years 7–10 Numeracy Indicators Australian Curriculum v.3
Queensland Studies Authority August 2012 Page 3 of 3