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Organisation of content into year levels is advisory. Teachers will continue to make professional
judgements about when to introduce content based on children’s prior learning and achievement.
*National Consistency in Curriculum Outcomes, Statement of Learning
Early adolescence: Mathematics/Number – Students use numbers and operations and the relationships between them efficiently and
flexibly.
Typical sequence of content:
Year 8
Year 9
Year 10
Understand numbers
Understand whole numbers and decimals
Integers, decimals and fractions
Rational and some irrational numbers
Real numbers
 recognising the direction and magnitude of an
integer
 defining rational and irrational numbers
 relationships between real, rational, irrational,
integer and natural numbers (eg the real numbers
include rational and irrational, integers include the
natural numbers)
 integers in real-life contexts* (eg ordering a set of
temperatures)
 locating integers, decimals and fractions on the
real number line*
 locating decimal approximations to some irrational
numbers on the real number line*
 writing scientific notation*
(eg 23 000 = 2.3 × 104 and 0.0023 = 2.3 × 10–3)
 scientific notation to interpret very small or large
numbers* (eg where a total national debt of $234
billion = 234 000 000 000 = 2.34 x 1011 is
represented as 2.34 E11)
 expressing numbers written in scientific notation as
common numerals (eg 1.2 x 10 – 7 = 0.00000012; 5
x 104 = 50 000)
 entering and reading scientific notation (E notation)
on a calculator* (eg 3·58 E03 = 3·58 × 103 = 3 580)
 applying scientific notation (eg interplanetary
distances, nanotechnology)
 the index laws of multiplication and division
 index laws to make order of magnitude checks for
numbers in scientific notation (eg (3.12 x 104) x
(4.2 x 106) ≈ 12 x 1010 ≈ 1.2 x 1011)
© Department of Education and Training Western Australia, Early adolescence: Mathematics/Number scope and sequence, December 2007
1
Organisation of content into year levels is advisory. Teachers will continue to make professional
judgements about when to introduce content based on children’s prior learning and achievement.
*National Consistency in Curriculum Outcomes, Statement of Learning
Typical sequence of content:
Year 8
Year 9
Year 10
Understand whole numbers and decimals (continued)
 positive and negative powers of 10
(eg 0·001 = 10-3; 100 000 = 105)
 positive integer powers*
 common fractions have exact or rounded decimal
 some rational numbers can be written as recurring
decimals* (eg 0.333 33 … = 0.3 ,
representations* (eg
1
4
=
0.25, 1
3
 0.3333)
(eg
(– 1
2
)5 =
– 1
32
;
34
= 3 × 3 × 3 × 3)
0.345 345 345 … = 0.345 )
Compare and order integers, decimals and
fractions
 recalled approximations to square roots to estimate
values for expressions
(eg 2 ≈ 1.4, so 2 + 1 ≈ 2.4)
 recurring decimals can be represented as rational
numbers (eg 0.3 = 1 , 0.4 = 4 )
3
9
Compare and order rational and some irrational
numbers
Compare and order real numbers
 decimal approximations to irrational numbers in a
measurement context* (eg a square with area
90 m2 has a side length of 90 ≈ 9.49 m to the
nearest centimetre)
 decimal approximations to irrational numbers in a
 comparing and ordering integers (eg using a depth
gauge to place – 18·3 m between – 18 and – 19)
 equivalent fractional, decimal and percentage
forms* (eg 50% is the same as
1
2
, one-third off is
better than 30% off; 12·5% = 1 = 0·125)
measurement context (eg sin 45 o =
1
2
 0.7071)
8
 the multiplicative relationship between decimal
places (eg using a calculator to repeatedly divide
by 10 to generate the sequence 0.2, 0.02,
0.002 …)
© Department of Education and Training Western Australia, Early adolescence: Mathematics/Number scope and sequence, December 2007
2
Organisation of content into year levels is advisory. Teachers will continue to make professional
judgements about when to introduce content based on children’s prior learning and achievement.
*National Consistency in Curriculum Outcomes, Statement of Learning
Typical sequence of content:
Year 8
Year 9
Year 10
Understand fractions
Compare quantities and equivalents of fractions
and percentages
Equivalent fractional, decimal and percentage
forms
 finding equivalent fractions in order to compare*
 converting between different representations of
rational numbers* (eg if a computer file repair
process is successful on average 5 out of 7
times, then it has a success rate of
(eg
2
5
is smaller than
3
7
, as the first can be
expressed as 14 and the second as 15 )
35
35
5
7
Equivalent fractional, decimal and percentage
forms
= 0.714285 ≈ 71.43%)
 common fractions have exact or rounded decimal
and percentage representation that can be used for
comparison
 expressing one quantity as a fraction or a
percentage of another (eg 15 minutes is 1
4
or 25% of an hour)
 interpreting percentages greater than 100%
(eg an increase from 6 to 18 is an increase of
200%; 150% of $2 is $3)
 interpreting and analysing published percentages
(eg stating what ‘increased by 200%’ means and
whether it is used correctly in the context)
 using index laws to define fractional indices for
square and cube roots, and to demonstrate the
reasonableness
1
1
(eg ( 9 )2 = 9 and (9 )2 = 9, hence = 9 )
2
© Department of Education and Training Western Australia, Early adolescence: Mathematics/Number scope and sequence, December 2007
2
3
Organisation of content into year levels is advisory. Teachers will continue to make professional
judgements about when to introduce content based on children’s prior learning and achievement.
*National Consistency in Curriculum Outcomes, Statement of Learning
Typical sequence of content:
Year 8
Year 9
Year 10
Understand fractions (continued)
Simplify ratios
Equivalent ratios
Interpret ratios
 relative order and size of ratios*
(eg 2:3 [2 parts to 3] is a stronger concentration
than 3:5 [3 parts to 5])
 equivalence of ratio expressions (eg 3:5 is the
same as 6:10)
 interpreting published ratios and rates in order to
make comparisons (eg using ABS data to find birth
rates and death rates and using these to determine
the population growth, or decline, over the last
decade)
 ratios can be written in various forms
 interpreting ratios that involve more than two
numbers (eg Tom, Rick and Harry shared their
winnings in the ratio of 3:4:6)
(eg
4
6
, 4:6, 4 to 6)
Understand operations
Addition and subtraction of integers, decimals and
fractions
Addition and subtraction of rational and some
irrational numbers
 relationships between the four operations with
integers, decimals and fractions
 relationships between the four operations with
rational and some irrational numbers
 addition and subtraction of directed numbers
 addition and subtraction of rational numbers
Multiplication and division of integers, decimals
and fractions
Multiplication and division of some irrational
numbers
 applying order of operations to simplify
expressions* (eg  (122 – 82) =  (144 – 64) =
 (80) = 80  ?)
 distributive property of multiplication over addition
and its use in simplifying expressions as an
alternative to the rule of order
(eg A =  (122 – 82) = .122 – .82)
© Department of Education and Training Western Australia, Early adolescence: Mathematics/Number scope and sequence, December 2007
4
Organisation of content into year levels is advisory. Teachers will continue to make professional
judgements about when to introduce content based on children’s prior learning and achievement.
*National Consistency in Curriculum Outcomes, Statement of Learning
Typical sequence of content:
Year 8
Year 9
Year 10
Understand operations (continued)
 appropriate operations for dealing with rates such
as scale, simple interest, price or speed (eg ‘If the
car is travelling at an average of 80 km/h, how long
will it take us to travel 450 km?’)
 multiplication and division of directed numbers*
(eg -10 x 5 = -50; -12 x (-3) = 36)
 finding prime factors* (eg factor trees)
 expressing any natural number as a product of
powers of primes* (eg the factor tree for 36 000 =
2 5 x 3 2 x 5 3 ; investigating factors of very large
numbers and the exsistence of large prime
numbers)
 using the notation for square root
root
 
and cube
 *
3
 the link between squares and square roots and
cubes and cube roots (eg 23 = 8 and 3 8  2 )
© Department of Education and Training Western Australia, Early adolescence: Mathematics/Number scope and sequence, December 2007
5
Organisation of content into year levels is advisory. Teachers will continue to make professional
judgements about when to introduce content based on children’s prior learning and achievement.
*National Consistency in Curriculum Outcomes, Statement of Learning
Typical sequence of content:
Year 8
Year 9
Year 10
Understand operations (continued)
Powers
Powers including square and cube roots
Index laws
 expressing positive integers as products of powers
of prime numbers (eg 50 = 2 x 52)
 finding square roots of rational numbers
(eg 0.25 = 0.5)
Product of powers: am x an = am+n
am x a = am+1
 integer powers can be used to abbreviate
multiplication (eg 73 = 7 x 7 x 7)
 index laws for multiplication and division, with
whole number indices (eg 3 × 3 × 3 × 3 = 34;
56 ÷ 52 = 54; (73) 4 = 712)
Power of a power:
(am)n = amxn
Quotient of powers:
am
an
am
an
=
am
am
= 1 where a  0
1
an  m
= am-n (m > n)
(n > m)
Power of a product:
(ab)m = ambm
Power of a quotient:
m
( a )m = a m
(1
b
)m
Zero index:
1
bm
=
)-1
where b  0
a0 = 1 where a  0
Negative indices:
(a
b
a
(
b
b
b
a-n = 1n
a
=b
a
)-n = ( b )n where a, b, n  0
a
© Department of Education and Training Western Australia, Early adolescence: Mathematics/Number scope and sequence, December 2007
6
Organisation of content into year levels is advisory. Teachers will continue to make professional
judgements about when to introduce content based on children’s prior learning and achievement.
*National Consistency in Curriculum Outcomes, Statement of Learning
Typical sequence of content:
Year 8
Year 9
Year 10
Calculate
Strategies to mentally calculate with integers,
decimals and fractions
Strategies to mentally calculate with rational and
some irrational numbers
 apply number facts and properties to carry out
mental calculations* (eg the GST on $156 is
$15.60 which gives a total of $171.60;
39 x 6 = (30 x 6) + (9 x 6) = 180 + 54 = 234
or (40 x 6) – 6 = 240 – 6 = 234)
 calculating simple powers and square roots
mentally* (eg 34= 3 x 3 x 3 x 3 = 9 x 9 = 81,
 factors and multiples to assist calculations
(eg partitioning 25 × 12 = 25 × 4 × 3 = 100 × 3
= 300)
 multiplication of numbers expressed as indices
using factors (eg 23 x 25 = (2 x 2 x 2) x
(2 x 2 x 2 x 2 x 2) = 28)
Strategies to mentally calculate with real numbers
( 1 )3 = 1 x 1 x 1 = 1 , 0.62 = (6 x 6) ÷ 100 = 0.36,
2
2
16
9
4
3
=
2
2
8
)
 division of numbers expressed as indices using
factors (eg 37 ÷ 33 = 3x3x3x3x3x3x3 = 34)
3x3x3
 division can be achieved by multiplying by the
reciprocal
 calculating of common percentages of quantities
50%, 33 1 %, 25%, 10%, 5% (eg using common
3
fraction equivalents, rounding appropriately,
partitioning)
 increasing or reducing a quantity in a given ratio or
by a given percentage (eg converting a recipe for
six people to cater for ten people; If a bicycle costing
$225 is advertised at 20% off, how much will it
cost?)
 increasing or reducing a quantity in a given ratio or
by a given percentage using shortcuts (eg ‘How
much will a $225 000 house cost if it appreciated
by 10% over two years?’ This can be answered by
calculating 110% of $225 000)
 increasing or decreasing a quantity by a
percentage is multiplying by a number greater or
less than one (eg to add 5% is to multiply by 1.05;
to subtract 5% is to multiply by 0.95 and to add 5%
a year for 3 years is to multiply by 1.05, 3 times)
© Department of Education and Training Western Australia, Early adolescence: Mathematics/Number scope and sequence, December 2007
7
Organisation of content into year levels is advisory. Teachers will continue to make professional
judgements about when to introduce content based on children’s prior learning and achievement.
*National Consistency in Curriculum Outcomes, Statement of Learning
Typical sequence of content:
Year 8
Year 9
Year 10
Calculate (continued)
 expressing profit and/or loss as a percentage of
cost price or selling price
 calculating and using percentage change in
practical situations (eg discounts)
Efficient written methods involving integers,
decimals and fractions
Efficient written methods involving rational and
some irrational numbers
Efficient written methods involving real numbers
 appropriate non-calculator methods to divide two
and three-digit numbers by two-digit numbers
 calculating involving two integers and a single
operation using effective written methods* (eg the
amount left to be paid off at a given time on a
house loan based on a recent statement from the
bank; 546 x –389; 20 billion divided by 350 000)
 calculating for problems involving real numbers
(eg computations involving  or square roots)
 recording stages in adding and subtracting
fractions that can not be done mentally
(eg 2 3 + 3 1 = 5 + 3 + 1 = 5 + 3 + 2 = 5 + 5
=5+
4
2
11
4
61
4
=
4
2
4
4
4
)
 calculating rates from given information
(eg 150 kilometres travelled in 2 hours is 75 km/h)
 finding quantities from familiar rates (eg finding the
interest for 6 months at 11 % per annum;
calculating the number of worm tablets a dog
needs based on its weight and the information on
the label)
 converting rates from one set of units to another
(eg convert 60 km/h to m/s)
 corresponding rates given a ratio of two or more
decimal numbers* (eg if the exchange rate for one
Australian dollar on a given day is 0.8304 US
dollars, find how many US dollars $AU550 obtains
and how many Australian dollars $US200 obtains)
© Department of Education and Training Western Australia, Early adolescence: Mathematics/Number scope and sequence, December 2007
8
Organisation of content into year levels is advisory. Teachers will continue to make professional
judgements about when to introduce content based on children’s prior learning and achievement.
*National Consistency in Curriculum Outcomes, Statement of Learning
Typical sequence of content:
Year 8
Year 9
Year 10
Calculate (continued)
 solving problems involving proportional quantities
using methods such as the unitary method
(eg finding the cost of 4.5 kg of apples, knowing
the price of 3 kg, by first calculating the cost of
1 kg)
 solving problems involving ratio and direct
proportion* (eg bananas cost $4.99 a kilo. The
more bananas you buy the more it will cost:
Cost = $4.99 x kilos of bananas)
 solving problems involving inverse proportion
(eg the distance from home to work is 5 km. If I
travel 30 km/h, then it only takes me 10 minutes to
get home. If I want to get home in 5 minutes, I
would need to increase my speed to 60 km/h)
Use a calculator to calculate with integers,
decimals and fractions
Use a calculator to calculate with rational and
some irrational numbers
Use a calculator to calculate with real numbers
 addition and subtraction of fractions using the
fraction mode of a graphics calculator
 using the x y key on a calculator
1
 using the x key on a calculator
y
 use and limitations of the ‘fix’ mode on a calculator
to give the answer to a simple computation to a
fixed number of decimal places
 using technology to calculate more difficult powers
and square roots* (eg 26.5313 = 18 675.010 679
291, 115 = 161 051, 4509 = 67.15 rounded correct
to two decimal places)
 carrying out, with technology, computations
involving decimal approximations to irrational
numbers in measurement contexts* (eg the
diagonal of a rectangle with length 10 m and
breadth 5 m is 125 ≈ 11.2 m)
 complex calculations using a calculator, including
the use of the brackets and the memory/store
functions
Checking results
Making estimates to check results
Factors affecting accuracy
 estimating results before calculating to help check
reasonableness
 finding upper and lower estimates for calculations,
form closer estimates within this interval for
computation in a given context* (eg spilting a
restaurant bill between several people)
 forming estimates for square roots (eg 500 is
between 20 and 30) and for computations involving
the constant * (eg 2 x  x 83.49 ≈ 480)
© Department of Education and Training Western Australia, Early adolescence: Mathematics/Number scope and sequence, December 2007
9
Organisation of content into year levels is advisory. Teachers will continue to make professional
judgements about when to introduce content based on children’s prior learning and achievement.
*National Consistency in Curriculum Outcomes, Statement of Learning
Typical sequence of content:
Year 8
Year 9
Year 10
Calculate (continued)
 checking the reasonableness of an answer in the
context of the problem (eg ‘My answer means that
Jamal weighs 5 kg but that cannot be right
because a bag of potatoes weighs that much’)
 checking the reasonableness of an answer in the
context of the problem
 checking the reasonableness of an answer
(eg knowing which multipliers make the answer
‘bigger’ or ‘smaller’ and which divisors make the
answer ‘bigger’ or ‘smaller’)
 choosing a suitable level of accuracy for
computation* (eg calculating the cost for a quantity
of soil and mulch for a garden bed at a given cost
per cubic metre and deliverable in half or full cubic
metre)
 truncating or rounding during calculations can
affect the accuracy of the results
© Department of Education and Training Western Australia, Early adolescence: Mathematics/Number scope and sequence, December 2007
10