Download Mathematics

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 – Mathematics
Middle childhood: Mathematics/Number – Students use numbers and operations and the relationships between them efficiently and
flexibly.
Typical sequence of content:
Year 4
Year 1
Year 2
Year 3
Year 5
Year 6
Year 7
Understand numbers
Understand whole numbers and decimals
Numbers to ten thousand
Numbers to hundreds of thousands
and decimal numbers to hundredths
Numbers into the millions and
decimal numbers to hundredths
Numbers into the millions and
beyond, decimal numbers to
thousandths and negative numbers
in real life contexts
 read, write and say whole numbers
up to ten thousand, leaving a space
between each set of three digits from
right to left
 read, write and say whole numbers
up to one million using the recurring
pattern of H T O in the thousands
and H T O in the ones
 use place value to read, write and
say whole numbers into the millions
and decimal numbers into the
hundredths places (eg 3.4 is larger
than 3.25 because there is a 4 in the
tenths place)
 use place value to read, write and
say whole numbers beyond the
millions and decimal numbers into
the thousandths (eg 3.4 is larger
than 3.289 because 4 tenths equals
 to order and locate numbers on a
suitably scaled number line
(eg order and locate 2 250, 2 750
and 2 500 on a number line from
2 000 to 3 000)
 to order and locate numbers on a
suitably scaled number line*
(eg order and locate 30 000,
10 000 and 25 000 on a number line
from 0 to 50 000)
 to order and locate numbers on a
number line (eg locate 25, 50 and 75
on a number line from 0 to 100)
 to order and locate numbers on a
suitably scaled number line
(eg locate 200, 400 and 800 on a
number line from 0 to 1 000)
 read, write and say correctly decimal
numbers to two decimal places
(eg 6.9 is ‘six point nine’ and 4.05 is
‘four point zero five’)
400
1000
, which is bigger than 289 )
1000
 investigate negative numbers in real
life contexts* (eg temperature, bank
balances, debit)
© Department of Education and Training Western Australia, Middle childhood: 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 – Mathematics
Typical sequence of content:
Year 4
Year 1
Year 2
 represent
whole numbers in various
Year
3
Year 5
Year 6
Year 7
Understand whole numbers and decimals (continued)
 represent whole numbers and
decimal fractions in various ways*
(eg represent decimals to two
places, on an array, a 10 x 10 grid or
a number line)
 represent whole numbers and
decimal fractions in various ways
(eg represent decimals to two places
on an array, a 10 x 10 grid or a
number line)
 the name and value of places in
numbers up to ten thousand
 the name and value of places in
numbers up to hundreds of
thousands and decimals up to two
decimal places
 the name and value of places into
the millions and decimals up to two
decimal places
 the name and value of places
beyond the millions and decimals up
to three decimal places
 the properties and patterns of odd
and even numbers (eg even
numbers are always divisible by two,
where odd numbers are not)
 identify factors and multiples of
some two and three-digit numbers*
(eg the factors of 80 are 1, 2, 4, 5, 8,
10, 16, 20, 40 and 80 and the first
four multiples of 25 are 25, 50, 75,
100)
 properties of prime and composite
numbers (eg use Eratosthenes’
Sieve to the find the prime and
composite numbers between 1 and
100)
 properties of triangular numbers and
square numbers (eg all square
numbers end in 0, 1, 4, 5, 6 or 9)
 count in decimal amounts to two
decimal places forwards and
backwards from a given number
(eg 2.34, 2.33, 2.32, 2.31)
 count forwards and backwards in
decimal amounts to three decimal
places, from a given number
(eg 2.341, 2.342, 2.343)
ways (eg symbols, words, concrete
materials, calculators)
 patterns in the multiples of numbers*
(eg multiples of 5 end in 5 or 0) and
prime and composite numbers to 20,
determining that a prime number has
two factors, 1 and the number itself
 count in tenths* (eg 2.3, 2.4, 2.5)
and hundredths for money and
measures (eg use the scale on a
tape measure to count forwards by
0.05 m from a given length [0.90 m,
0.95 m, 1.00 m, 1.05 m])
© Department of Education and Training Western Australia, Middle childhood: 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 – Mathematics
Typical sequence of content:
Year 4
Year 1
Year 2
Year 3
Year 5
Year 6
Year 7
Understand whole numbers and decimals (continued)
 recognise different representations
of numbers involving decimal
fractions*
(eg 1.4 =
2+
5
10
+
1 4 and
10
8
)
100
2.58 = 2 +
58
100
or
 write decimals as fractions and
fractions as decimals
(eg 0.65 =
65
100
and
2 4
10
= 2.4)
 know decimal equivalents for
1
2
, 1 , 1 , 1 , 1 , 1 and use these
3
4
5
8
10
to find decimal and percentage
equivalents* (eg 1 = 0.25 = 25%
4
and
 partition decimals in standard ways
to two decimal places
(eg 5.37 = 5 + 3 + 7 )
10
100
1
8
= 0.125 = 12.5%)
 partition decimals in standard and
non-standard ways (eg 2.46 =
2 + 0.46 as well as 2.2 + 0.26 as well
as 2 + 4 + 6 )
10
Money and measures using a
decimal point
Amounts of money and measures
using a decimal point
Connections between money,
measures and decimals
 write money amounts with a decimal
point between the whole number
(dollar) part and the fractional (cents)
part
 interpret a calculator display
involving money (eg that, in a money
context, 1.5 on the calculator screen
translates to $1.50)
 read, write and order money and
measures where a decimal point is
used (eg 3.2 kg is heavier than
3.12 kg)
 write money with only one symbol
(eg seventy five cents is written as
75c or $0.75 not $0.75c)
 round money to the nearest 5c
(eg amounts ending in 1, 2, 6 or 7
round down, so 32c would be
rounded to 30c and 37c rounded to
35c)
 interpret a calculator display
involving money and measurements
when the number has been
truncated (eg 1.2 on the calculator
might relate to 1.2 m, 120 cm or
$1.20)
© Department of Education and Training Western Australia, Middle childhood: Mathematics/Number scope and sequence, December 2007
100
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 – Mathematics
Typical sequence of content:
Year 4
Year 1
Year 2
 identify
the whole part and the
Year
3
fractional part in measurements
(eg 6.3 m has 6 whole metres and
3
10
of a metre)
Year 5
Year 6
Year 7
Understand whole numbers and decimals (continued)
 identify the whole part and the
fractional part in measurements*
(eg 5.34 m has 5 whole metres and
34
100
of a metre)
Standard and non-standard
partitions of two-digit and three-digit
numbers
Standard and non-standard placevalue partitions of numbers into the
thousands
Standard and non-standard
partitions of numbers into the
thousands and decimals to two
decimal places
Standard and non-standard
partitions of whole numbers and
decimals to three decimal places
 that numbers can be partitioned in
standard ways (eg 376 =
300 + 70 + 6) or non-standard ways
(eg 36 = 30 + 6 but also 18 + 18 or
20 + 16 and so on)
 that numbers can be partitioned in
standard ways* (eg 536 + 428 is
500 + 400 and 30 + 20 and 6 + 8)
and non-standard ways* (eg 376 =
200 + 176 or 150 + 150 + 76 and so
on)
 ways to partition (eg 4.26 + 5.23 is
4 + 5 and 0.2 + 0.2 and 0.06 + 0.03
which is 9 + 0.4 + 0.09 = 9.49)
 ways to partition whole numbers
(eg 15 x 6 can be 10 x 6 and 5 x 6 or
30 x 3)
Compare and order numbers to ten
thousand
Compare and order numbers to
hundreds of thousands, including
money and measures
Additively and multiplicatively
compare and order whole numbers
into the millions
Additively and multiplicatively
compare and order whole numbers
and decimals to 3 decimal places
 order numbers using place value
(eg 76 is bigger than 67 because
there is a 7 in the tens place)
 use place value to compare and
order numbers* (eg 7 896 is bigger
than 7 096 because there is an 8 in
the hundreds place and 3.4 m is
longer than 3.25 m because there is
a 4 in the tenths place)
 use place value to order larger whole
numbers in ascending or descending
order (eg 25 296 is bigger than
24 987 because there is a 5 in the
ten thousands place)
 use place value to order numbers of
any size in ascending or descending
order (eg 235 500 is larger than
234 500 because there is a 5 in the
thousands place)
© Department of Education and Training Western Australia, Middle childhood: 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 – Mathematics
Typical sequence of content:
Year 4
Year 1
Year 2
 the
Year
3 relative size of numbers
Year 5
Year 6
Year 7
Understand whole numbers and decimals (continued)
 the relative size of larger numbers
(eg 1 000 is ten times as big as 100)
 the constant relationship between
the places, and that the positions
increase in powers of 10 from right
to left (eg 100 is a hundred times
smaller than 10 000)
 the constant relationship between
the places, and that the positions
increase in powers of 10 from right
to left (eg 300 is a hundred times
larger than 3 and 1 000 times larger
than 0.3)
 count forwards and backwards in
tenths from any number, including
amounts of money (eg $2.70, $2.80,
$2.90 and 78c, 68c, 58c)
 count forwards and backwards in
tens, hundreds and thousands from
any number (eg 4 500, 4 400, 4 300)
 count forwards and backwards in
tens, hundreds, thousands and ten
thousands from any number
(eg 32 000, 31 000, 30 000)
 order and compare numbers and
numerical statements using = and ≠,
< and > symbols
(eg 386 > 300 + 50 + 9)
 rounding up and down to the nearest
10 or 100 for practical purposes
 rounding up and down to the nearest
100, 1 000 or 10th for practical
purposes
 rounding up and down to the nearest
100, 1 000 or 10th for practical
purposes
 rounding up and down to the nearest
100, 1 000, 10th or 100th for practical
purposes
(eg 2 is quite small compared
with 200)
 different ways of counting a
collection (eg by twos, fives, tens)
© Department of Education and Training Western Australia, Middle childhood: 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 – Mathematics
Typical sequence of content:
Year 4
Year 5
Year 1
Year 2
Partition
Year
3 objects, collections and
quantities into equal parts and read,
write and count with unit fractions
 to represent common fractions
(eg
1
3
,
1
2
,
1
4
) orally, in drawings,
(eg number lines, shapes), models
(eg counters, objects) and in written
forms
Year 6
Year 7
Understand fractions
Simple fraction equivalences and
comparisons using a range of
models, including number lines
Compare and find equivalences for
simple fractions and key
percentages using a range of
models, including number lines
Compare and find equivalences for
simple fractions and key percentages
using a range of models, including
number lines
 read, write and say unit fractions
using drawings, oral and written
forms, in everyday contexts* (eg a
quarter of an hour is fifteen minutes.
This can be shown on the clock
face)
 compare fractions using models,
drawings and number lines (eg use
 read, write and order proper
fraction strips to show
1
3
=
2
6
=
3
9
fractions (eg 1 ) improper fractions
3
)
(eg
7
5
) and mixed numerals*
(eg 3 3 )
4
 partition an object or collection into
equal parts (eg cut a piece of ribbon
into 12 pieces and give three people
a quarter of the original length)
 partition an object or collection in a
variety of ways to show equal parts*
(eg to find a quarter of 20 cards, deal
out 20 cards to 4 students)
 partition an object or collection in a
variety of ways to show equal parts
(eg three fifths of the class is girls,
that is 0.6 or 60% of the class)
 find fractional amounts of a thing,
quantity or collection of things
(eg find 3 of a class of 28 students,
4
2
3
of a bag of marbles, 4 of a glass
10
of water)
 recognise simple equivalences of
fractions through diagrams and
models (eg fold a page in half and
half again to see 2 = 1 )
4
2
 recognise simple equivalences of
fractions to tenths through diagrams
and models* (eg fold a page in half
and half again to see 2 = 1 )
4
2
 recognise simple equivalences of
fractions including mixed numerals
and improper fractions through
diagrams and models (eg colour
1 6 grids to see it equals 1 3 or 7 )
8
4
4
 recognise simple equivalences of
fractions including mixed numerals
and improper fractions through
diagrams and models* (eg colour
2 3 grids to see it equals 11 )
4
4
 use terminology of unit fractions in
context (eg a pie cut into six equal
parts has one-sixth as its unit
fraction)
© Department of Education and Training Western Australia, Middle childhood: 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 – Mathematics
Typical sequence of content:
Year 4
Year 1
Year 2
 half
Year
3 of a half is one-quarter
(eg show by cutting, folding,
measuring, dealing out)
 order unit fractions using diagrams
and models (eg
‘1
2
more than 1 of it’)
3
of this snake is
Year 5
Year 6
Year 7
Understand fractions (continued)
 that parts of a whole can look
different but still be equal in size
(eg two halves do not have to be
symmetrical to be half, but must
have the same quantity)
 the size of fractions are relative to
the whole (eg ‘ 1 of your pocket
3
money might be more or less than
1
3
of mine’)
 count in fractional amounts
(eg one-third, two-thirds, one whole,
one and one-third)
 count in fractional amounts
(eg four-fifths, one whole, one and
one-fifth or four-fifths, five-fifths, six
fifths)
 count in fractional amounts
(eg one and one-third, one and twothirds, two, two and one-thirds)
 order unit fractions using diagrams,
 order easily visualised fractions, with
like and unlike denominators, by
placing them on a number line, using
 order easily visualised fractions, with
like and unlike denominators, by
placing them on a number line, using
number lines and models* (eg
1
3
of
twelve counters is more than 1 ; on
4
a grid of two rows of five, show
which is bigger, 7 or 3 ; order and
10
5
reference points such as 0, 1 and 1
2
(eg place
3
4
and
and compare)
1
2
on a number line
reference points such as 0, 1 and 1*
2
(eg place
3
4
and
6
10
on a number
line and compare)
locate mixed numbers such as 2,
2 1 , 3, 3 1 , 4 on a number line)
2
2
 compare simple fractions and
percentages based on multiples of
10% and 25% from a model or
diagram (eg 25% of 2 litres equals
50% of 1 litre)
© Department of Education and Training Western Australia, Middle childhood: 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 – Mathematics
Typical sequence of content:
Year 4
Year 1
Year 2
Year 3
Year 5
Year 6
Year 7
Understand fractions (continued)
Simple rates
 rates are used in everyday situations
(eg price per kilogram, cost per litre
of petrol, cost per text message)
Simple ratios
Simple ratios
 ratios are used to describe
straightforward scales and
concentrations (eg cordial is made
up of one part cordial to four parts
water. The ratio is 1:4)
 ratios are used to describe
straightforward scales and
concentrations (eg in a Year 7 class
of 14 girls and 8 boys, the girl/boy
ratio is 14:8 or 7:4)
Understand operations
Represent number stories involving
change, combine and compare
situations, using diagrams and
addition and subtraction number
sentences
Represent the full range of additive
problems using diagrams as needed
and addition and subtraction number
sentences (equations) identifying the
part or the whole as the unknown
Represent the full range of additive
problems using diagrams as needed
and addition and subtraction number
sentences (equations) identifying
unknowns
Use addition and subtraction
equations (and diagrams as needed)
to represent the full range of additive
situations and situations that involve
more than one problem type
 write number sentences using the
terms change, combine and
compare (eg ‘Combine Tim’s 14
marbles with Lisa’s 36 marbles and
find the total’ is written as ‘14 + 36 =
’; ‘Lisa has 12 party hats and 15
friends, how many friends will not get
a hat?’ is written as ’15 – 12 = ’)
 write number sentences* (eg ‘Ted
began with 26 marbles and now has
12, how many did he lose?’ is written
as ‘26 –  = 12’; ‘Compare the
height of two rose bushes, one is
95 cm tall, the other is 87 cm tall’ is
written as ‘95 – 87 =  cm’)
 identify and write number sentences
for all types of problems (change,
combine, equalise or compare
situations), including those with
larger whole numbers and where
money, measurements and simple
fractions are involved
 identify and write number sentences
for problems, including contexts
where the clues to assist in choosing
the operation are not obvious, and
where larger whole numbers,
money, measurements and simple
fractions are involved*
© Department of Education and Training Western Australia, Middle childhood: 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 – Mathematics
Typical sequence of content:
Year 4
Year 1
Year 2
 write
Year
3 number stories to match given
number sentences write
(eg for ‘25 – 12 = ’ write ‘A farmer
had 25 sheep and sold 12, how
many are left?’)
Year 5
Year 6
Year 7
Understand operations (continued)
 write number stories to match given
number sentences write
(eg for ‘58 + 12 – 7 = ’ write ‘Tom
had 58 football cards and bought
another packet of 12. He then gave
7 of his cards to his cousin, how
many cards were left?’)
Match the semantics (meaning) of
addition and subtraction problem
types with the numbers and symbols
in their number sentences,
identifying the unknowns
Use the whole amount and the parts
within number stories and in open
number sentences to link and
choose between addition and
subtraction for two and three-digit
numbers
Use the inverse relationship between
addition and subtraction for large
whole numbers, money and familiar
measures
Use the inverse relationship between
addition and subtraction for large
whole numbers and decimals to two
decimal places and readily visualised
fractions
Use the inverse relationship between
addition and subtraction for large
whole numbers and decimals to
three decimal places and readily
visualised fractions
 state subtraction facts from known
addition facts (eg 6 + 8 = 14
therefore 14 – 8 = 6 and 14 – 6 = 8)
 use the inverse relationship to
restate the problem* (eg 36 + 24 =
60 therefore 60 – 24 = 36 and
60 – 36 = 24)
 use the inverse relationship to
restate the problem
(eg 3.8 + 4.6 = 8.4 therefore
8.4 – 4.6 = 3.8 and 8.4 – 4.6 = 3.8)
 use the inverse relationship to
restate and simplify the problem*
(eg for 13.06 – 9.82 =  ‘I know
9.82 + 3.24 = 13.06 so
13.06 – 9.82 = 3.24’)
 solve missing number problems (eg
15 + 7 = 22 to work out 22 –  = 15)
 use the inverse relationship for
calculator work to find missing
numbers* (eg for 18 +  = 25, key in
‘25 – 18 = ’)
 use the inverse relationship for
calculator work to find missing
numbers (eg for 45 +  = 63, key in
‘63 – 45 =’)
 use the inverse relationship for
calculator work to find missing
numbers (eg for 45 +  = 63, key in
‘63 – 45 =’)
© Department of Education and Training Western Australia, Middle childhood: 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 – Mathematics
Typical sequence of content:
Year 4
Year 1
Year 2
 work
Year
3 out the unknown
Year 5
Year 6
Year 7
Understand operations (continued)
(eg 40 + 60 = 100 so 40 + 70 is ten
more, 110)
Represent number stories involving
equal groups, sharing, simple rates,
arrays, combinations and ratio
comparison using materials, drawing
a picture or acting out, and using
addition, subtraction, multiplication
and division number sentences
Represent the full range of
multiplicative problems using
diagrams as needed and
multiplication and division number
sentences (equations)
Represent the full range of
multiplicative problems using
diagrams as needed and
multiplication and division number
sentences (equations) identifying
unknowns
Use multiplication and division
equations (and diagrams as needed)
to represent the full range of
multiplicative situations and
situations that involve more than one
problem type
 multiplication can be used for:
o repeating equal quantities
(eg three and three oranges is
six, which is the same as two
lots of three oranges)
o rates (eg ‘If velvet ribbon costs
$1 a metre, how much does
four metres of ribbon cost?’)
o arrays (eg ‘If there are five rows
each with six books, how many
books in total?’)
o simple combination problems
(eg ‘How many different outfits
do I have for the holiday if I
pack three tops and two skirts?)
 multiplication can be used for:
o repeating equal quantities*
(eg eight and eight caravans is
six, which is the same as two lots
of eight caravans)
o rates (eg ‘If ice-cream costs $4
for 4 litres, how much would
20 litres of ice-cream cost?’)
o arrays (eg ‘If there are eight
rows each with nine cars, how
many cars are in the car park in
total?’)
o simple combination problems
(eg ‘How many different pizza
topping combinations can I
have if I can use three different
meats and three vegetables?’)
 multiplication and division can be
used for repeated equal quantities,
ratio comparisons, arrays, scales
and combinations, and products of
measures (eg ‘What is the area of a
rectangle 12 cm by 14 cm?’)
 multiplication and division can be
used for repeated equal quantities,
ratio comparisons, arrays, scales
and combinations, and products of
measures (eg ‘If the area of a
rectangle is 50 m2, what are the
lengths of the sides if the length is
twice the width?’)
© Department of Education and Training Western Australia, Middle childhood: Mathematics/Number scope and sequence, December 2007
10
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 – Mathematics
Typical sequence of content:
Year 4
Year 1
Year 2
 division
can be used for sharing or
Year
3
partitioning a collection, quantity or
object (eg Tom arranged his 15
trophies evenly on three shelves,
how many were on each shelf?)
Year 5
Year 6
Year 7
Understand operations (continued)
 division can be used for:
o arrays (eg ‘Amy has 45 cabbages
in five equal rows, how many in a
row?’)
o ratios (eg ‘Lee has 28 marbles
which is four times the amount
Pete owns. How many marbles
does Pete have?)
 the relationship between fractions,
decimals and division (eg enter
into the calculator by keying in
‘3  4 = ’)
3
4
 the relationship between fractions,
decimals, percentages and division*
(eg enter 7 = 0.7 = 70%)
10
 for division the result may take many
forms, depending upon the context
of the problem (eg 18  4 can be
represented as:
o 4 1 units each
2
o each ribbon is 4.5 m long
o $18  4 = $4.50
o 18 people with 4 in each car will
need 5 cars)
© Department of Education and Training Western Australia, Middle childhood: Mathematics/Number scope and sequence, December 2007
11
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 – Mathematics
Typical sequence of content:
Year 4
Year 1
Year 2
Match
Year
3 the semantics of
multiplication and division problem
types with the numbers and symbols
in number sentences, identifying the
unknowns
 select appropriate operations for
number sentences (eg ‘Sam bought
4 lollipops costing $1.20 each. How
much change did he get from $5?’
requires multiplication and
subtraction)
Year 5
Year 6
Year 7
Understand operations (continued)
Match the semantics of
multiplication and division problem
types with the numbers and symbols
in number sentences, identifying the
unknowns
The order of operations
The order of operations
 select appropriate operations for
number sentences (eg ‘Jade, Katie
and Mark have a combined weight of
100 kg. Mark is 5 kg heavier than
Katie who weighs 30 kg. What is
Jade’s weight?’ requires addition
and subtraction)
 the acronym BIMDAS represents the
order:
o Brackets
o Indices
o Multiplication and
o Division (in the order they
appear)
o Addition and
o Subtraction (in the order they
appear) (eg use simple examples
such as ‘26 – 5 x 4 = 26 – [5 x 4]
= 26 – 20 = 6’)
 the acronym BIMDAS represents the
order:
o Brackets
o Indices
o Multiplication and
o Division (in the order they
appear)
o Addition and
o Subtraction (in the order they
appear)* (eg ‘45 – 36 + 8 x 5.8 =
45 – 36 + [8 x 5.8] =
45 – 36 + 46.4 = 55.4)
© Department of Education and Training Western Australia, Middle childhood: Mathematics/Number scope and sequence, December 2007
12
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 – Mathematics
Typical sequence of content:
Year 4
Year 1
Year 2
Use the
Year
3 size of the groups, the
number of groups and the whole
amount within number stories to
write and link multiplication and
division number sentences for
small quantities
 remainders in division can be left or
shared into parts of a whole
(eg when 13 apples are shared
between 4, each person receives 3
whole apples and 1 apple is left)
Year 5
Year 6
Year 7
Understand operations (continued)
Use the size of the groups, the
number of groups and the whole
amount within number stories, and
in open number sentences, to link
and choose between multiplication
and division for whole numbers
Use the size of the groups, the
number of groups and the whole
amount within number stories and
in open number sentences to link
and choose between multiplication
and division number sentences for
whole numbers, money and familiar
measures
Use the inverse relationship between
multiplication and division for whole
and decimal numbers
 remainders in division can be left or
shared into parts of a whole
(eg when 13 chalks are shared
between four each person receives
three whole sticks of chalk and a
quarter piece each)
 remainders in division can be shared
into parts of a whole which is a
fraction of the divisor
 remainders in division can be
represented in decimal form
(eg 29 ÷ 4 = 7.25)
(eg 27  4 = 6 3 )
4
 the numbers in a multiplication can
refer to the number of groups or the
number of objects in each
 the inverse relationship
(eg 3 x 8 = 24, so 24 ÷ 8 = 3
and 24  3 = 8)
 the inverse relationship*
(eg 3 x 8 = 24, so 24  8 = 3
and 24  3 = 8)
 use the inverse relationship to solve
missing number problems
(eg 5 x 8 = 40 to work out
40   = 8)
 use the inverse relationship to solve
missing number problems*
(eg 7 x 8 = 56 to work out
56   = 8)
© Department of Education and Training Western Australia, Middle childhood: Mathematics/Number scope and sequence, December 2007
13
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 – Mathematics
Typical sequence of content:
Year 4
Year 1
Year 2
Identify
Year
3 different equal groupings
Year 5
Year 6
Year 7
Understand operations (continued)
within whole numbers and represent
as arrays and multiplication and
division number sentences
 multiplication can be performed in
any order, without altering the
answer (eg use materials to
demonstrate that 3 x 4 results in the
same quantity as 4 x 3)
 collections may be arranged into
equal sized groups (eg students
arrange 24 blocks into arrays: 1 row
of 24, 24 rows of 1, 2 rows of 12, 12
rows of 2, 3 rows of 8, 8 rows of 3, 4
rows of 6, 6 rows of 4)
 identify ‘multiples’, ‘products’ and
‘factors’ (eg 12 is a multiple of 4, 12
is the product of 3 x 4 and 3 and 4
are factors of 12)
 identify ‘prime’ numbers (eg prime
numbers to 20 are 2, 3, 5, 7, 11, 13,
17 and 19) and determine that they
have exactly two factors* (eg the
factors of 5 are 1 and 5; the factors
of 17 are 1 and 17)
© Department of Education and Training Western Australia, Middle childhood: Mathematics/Number scope and sequence, December 2007
14
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 – Mathematics
Typical sequence of content:
Year 4
Year 1
Year 2
Strategies
to mentally add and
Year
3
Year 5
Year 6
Calculate
subtract to 100, drawing on
remembered facts
Strategies to mentally add and
subtract numbers to 100 and
extension of remembered addition
facts into the hundreds
 change a subtraction into an addition
(eg 13 – 8 can be thought of as
8 +  = 13)
 change a subtraction into an
addition* (eg 56 – 23 can be thought
of as 23 +  = 56)
 use standard partitioning (eg 24 + 37
= [20 + 30] + [4 + 7] = 50 + 11 = 61;
for 34 – 27 recall 30 – 27 = 3 then
add back the 4)
Year 7
Strategies to mentally add and
subtract two-digit numbers
Strategies to mentally add and
subtract two-digit numbers
 use known basic facts in all
operations to work out those they do
not remember
 ‘bridge the tens’ (eg 9 + 4 can be
thought of as ‘one more to make 10’,
so it becomes 10 + 3)
 ‘bridge the tens and/or hundreds’
(eg 98 + 14 can be thought of as
‘two more to make 100’, so it
becomes 100 + 12)
 ‘bridge the tens and/or hundreds’*
(eg 89 + 27 can be thought of as
90 + 26 and 68 – 34 can be thought
of as 70 – 36)
 use standard partitioning
(eg 24 + 37 = [20 + 30] + [4 + 7])
and non-standard partitioning*
(eg 39 – 17 = 19 – 17 + 20)
 use standard partitioning
(eg 24 + 37 = [20 + 30] + [4 + 7])
and non-standard partitioning
(eg 39 – 17 = 19 – 17 + 20)
 use standard and non-standard
partitioning* (eg 36 + 59 =
30 + 50 + 10 + 5 = 95)
 use standard partitioning for
decimals (eg 6.4 + 7.3 =
6 + 7 + 0.4 + 0.3 = 13 + 0.7 = 13.7)
 extend basic addition and
subtraction facts using patterns
(eg 7 + 2 = 9 so 70 + 20 = 90)
 extend basic addition and
subtraction facts using patterns
(eg 5 + 4 = 9 so 50 + 40 = 90 and
90 – 40 = 50)
 extend basic addition and
subtraction facts using patterns
(eg 5 + 7 = 12 so 50 + 70 is
120 and 120 – 50 = 70)
© Department of Education and Training Western Australia, Middle childhood: Mathematics/Number scope and sequence, December 2007
15
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 – Mathematics
Typical sequence of content:
Year 4
Year 1
Year 2
 use
Year
3 doubles and near doubles
(eg 8 + 14 = 10 + 10 + 2 = 20 plus 2
more so 32)
Year 5
Year 6
Year 7
Calculate (continued)
 use doubles and near doubles
(eg 15 + 17 = 15 + 15 + 2 = 30 plus
2 more so 32)
 rearrange the order to use
compatible numbers (eg look for tidy
sums when adding 6 + 7 + 5 + 4 + 3
thus add 6 + 4 then 7 + 3 and finally
add 5)
 rearrange the order to use
compatible numbers* (eg look for
tidy sums when adding 68 + 27 + 12
= 68 + 12 + 27 = 80 + 27 = 107)
 take some from one number to give
to another (eg 9 + 5 is the same as
10 + 4)
 take some from one number to give
to another* (eg 38 + 7 is the same
as 40 + 5)
 change the numbers by adding or
subtracting the same amount
(eg change ‘32 – 17’ to ‘35 – 20’ or
‘30 – 15’)
 change the numbers by adding or
subtracting the same amount*
(eg change ‘32 – 17’ to ‘35 – 20’ or
‘30 – 15’)
 start with the biggest place (front
loading) (eg 26 + 35 is 36, 46, 56
and 5 more; 20 + 30 and 6 + 5, so
50 + 11 is 61)
 start with the biggest place (front
loading)* (eg 26 + 35 is 36, 46, 56
and 5 more; 20 + 30 and 6 + 5, so
50 + 11 is 61)
 use known addition and subtraction
facts to work out those they do know
(eg find 7 + 9 by relating it to 8 + 8)
 use known addition and subtraction
facts to work out those they do know
(eg find 7 + 9 by relating it to 8 + 8)
 adding in tens to solve
(eg 24 + 32 = 24, 34, 44, 54
add 2 = 56)
 adding in tens, twenties and thirties,
hundreds etc from any starting point
(eg 24, 44, 64 …)
 rearrange the order to use
compatible numbers (eg look for tidy
sums when adding 26 + 34 + 74 thus
adding 26 + 74 to get 100 then add
34 to get 134)
 rearrange the order to use
compatible numbers* (eg look for
tidy sums when adding 26 + 34 + 74
thus adding 26 + 74 to get 100 then
add 34 to get 134)
 describe methods used for mentally
adding and subtracting in a way that
shows they understand why it works
 describe methods used for
calculating mentally in a way that
shows they understand why it works
© Department of Education and Training Western Australia, Middle childhood: Mathematics/Number scope and sequence, December 2007
16
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 – Mathematics
Typical sequence of content:
Year 4
Year 1
Year 2
Strategies
to mentally multiply and
Year
3
divide single digit numbers and
remember some multiplication facts
 observe patterns in multiplication
tables (eg repeating final digit
patterns):
o
0, 2, 4, 6, 8, 10, 12 for the 2 x
table
o
0, 5, 0, 5, 0, 5 for the 5 x table
o
the 9 x table has decreasing
digits in the ones column
because you add 10 and take 1
 make links between the tables
(eg the 4 x table is double the 2 x
tables plus the 8 x table is double
the 4 x table)
Year 5
Year 6
Year 7
Calculate (continued)
Strategies to mentally multiply and
divide single digit numbers and
remember most multiplication facts
Strategies to mentally multiply and
divide larger numbers related to
basic facts
 change a division into a
multiplication* (eg 24  6 can be
thought of as ‘How many sixes make
24?’)
 change a division into a
multiplication (eg 63  9 can be
thought of as ‘How many nines make
63?’)
 make links between the tables
(eg the 6 x table is double the 3 x
tables)
Strategies to mentally multiply and
divide larger numbers
 rounding a number and adjusting it
(eg 6 x 9 is 6 tens take 6 ones)
 rounding a number and adjusting it
(eg 99 x 7 is 100 times 7 take 7)
 doubling and halving
(eg 4 x 6 = [2 x 6] x 2)
 doubling and halving (eg 35 x 12 is
the same as 70 x 6 so 420)
 take a factor from one to give to
another (eg 15 x 6 is 15 x 2 x 3,
which is 30 x 3 = 90)
 use factors of numbers, including
prime factors to assist in mental
computation*
(eg 72 = 6 x 12 = 2 x 3 x 2 x 6 =
2 x 3 x 2 x 2 x 3 = 23 x 32)
 change the numbers by multiplying
or dividing by the same amount
(eg 90 ÷ 5 is the same as 180 ÷ 10)
 change the numbers by multiplying
or dividing by the same amount
(eg 87 ÷ 5 is the same as 174 ÷ 10)
© Department of Education and Training Western Australia, Middle childhood: Mathematics/Number scope and sequence, December 2007
17
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 – Mathematics
Typical sequence of content:
Year 4
Year 5
Year 6
Year 1
Year 2
Year 3
Year 7
Calculate (continued)
 place value partitions (eg 6 x 25 is
6 x 20 add 6 x 5, so 120 + 30)
 place value partitions (eg 6 x 25 is
6 x 20 add 6 x 5, so 120 + 30)
 use known multiplication facts to
work out unknown multiplication
facts (eg 5 x 8 = 40, so 6 x 8 is
40 + 8 = 48)
 use known multiplication facts to
work out unknown multiplication
facts (eg 5 x 8 = 40, so 6 x 8 is
40 + 8 = 48)
 use known multiplication facts to
work out unknown multiplication
facts (eg 5 x 8 = 40, so 6 x 8 is
40 + 8 = 48)
 multiply and divide numbers by 10
and 100 and display changes using
models such as place value charts*
(eg multiply 1.5 repeatedly by 10 and
colour in the 1 000s chart)
 extend basic multiplication facts to
multiply and divide numbers by
multiples of 10 and 100
(eg 3 x 4 = 12 so 1 200 ÷ 3 = 400)
 extend basic multiplication facts to
multiply and divide numbers by
multiples of 10 and 100*
(eg 27 x 1 000 = 27 x 10 x 10 x 10 =
27 x 103)
Use counting by unit fractions to
mentally add and subtract orally
presented fractions with like
denominators
Use counting by unit fractions to
mentally add and subtract orally
presented fractions with like
denominators
Strategies to mentally add and
subtract readily visualised fractions
and find a unit fraction of a whole
number
Strategies to mentally add and
subtract readily visualised fractions
and find a unit fraction of a whole
number
 count forwards or backwards (eg for
 count forwards or backwards*
 use known number facts
 add and subtract fractions with like
1
4
+
3
4
find 1)
=  count on
2
4
,
3
4
,
4
4
to
(eg for ‘I took home
5
8
7
8
of a cake and
was eaten, how much was left?
(eg for
3
8
+
7
8
10 eighths =
= [3 + 7] eighths =
12
8
or
11
4
)
denominators (eg solve 2 1 + 1 1 by
3
3
visualising)
count back 7 , 6 , 5 , 4 , 3 and 2 )
8
8
8
8
8
8
© Department of Education and Training Western Australia, Middle childhood: Mathematics/Number scope and sequence, December 2007
18
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 – Mathematics
Typical sequence of content:
Year 4
Year 1
Year 2
Year 3
Year 5
Year 6
Year 7
Calculate (continued)
 use number lines, arrays and
fraction walls to perform mental
calculations with common fractions*
(eg use a fraction wall to answer
1
2
+
1
4
= )
 find a unit fraction of a whole
number by dividing the whole
number by the amount of groups
(eg find
1
3
1
3
of 18, divide 18 by 3,
 find a unit fraction of a whole
number by dividing the whole
number by the amount of groups (eg
to find a quarter of 24, divide 24 by
4, therefore 1 equals 6)
4
of 18 = 6)
Add and subtract whole numbers
into the 100s and money using their
own and pencil methods
Add and subtract whole numbers
into the 100s, money and simple
measures using their own and pencil
methods and informal written
methods for readily visualised
fractions
Add and subtract whole numbers,
money and measures using their
own methods or conventional
algorithms and informal written
methods for readily visualised
fractions
Add and subtract whole numbers,
money and measures using their
own methods or conventional
algorithms and informal written
methods for readily visualised
fractions
 informal paper-and-pencil methods
(eg diagrams, jottings) when
problems go beyond mental
calculation capabilities
(eg 128 + 379 = )
 informal and formal paper-and-pencil
strategies* (eg diagrams, jottings,
algorithms) when problems go
beyond mental calculation
capabilities
(eg 6.83 m – 1.25 m = )
 use own methods or conventional
algorithms to add and subtract larger
whole numbers and decimals, where
numbers go beyond mental
capabilities
 use own methods or conventional
algorithms to add and subtract larger
whole numbers and decimals, where
numbers go beyond mental
capabilities*
 everyday language to explain
strategies used to solve a problem or
number sentence problem or
number sentence
 everyday language to explain
strategies used to solve a problem or
number sentence problem or
number sentence*
© Department of Education and Training Western Australia, Middle childhood: Mathematics/Number scope and sequence, December 2007
19
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 – Mathematics
Typical sequence of content:
Year 4
Year 1
Year 2
 use
Year
3 standard partitioning to add and
subtract two-digit whole numbers
without regrouping (eg 42 + 37 can
be written as 40 + 30 = 70 and
2 + 7 = 9, so 79, and recorded with
words, numbers and/or signs)
Year 5
Year 6
Year 7
Calculate (continued)
 use standard partitioning, into the
hundreds, to add and subtract twodigit whole numbers with and without
regrouping (eg 54 – 28 can be
written as (40 – 20) + (14 – 8) =
20 + 6 = 26)
 partition larger numbers and
decimals to add and subtract with
and without regrouping (eg 6.5 – 2.8
can be written as (5 – 2) and
[1.5 – 0.8] = 3 + 0.7 = 3.7)
 partition larger numbers and
decimals to add and subtract with
and without regrouping (eg 6.5 – 2.8
can be written as [5 – 2] and
[1.5 – 0.8] = 3 + 0.7 = 3.7)
 add and subtract fractions with
unlike denominators by writing the
fractions in different ways
 add and subtract fractions with
unlike denominators by writing the
(eg 1 = 2 so 1
2
4
2
2
1
3
+
= )
4
4
4
+
1
4
can be
fractions in different ways* (eg 1 =
2
4
so
1
2
+
1
4
can be
2
4
+
1
4
=
2
3
)
4
Informal written strategies to
multiply and divide, interpreting
remainders appropriately
Informal written strategies to
multiply and divide, interpreting
remainders appropriately
Informal written strategies to
multiply and divide whole numbers,
money and measures (multipliers
and divisors to at least 10)
Use own methods or conventional
algorithms to multiply and divide
whole numbers, money and
measures
 factorise numbers and represent
them in different ways (eg use 12
blocks to find the arrays 12 x 1,
2 x 6, 3 x 4 and 4 x 3)
 factorise numbers and represent
them in different ways*
(eg 12 = 2 x 6 and 3 x 4, 12  2 = 6
and 12  4 = 3)
 factorise products to represent them
in different ways (eg 64 = 2 x 32,
8 x 8, 4 x 16, 2 x 2 x 16)
 rewrite larger whole numbers as a
product of factors, including prime
factors (eg factor trees)
 express the ‘left over’ after a division
as a remainder (eg 23 ÷ 7 = 3 r 2)
 express the remainder after division
as a remainder or a fraction
 express the remainder after division
as a remainder or a fraction of the
 express the remainder after division
as a remainder or a fraction of the
(eg 23 ÷ 4 = 5 r 3 or 5 3 )
4
divisor (eg 53 ÷ 4 = 13 1 or 13.25)
4
divisor (eg 73 ÷ 8 = 9 r 1 or 9 1 or
8
9.125)
© Department of Education and Training Western Australia, Middle childhood: Mathematics/Number scope and sequence, December 2007
20
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 – Mathematics
Typical sequence of content:
Year 4
Year 1
Year 2
Year 3
Year 5
Year 6
Year 7
 use place value to multiply and
divide a two-digit whole number by a
single-digit whole number (eg 24 x 6
equals (20 x 6) + (4 x 6) = 120 + 24
= 144)
 use place value to multiply and
divide a two-digit whole number by a
single-digit whole number
(eg 145 x 4 equals (100 x 4) +
(40 x 4) + (5 x 4) = 400 + 160 + 20 =
580)
Calculate (continued)
 interpret remainders in the context of
the question (eg 23 children are to
be driven in cars to the concert. If
only 4 children can fit in each car,
how many cars are needed?
23 ÷ 4 = 5 r 3, so 6 cars are needed)
 multiply and divide larger whole
numbers and decimals by a single or
double digit number, where numbers
go beyond mental capabilities*
 how to find the fraction of a number
using multiples (eg find
saying ‘6 x 5 = 30 so
be 6’)
1
5
1
5
of 30 by
of 30 must
 how to find the fraction of a number
using multiples*
(eg find 3 of 40 by saying
5
‘8 x 5 = 40 so 1 of 40 must be 8 and
5
3
5
of 40 is 24’ and ‘the number of
one-eighth slices in three pizzas is
24’)
© Department of Education and Training Western Australia, Middle childhood: Mathematics/Number scope and sequence, December 2007
21
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 – Mathematics
Typical sequence of content:
Year 4
Year 1
Year 2
Year 3
Year 5
Year 6
Year 7
Calculate (continued)
 compare simple fractions from a
model or diagram (eg
1
2
>
1
3
>
1
4
)
 equivalence between commonly
used fractions and decimal fractions
(eg 1 = 0.5, 1 = 0.2, 3 = 0.75)
2
5
4
 compare simple fractions and
percentages based on multiples of
10% and 25% from a model or
diagram* (eg 25% of 2 litres equals
50% of 1 litre)
 equivalence between common
fractions, decimal fractions and
percentages* (eg 1 = 0.5 = 50%,
2
1
5
= 0.2 = 20%,
3
4
= 0.75 = 75%)
 use a number line or materials to
solve practical problems involving
negative numbers* (eg show that an
overnight change in temperature
from 5˚C to –7˚C is a drop of 12 °C)
 use rates to calculate cost given
price and quantity
(eg 9 packets @ $1.25)
 use rates to calculate:
o cost given price and quantity
(eg 34 packets @ $1.25)
o speed given distance and time*
(eg 120 km covered in 2 hours
is 60 km/h)
 simplify ratios (eg 4:6 = 2:3,
 simplify ratios* (eg 6:8 = 3:4,
1
2
:2 = 1:4)
1
2
:4 = 1:8)
© Department of Education and Training Western Australia, Middle childhood: Mathematics/Number scope and sequence, December 2007
22
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 – Mathematics
Typical sequence of content:
Year 4
Year 1
Year 2
Year 3
Year 5
Year 6
Year 7
Calculate (continued)
 use ratio to compare quantities of
the same type (eg in a Year 7 class
of 14 girls and 8 boys, the girl/boy
ratio is 14:8 or 7:4)
 use ratio to compare quantities of
the same type* (eg in a Year 7 class
of 14 girls and 8 boys, the girl/boy
ratio is 14:8 or 7:4)
 calculate proportions of a given
ratio* (eg change a recipe for four
people to cater for two)
Use a calculator for all four
operations
Use a calculator for all four
operations
Use calculator functions for all four
operations and memory, interpreting
decimal quotients appropriately
Use calculator functions for all four
operations and memory, interpreting
decimal quotients appropriately,
converting between fractions,
decimals and percentages
 the efficiency of using the x key
instead of repeated addition, and the
÷ key instead of repeated subtraction
on a calculator
 use a calculator for whole and
decimal numbers, where numbers
go beyond mental capabilities
 use a calculator for whole and
decimal numbers and fractions
where numbers go beyond mental
capabilities
 use a calculator for whole and
decimal numbers and fractions,
where numbers go beyond mental
capabilities*
 multiplication can be entered on a
calculator in a different order and still
have the same result
(eg 4 x 5 = 5 x 4)
 calculators are the sensible choice
for laborious or repetitive
computations
 calculators are the sensible choice
for laborious or repetitive
computations
 use calculators to carry out more
complex or repetitive computations
with attention to order of operations*
(eg include GST and fixed packaging
and postage costs for a list of items
from a catalogue to calculate total
cost for several orders)
© Department of Education and Training Western Australia, Middle childhood: Mathematics/Number scope and sequence, December 2007
23
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 – Mathematics
Typical sequence of content:
Year 4
Year 1
Year 2
Year 3
Year 5
Year 6
Year 7
Calculate (continued)
 use calculator functions to find the
solution to a sequence of
calculations (eg enter (2.75 x 35) +
(0.54 x 27))
 division must be entered on a
calculator in the correct order
 use the context to interpret calculator
answers (eg 5 children share $37,
the display shows 7.4, interpret as
$7.40)
 use the context to interpret calculator
answers (eg 5 children share $37,
the display shows 7.4, interpret as
$7.40)
Use number lines and rounding to
check calculations
Use appropriate strategies to check
calculations
Use appropriate strategies to check
calculations
Use appropriate strategies to check
calculations
 check a calculation by doing it in a
different way (eg check the result of
an addition by adding the numbers in
a different order)
 check a calculation by doing it in a
different way* (eg check the result of
addition by subtracting an addend
from the total)
 check a calculation by doing it in a
different way (eg check a product by
repeatedly subtracting one of the
original factors)
 check a calculation by doing it in a
different way (eg check a product by
dividing it by one of the original
factors)
 estimate and approximate the
answers (eg 16 + 19 cannot be 25
because 15 + 15 is 30, so it has to
be more than 30)
 estimate and approximate the
answers* (eg 3 x 46 must be
between 120 and 150 because
3 x 40 = 120 and 3 x 50 is 150)
 estimate and approximate the
answers (eg 78 ÷19 ≈ 4 because 78
is about 80 and 19 is about 20)
 estimate and approximate the
answers (eg 3 468 – 876 ≈ 2 400
because 3 468 is about 3 500 and
876 is about 900)
 round numbers (up or down
depending upon the context) to the
nearest 10 to approximate
calculations (eg 47 + 8 will be about
50 + 10 so the answer should be just
under 60)
 round numbers (up or down
depending upon the context) to the
nearest 5, 10 or 100 to approximate
calculations* (eg 374 + 75 ≈ 500
when rounded to hundreds. The
answer is less than 500 as both
numbers were rounded up)
 when rounding whole numbers to the
nearest 5, 10, 100 or 1 000, the
same number may need to be
rounded up or down (eg 4 381 to the
nearest 10 goes down to 4 380, but
to the nearest hundred rounds up to
4 400)
 round decimal numbers (up or down
depending upon the context) to the
nearest whole number or to the
nearest one or two decimal places
when approximating calculations*
(eg 29 643 ÷ 87 will be
approximately 30 000 ÷ 100 or
27 000 ÷ 90, that is around 300)
© Department of Education and Training Western Australia, Middle childhood: Mathematics/Number scope and sequence, December 2007
24
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 – Mathematics
Typical sequence of content:
Year 4
Year 1
Year 2
 use
Year
3 the properties of operations to
check calculations (eg ‘I have taken
a whole number from a larger whole
number so the answer must be
smaller than what I started with’)
 check the accuracy of results against
the context of the problem (eg the
winner of the race should have the
shortest time for the race)
Year 5
Year 6
Year 7
 use the properties of operations to
check calculations* (eg ‘If I multiplied
by a number larger than one and got
a smaller answer, it cannot be right’)
 use the properties of operations to
check calculations (eg ‘If I multiplied
by a number larger than one and got
a smaller answer, it cannot be right’)
 use the properties of operations to
check calculations (eg 0.2 x 0.3 must
be less than 0.2 because it is
multiplied by a number less than
one)
 check the accuracy of results against
the context of the problem* (eg Jack
takes 20 seconds to run 100 m but
he will probably take longer than 80
seconds [4 x 20] to run 400 m)
 check the accuracy of results against
the context of the problem (eg ‘If I
 check the accuracy of results against
the context of the problem* (eg the
answer cannot be right if the
average height worked out is greater
than that of anybody in the group)
Calculate (continued)
am looking for 4 of 90, then the
5
answer has to be less than 90’)
© Department of Education and Training Western Australia, Middle childhood: Mathematics/Number scope and sequence, December 2007
25