Transcript NSW Curriculum and Learning Innovation Centre

NSW Curriculum and Learning Innovation Centre
Exploring Place value
Building capacity with the new syllabuses
Multi-unit place value
This aspect deals with more than just knowing the positional name of
numbers. E.g The 3 is in the hundreds column in the number 347.
The Place value levels focus on the structure of numbers, the
relationships between numbers and the strategies that students
use when solving two- and three-digit addition and subtraction
questions.
Multi-unit place value is evident when students can flexibly
regroup hundreds, tens and ones.
Having an understanding of ten as a countable unit (composite unit) is
central to place value concepts.
NSW Curriculum and Learning Innovation Centre
Pre-place value understanding
Not all students will be able to be placed on the Place value aspect.
A student must be at least at the counting-on-and-back stage on
the EAS aspect before being considered to be placed on the Place
value aspect.
At level 0 of the Place value aspect, Pre-place value, students have
an abstract understanding of a number being a completed count
and are able to count on or back from the number by ones.
NSW Curriculum and Learning Innovation Centre
Level 0: Ten as a count (pre-place value)
Level
description
Video
The student can
count-on by ones
and can count by
tens on the decade
10,20,30…
The student treats
‘ten’ as ten ones
but cannot treat
ten as a unit of ten
at the same time as
thinking of it as
ten ones. Typically
the student
reconstructs the
units of ten by
counting them by
ones.
Click on the image
to view the video
This video and
following work
sample show
evidence of
students
counting on
by ones
work sample
Syllabus
outcomes
Key ideas in
the syllabus
Sample related
content
MA1-5NA
Uses a range
of strategies
and informal
recording
methods for
addition and
subtraction
involving oneand two-digit
numbers
Use a range of
mental strategies
for addition and
subtraction of
two-digit numbers
Use and record a range
of mental strategies to
solve addition and
subtraction problems,
including:
- counting-on from
the larger number
to find the total of
two numbers
- counting-back from
a number to find
the number
remaining
- counting-on or
counting-back to
find the difference
between two
numbers.
Solve word
problems
involving addition
and subtraction
NSW Curriculum and Learning Innovation Centre
Level 1: Ten as a unit
Level description
The student can solve
two-digit addition and
subtraction problems by
counting by tens and
ones both on the decade
and off the decade.
The student uses
materials to represent
one of the numbers and
to support the counting
when adding or finding
the difference.
The student treats ten as
a single unit while
recognising that it
contains ten ones.
Video
Click on the image to
view the video
This video
shows a student
counting on by
tens and ones
with the support
of material.
Syllabus
outcomes
MA1-5NA
Uses a range
of strategies
and informal
recording
methods for
addition and
subtraction
involving oneand two-digit
numbers
Key ideas in
the syllabus
Use a range of
mental
strategies for
addition and
subtraction of
two-digit
numbers
Sample
related
content
Use and record a
range of mental
strategies to
solve addition
and subtraction
problems
involving twodigit numbers.
Solve word
problems
involving
addition and
subtraction
NSW Curriculum and Learning Innovation Centre
Level 2: Tens and ones
Level
description
The student can
solve two-digit
addition and
subtraction
problems
mentally using a
range of
strategies. Two
important
methods are the
jump strategy and
the split strategy.
Video
Click on the image to
view the video
This video
shows a
student
mentally
solving a twodigit addition
question by
using the jump
method.
Syllabus
outcomes
MA1-5NA
Uses a range of
strategies and
informal recording
methods for
addition and
subtraction
involving one- and
two-digit numbers
MA2-5NA
Uses mental and
informal written
strategies for
addition and
subtraction
involving two-,
three- and fourdigit numbers
Key ideas in
the syllabus
Solve word
problems
involving addition
and subtraction
Use and record a
range of mental
strategies for the
addition and
subtraction of
two-, three- and
four-digit
numbers
Sample related
content
Use and record a
range of mental
strategies to solve
addition and
subtraction
problems involving
two-digit numbers,
including:
- the jump strategy
on an empty
number line
- the split strategy
NSW Curriculum and Learning Innovation Centre
Level 3: Hundreds, tens and ones
Level description
Work
sample
Syllabus
outcomes
Key ideas
in the
syllabus
Sample related
content
The student can
mentally solve addition
and subtraction of two
three-digit numbers
using two key methods
(a) partitioning
numbers into
hundreds, tens and
ones and increment
or decrement by
hundreds and tens
(jump method)
(b) flexibly regroup
hundreds, tens and
ones (split method).
The student has a partwhole knowledge of
numbers to 1000
The following
work sample
suggests that
the student is
able to
partition the
15 into 5 and
10 before
finding the
corresponding
multiples of
20.
MA2-5NA
Uses mental
and informal
written
strategies for
addition and
subtraction
involving two-,
three- and
four-digit
numbers
Use and record
a range of
mental
strategies for
addition and
subtraction of
two-, threeand four-digit
numbers
Apply single-digit
number facts to mental
strategies including
- The jump strategy on
a number line
- The split strategy
- Bridging the decades
- Using place value to
partition numbers
Work sample
Solve problems involving
purchases and the
calculation of change to
the nearest five cents
NSW Curriculum and Learning Innovation Centre
Level 4: Decimal place value
Level
description
The student
understands the
positional value
of decimals and
can compare the
value of one
decimal place to
numbers with
two or three
decimal places
The student can
multiply or
divide decimals
by ten or one
hundred.
Videos
Click on the image to
view the video
This video
shows a
common
misconception
about
decimals.
Syllabus
outcomes
Key ideas in
the syllabus
MA2-7NA
Represents,
models and
compares
commonly
used
fractions and
decimals
Apply the place
value system to
represent tenths
and hundreds as
decimals
Model, compare
and represent
decimals with up
to two decimal
places.
Sample related content
State the place value of
digits in decimal numbers
up to two decimal places
Use place value to partition
decimals of up to two
decimal places
Apply knowledge of
decimals to record
measurements
Interpret zero digit(s) at the
end of a decimal
Use a calculator to create
patterns involving decimal
numbers eg 1÷10, 2÷10,
3÷10
NSW Curriculum and Learning Innovation Centre
Level 5: System place value
Level description
The student
understands that the
place value system can
be extended
indefinitely left or
right of the decimal
point and can explain
what happens when a
number is multiplied
or divided by a given
power of ten.
The student has an
understanding of
- multiplying and
dividing decimals
by decimal.
- the relationship
between the
adjacent units in a
numeral
- repeating decimals.
Syllabus
outcomes
MA3-4NA
Orders, reads
and represents
integers of any
size and
describes
properties
MA3-7NA
Compares,
orders and
calculates with
fractions,
decimals and
percentages
MA4-5NA
Operates with
fractions,
decimals and
percentages
Key ideas in the
syllabus
State the place value of
digits in numbers of any
size
Sample related content
Record numbers of any size
using expanded notation
Recognise that the place value
system can be extended
beyond hundredths – express
thousandths as decimals
Use mental, written and
calculator strategies to:
- multiply decimals by
one- and two-digit whole
numbers
- divide decimals by onedigit whole numbers, 10,
100 and 1000
Apply the four operations
with fractions, including
decimals
Use mental strategies to
multiply simple decimals by
single-digit numbers
Divide decimals by a one-digit
whole number where the
result is a terminating decimal
Use the notation for recurring
decimals
Multiply and divide decimals
using efficient written
strategies
NSW Curriculum and Learning Innovation Centre
Where to next?
Consider assessing each student to determine where he or
she is on the Place value aspect.
Look
Plan
Look at the associated syllabus outcomes as indicated on
the numeracy continuum.
The syllabus content associated with each outcome will help
you to plan a teaching program aimed at progressing each
student to the next level along the continuum.
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