MATHS OVERVIEW-YEAR 3 TERM 1, 2013
CONTENT DESCRIPTORS
Number & Algebra
YEAR LEVEL
Year 3
DURATION
Term 1
LINKS TO OTHER LA’s
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ACMNA051 Investigate the conditions required for a number to be odd or even and identify odd and even numbers
ACMNA052 Recognise, model, represent and order numbers to at least 10 000
ACMNA053 Apply place value to partition, rearrange and regroup numbers to at least 10 000 to assist calculations and solve problems
ACMNA054 Recognise and explain the connection between addition and subtraction
ACMNA055 Recall addition facts for single-digit numbers and related subtraction facts to develop increasingly efficient mental strategies for
computation
ACMNA056 Recall multiplication facts of two, three, five and ten and related division facts
ACMNA058 Model and represent unit fractions including 1/2, 1/4, 1/3, 1/5 and their multiples to a complete whole
ACMNA059 Represent money values in multiple ways and count the change required for simple transactions to the nearest five cents
ACMNA060 Describe, continue, and create number patterns resulting from performing addition or subtraction
Measurement & Geometry
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ACMMG061 Measure, order and compare objects using familiar metric units of length, mass and capacity
ACMMG062 Tell time to the minute and investigate the relationship between units of time
ACMMG063 Make models of three-dimensional objects and describe key features
ACMMG066 Identify symmetry in the environment
ACMMG064 Identify angles as measures of turn and compare angle sizes in everyday situations
Statistics & Probability
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ACMSP067 Conduct chance experiments, identify and describe possible outcomes and recognise variation in results
ACMSP068 Identify questions or issues for categorical variables. Identify data sources and plan methods of data collection and recording
ACMSP069 Collect data, organise into categories and create displays using lists, tables, picture graphs and simple column graphs, with and
without the use of digital technologies
ACMSP070 Interpret and compare data displays
DEVELOPING INQUIRING & REFLECTIVE LEARNERS
☐COMMUNITY CONTRIBUROR
☐ACTIVE INVESTIGATOR
☐LEADER AND COLLABORATOR
☐DESIGNER AND CREATOR
☐EFFECTIVE COMMUNICATOR
☐QUALITY PRODUCER
Achievement Standard
By the end of Year 3, students recognise the connection between addition and subtraction and solve problems using efficient strategies for multiplication. They model andrepresent unit
fractions. They represent money values in various ways. Students identify symmetry in the environment. They match positions on maps with given information. Students recognise angles in
real situations. They interpret and compare data displays.
Students count to and from 10 000. They classify numbers as either odd or even. They recall addition and multiplication facts for single digit numbers. Students correctly count out change
from financial transactions. They continue number patterns involving addition and subtraction. Students use metric units for length, mass and capacity. They tell time to the nearest minute.
Students make models of three-dimensional objects. Students conduct chance experiments and list possible outcomes. They carry out simple data investigations for categorical variables.
Proficiency Strands
Understanding includes connecting number representations with number sequences, partitioning and combining numbers flexibly, representing unit fractions, using appropriate language to
communicate times, and identifying environmental symmetry
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Fluency includes recalling multiplication facts, using familiar metric units to order and compare objects, identifying and describing outcomes of chance experiments, interpreting maps and
communicating positions
Problem Solving includes formulating and modelling authentic situations involving planning methods of data collection and representation, making models of three-dimensional objects and
using number properties to continue number patterns
Reasoning includes using generalising from number properties and results of calculations, comparing angles, creating and interpreting variations in the results of datacollections
and data displays
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MAG Planning Term 1 Year 3
TOPIC
CONTENT DESCRIPTOR
KEY IDEA
Pre-ASSESS
ASSESSMENT
INVESTIGATION
ACMNA051
Investigate the
conditions required for
a number to be odd or
even and identify odd
and even numbers.
There are many
ways to represent
numbers. How do
they look the
same? How are
they different?
What makes 5 a
special number?
Choose two of
these numerals.
1234567890
• recognise and explain number
patterns, eg odds and evens,
numbers ending with five
• model odd and even numbers
using arrays and other
collection-based diagrams [L]
What numbers are
in the pattern
2,4,6,8,….. and also
in the pattern
5,10,15,20….? Do
children realise
that all multiples of
10 will be in both
patterns because
they are even
numbers and that
multiples of 5 will
not be in the 2’s
pattern because
they are odd
numbers?
3.1.1
Odd and
Even
Numbers
TOPIC
CONTENT DESCRIPTOR
ACMNA052 Recognise,
model, represent and
order numbers to at
least 10 000
3.1.2
Numbers to
10 000
(1)
KEY IDEA
Numbers tell us
how much and
how many
Pre-ASSESS
What real life
situations might
this number
describe?
Option 1 100
Option 2 1000
Students choose
one options but
will still benefit
from class
discussion
ASSESSMENT
INVESTIGATION
First Steps in Mathematics –
Number Course Book
Diagnostic Task – Up to and
over 100 page 16
Diagnostic Task – Up to and
through the 100s
page 16 (modify this task for Up
to and over 1000)
Make up a fourdigit PIN number
and say why it is
easy to remember.
The emphasis here
is on being able to
communicate the
reason to someone
else. You could
possibly make
restrictions such as
not using birth
years
STUDENT
JOURNAL
Can the student
give a definition of
an odd /even
number? Can the
student identify
odd and even
numbers, and give
reasons why they
are odd/even? Can
the student
identify a four digit
number, for
example: 4327 as
odd or even, with
an explanation?
STUDENT
JOURNAL
• represent
numbers up to
four digits using
numerals, words,
objects and digital
displays
• make the largest
and smallest
number from four
given digits (U) (F)
[CCT]
• identify the
number before
and after a given
two-, three- or
four-digit number
• use place value
to compare and
explain the relative
RESOURCES
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Counters / straws
Hundreds Board
Odd or even investigation sheet
1-100 cards
Calculator
Individual whiteboards
and washable pens
FISH Kit
RESOURCES
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Number Board
Sticky notes
Place value chart
Tiny 100, 10 , 1
Flip chart
Digits
Place value arrows
Calculator
FISH Kit
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TOPIC
3.1.3
Place Value
(1)
TOPIC
3.1.4
Connecting
Addition &
Subtraction
CONTENT DESCRIPTOR
KEY IDEA
Pre-ASSESS
ACMNA053 Apply place
value to partition,
rearrange and regroup
numbers to at least 10
000 to assist
calculations and solve
problems.
Number
benchmarks are
useful for relating
numbers and
estimating
amounts
How many years
old is someone
who is 1 000
days? Are you
older or younger
than this?
CONTENT DESCRIPTOR
ACMNA054 Recognise
and explain the
connection between
addition and
subtraction.
KEY IDEA
Doing and
undoing –
understanding
the process and
being able to
work backwards
ASSESSMENT
First Steps in Mathematics –
Number Course Book
Diagnostic Task –
Lollies/Candies/Sweets
INVESTIGATION
Display my number
– Using base ten
materials. Give
students a number
e.g. 256. Ask them
to use the material
to show how many
different ways you
can model the
number (e.g. 256
ones, 25 tens and 6
ones, 2 hundreds 1
ten and 15 ones
etc.)
Pre-ASSESS
ASSESSMENT
INVESTIGATION
Draw pictures to
match the
number
sentences
8–2=6
6+2=8
• Students can consistently
apply a given rule (addition and
subtraction of numbers to 10);
and describe the inverse
operation.
• Students can describe the rule
(e.g. -2; +10) by looking at the
relationship between numbers
in the recording table.
Use the function
machine as per
normal but do not
tell the students
the rule, only the
‘function machine
worker’. When the
students’ card is
outputted, the
students then need
to work out what
the rule is that was
applied to their
size of four-digit
numbers (R) (U)
[CCT]
• use the symbols
for ‘is less than’
and ‘is greater
than’ to show the
relationship
between two
numbers
STUDENT
JOURNAL
• apply an
understanding of
place value and
the role of zero to
read, write and
order numbers up
to four digits
• interpret fourdigit numbers used
in everyday
contexts (U)
STUDENT
JOURNAL
Write an addition
number fact on
the board such as
8 + 7 = 15. Ask a
student to tell you
what the
subtraction fact
would be reverse
of this addition
fact. For 8 + 7 =
15, the reverse
subtraction fact is
15 – 7 = 8.
RESOURCES
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Tiny - Hundreds, Tens
and Ones
Place Value Chart Thousands
Rubber bands to bundle
the tiny hundred
frames.
MAB materials –
thousands hundreds
tens ones
Digits 0-9
Place Value Arrows
FISH Kit
RESOURCES
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Function Machine –
Arrows add +1, +2 and
subtract 1,2
Numerals 1 - 100
Recording table and
rules
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number.
TOPIC
CONTENT DESCRIPTOR
KEY IDEA
Pre-ASSESS
ASSESSMENT
INVESTIGATION
ACMNA055 Recall
addition facts for singledigit numbers and
related subtraction
facts to develop
increasingly efficient
mental strategies for
computation.
A critical aspect of
mathematical
thinking is the
recognition that
knowing one
thing about a
number can
provide other
information about
that number.
Use 3 ten frames
and display 10
and 15.
Ask students to
record similarities
such as • they are
both less than
• they are both
more than
• You can say
both numbers
when you count
by
Ask students to
record
differencies
• 10 is often
shown in
counting books
but 15 is not
• 10 can be
shown by using
one ten frame
but 15 can not
• 10 is 1 more
than 9, but 15 is
• Students choose efficient
strategies for addition and
subtraction
• Students record mental
strategies, eg ‘I added 20 to 159
to get 179, then I added 3 more
to get 182.’or use an empty
number line [L]
Write the number
42 on the board
and tell children
that it is the
answer to some
number sentences.
Explain that they
are allowed to use
any of the
following
calculator keys: + = and any of the
digit keys to find
number sentences
that equal 42. They
record their
findings. Note if
children use + and
– in the same
number sentence
or if they use
combinations of
more than two
numbers, for
example,
12+20+10=42.
3.1.5
Addition
Strategies
TOPIC
3.1.6
Subtraction
Strategies
CONTENT DESCRIPTOR
KEY IDEA
Pre-ASSESS
ASSESSMENT
INVESTIGATION
ACMNA055 Recall
addition facts for singledigit numbers and
related subtraction
facts to develop
increasingly efficient
mental strategies for
computation
There are many
different ways to
add and subtract
numbers
Review of year 2
strategies
• identify and choose efficient
strategies for addition and
subtraction, including:
• the jump strategy, eg 23 + 35;
23 + 30 is 52, 53 + 5 = 58
• the split strategy, eg 23 + 35;
20 + 30 + 3 + 5 = 5
the
compensation strategy, eg 63 +
29; 63 + 30 is 93, subtract 1 to
In pairs, students
choose a two-digit
number without
repeating any digit
or using zero, for
example: 38. The
student reverses
the order of the
digits to create a
Continue with
examples to 20.
STUDENT
JOURNAL
Give the students
a two digit
addition number
story, for example:
38+27=
Ask students to
add the numbers
together, showing
the strategies and
the steps they
have used to get
their answer. Note
if students can
select an
appropriate
strategy and
explain how they
have applied the
strategy to the
number problem
STUDENT
JOURNAL
Students are given
a calculation such
as 160-24=136 and
are asked to create
a number of
problems where
this calculation
would be needed.
Students share and
RESOURCES
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Addition and Subtraction
strategy practice cards
Subitisation dot cards 110 and Numerals 1-100
Red tens frames
Bundling sticks
Place value arrows
Number line 1-100
Partitioning part-partwhole cards
Mini- whiteboard and
washable pens
Double ten frames
Playing cards
FISH Kit
RESOURCES
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Addition and Subtraction
strategy practice cards
Subitisation dot cards 110 and Numerals 1-100
Number line 1-100
Partitioning part-partwhole cards
Who has game subtraction of 9 from
5
TOPIC
3.1.7
Money
TOPIC
CONTENT DESCRIPTOR
KEY IDEA
ACMNA059 Represent
money values in
multiple ways and
count the change
required for simple
transactions to the
nearest five cents.
Numbers tell how
many or how
much
Pre-ASSESS
How many ways
can $1 be
represented?
Proficiency Strand:
Problem Solving –
modelling authentic
situations.
CONTENT DESCRIPTOR
KEY IDEA
Pre-ASSESS
obtain 92
• using patterns to extend
number facts, eg 500 – 200;
since 5 – 2 = 3, so 500 – 200 is
300
• bridging the decades, egg 34 +
26; 34 + 6 is 40, 40 + 20 is
changing the order of addends
to form multiples of 10, eg 16 +
8 = 4; add 16 to 4 first
Students are asked to subtract
9, 8 and 7 from a two digit
number, explaining the
strategies they use.
second number,
for example: 83.
The student
subtracts the
smaller number
from the larger and
records this as a
number sentence.
The answer is used
to start another
reversal
subtraction. Play
continues until
zero is reached.
Students discuss
strategies used
and any patterns
they have
observed.
ASSESSMENT
INVESTIGATION
• Change from $1 – ask the
student to select a Catalogue
items up to $1 and calculate the
change from $1 using the coin
strips.
• Four ways to show money: Ask
students to show four different
ways to make up to $15 using
notes and coins.
The total on the
cash register is
$25.75. What
combination of
notes and coins
could you give? List
some possible
combinations.
Present your
findings with
pictures.
ASSESSMENT
INVESTIGATION
discuss responses.
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STUDENT
JOURNAL
Catalogue buys:
Provide small
groups of students
with supermarket
catalogues that
display items that
cost under $10. In
pairs students cut
out and paste
items they can
buy for $20.
Students record
the quantities and
use calculators to
check their
calculations. More
able students
could work out the
change they would
receive from $20.
STUDENT
two-digit number
Hundreds Boards –
routine and non-routine
Mini- whiteboard and
washable pens
Counters
FISH Kit
RESOURCES
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Collection of play coins
and notes
Shop items: cereal
boxes, egg cartons,
empty plastic drink
bottles, yoghurt
containers.
Catalogue items up to $1
Catalogue items – mixed
dollar and cents.
A collection of
catalogues from
supermarkets and toy
shops.
Money to $1 for number
line
Coin Strips
RESOURCES
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ACMMGO61 Measure,
order and compare
objects using familiar
metric units of length,
mass and capacity.
Applying
appropriate
techniques, and
tools to
determine
measurement
Describe three
things that weigh
less than a shoe.
Tell how you
know they weigh
less than a shoe
3.1.8
Metric Units
TOPIC
CONTENT DESCRIPTOR
M-MG3. Tell time to
the minute and
investigate the
relationship between
units of time.
3.1.9
Time to
Minute
KEY IDEA
Time is about
repeating events
CONTENT DESCRIPTOR
3.1.10
Data
ACMSP068 Identify
questions or issues for
categorical variables.
Identify data sources
and plan methods of
KEY IDEA
Selecting and
using appropriate
statistical
methods to
analyze data
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Ask students to
estimate and
measure how
many arbitrary
units make a
metre, for
example: felt
pens,
paperclips,
hand spans,
unifix cubes.
Record the
estimate and
the actual
measure.
Repeat above
for capacity
and mass.
Pre-ASSESS
ASSESSMENT
INVESTIGATION
Recording events
which are
regularly
repeated
• Give each student a piece of
paper and black pen. Simply ask
them to “to draw a clock”. Later
discuss the clock with each
student (tell me about your
clock; how do clocks work? What
time does your clock show? etc.)
to gain further insights.
Annotate these for future
reference.
• Ask students to draw in where
the hour hand should be at
these times: 12:50; 4:25; 9:30;
8:00; 8:45
Problem – the
hands of a clock
make an angle that
is less than a
quarter of a turn.
What time might it
be?
Pre-ASSESS
ASSESSMENT
INVESTIGATION
Use the IDEAL tally chart to
collect data on another topic of
interest, for example: favourite
icecream or favourite game.
Provide a 10x10 grid to students
If two more
children came into
our class, how
might this change
our graph? Draw
Proficiency Strand:
Understanding – using
appropriate language to
communicate times
TOPIC
Observe students as they
participate in each section of
the Activity Process. Ask
students to journal their
understandings about
measurement from these
activities.
Note students’ understanding of
• Use of comparative
language
• Ability to estimate
objects that are 1m, 1L
and 1 kg .
• Using scales to check
predictions
• Accuracy when
measuring.
How could you
sort a group of
toys and make a
graph to show
how many toys
JOURNAL
Record all the
things that we
measure in
metres. Make a list
and add to it when
another suggestion
is made
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STUDENT
JOURNAL
Ask students to
record times
(analogue and
digital) on the
Individual
whiteboard clock :
6:00; 1:10; 3:30;
11:55; 7:40: 10:25
STUDENT
JOURNAL
Collect data about
topics of interest
to children, for
example: favourite
game, favourite
Metre ruler
Streamers
Balance scale
Kitchen scale
1kg mass – for example
1kg rice.
Measuring jug (1litre)
Empty grocery items –
1kg and 1 litre
Early Years FISH Kit
RESOURCES
• Class clock – analogue and
digital time:
http://www.idealresources.com.au/index.php
• Class clock with second
(sweep) hand or
http://www.time-fortime.com/swf/myclox.swf
Individual whiteboard clocks
and pen
RESOURCES
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10x10 floor grid
Paper squares to fit grid
squares
10x10 paper grid
FISH Kit
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data collection and
recording.
ACMSP069 Collect data,
organise into categories
and create displays
using lists, tables,
picture graphs and
simple column graphs,
with and without the
use of digital
technologies
ACMSP070 Interpret
and compare data
displays
are in different
groups?
and ask them to create a column
graph to display the
information. Ask questions
about the data: most popular,
least popular, difference
between, how many chose… etc.
the new column
graph using your
new data. If I child
left, how might it
change the graph?
icecream, and
favourite flavour
of corn chip.
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