Download ProgramPlanner maths stage 3

Program Planner: Stage 3
Term 1
Week 1
Year 5
Year 6
Strand: Number
Outcome: NS3.2
Strand: Number
Outcome: NS3.2
3-digit addition (page 2)
Addition of 4-digit numbers (page 2)
Link the vertical algorithm to a base 10 model.
Learning to trade in an addition sum
Demonstrate the processes involved in adding 4-digit
numbers.
Hundreds
Tens
1
+
Thou.
Ones
1
3
3
1
1
9
2
5
2
Hund.
1
4
+
Step 1
9 ones plus 3 ones equals 12 ones. Exchange 10 ones for
1 ten. Record 2 in the ones column.
1
5
Tens
Ones
1
8
6
2
8
3
7
7
4
2
3
Step 1
Add the ones column, 7 + 6 = 13. Trade the ten into the
tens column. Record 3 on the answer line in the ones
column.
Step 2
1 ten plus 3 tens plus 1 ten equals 5 tens. Record 5 in the
tens column.
Step 2
Add the tens column, 3 + 8 + 1 = 12. Trade the 10 tens to
the hundreds column. Record 2 on the answer line in the
tens column.
Step 3
1 hundred plus 1 hundred equals 2 hundreds. Record 2 in
the hundreds column.
Step 3
Add the hundreds column, 8 + 5 + 1 = 14. Trade the 10
hundreds into the thousands column. Record 4 on the
answer line in the hundreds column.
Step 4
Add the thousands column, 2 + 4 + 1 = 7. Record 7 on the
answer line in the thousands column.
Complete examples.
Round addends to the nearest 100 to estimate the total
before calculating the exact total.
Complete examples.
267 g
261 cm
425 mL
$7.85
304 g
37 cm
362 mL
$8.85
165 g
53 cm
37 mL
+ 14 g
+ 410 cm
+ 124 mL
Use own strategies to solve problems.
$0.86
+
$8.58
Solve problems.
Outcome: NS3.3
Outcome: NS3.3
Multiplication facts (page 3)
Multiplication strategies (page 3)
Complete multiplication facts for 4, 5, 6, 7, 8 and 9.
Complete a multiplication grid.
Write division facts from multiplication facts, e.g.
Strategies:
7  5 = 35 so 35  5 = 7 and 35  7 = 5

extend basic facts to 10s and 100s, e.g. 4  5 =  40  5
=  400  5 = 

to multiply by 5, multiply by 10 then halve, e.g.

double and double again to multiply by 4

double, double and double again to multiply by 8, e.g.
Complete a table to show money banked, e.g.
Monthly banking
Number of months
Ann
Bree
Cal
Guy
Lou
$9
$10
$8
$6
$4
8
7
7
9
24  5 becomes 24  10 = 240  ½ = 120
8
Total
23  4  Think 23  2 = 46  2 = 92
1
Strand: Space and Geometry
Outcome: SGS3.2a
Strand: Space and Geometry
Outcome: SGS3.2a
Polygons (page 4)
2D shapes (page 4)
Recognise that a polygon has 3 or more straight sides.
Identify shapes by name and record their properties, e.g.
Identify shapes by name and record their properties, e.g.
Shape Name
triangle

3 sides

3 acute angles

3 lines of symmetry
Sides Angles
trapezium 4
4
Identify the parallelograms among a set of shapes.
Draw examples of shapes, e.g. square, rectangle, triangle,
hexagon, octagon, pentagon, rhombus and trapezium.
Match description to shape, e.g.
A rhombus is a parallelogram with 4 equal sides and two sets
of matching angles.
Strand: Measurement
Outcome: MS3.1
Strand: Measurement
Outcome: MS3.1
The kilometre (page 5)
Kilometres (page 5)
Recognise that 1 km = 1000 m
Recognise that:
Use a trundle wheel to measure a distance of 1 km broken
into 10 lots of 100 m

1000 m = 1 kilometre

‘km’ is short for kilometre
Plot a 1 km cross-country course in the school grounds.

road distances are expressed in kilometres
Refer to a table of distances to calculate distances between
towns, e.g.
Refer to a map with distances marked (concentric circles) to
calculate distances, e.g.
Bega and Wollongong (446 km – 78 km)
Sydney–Camden = 60 km
Refer to a street directory to identify locations that are:
Convert metres into kilometres, e.g.

less than 1 km from school

about 1 km from school

Solve a problem based on average speed, e.g.
more than 1 km from school
4½ hrs @ 60 km/h
9154 m = 9.154 km
Strand: Patterns and Algebra
Strand: Patterns and Algebra
Strand: Chance and Data
Strand: Chance and Data
2
Week 2
Year 5
Year 6
Strand: Number
Outcome: NS3.2
Strand: Number
Outcome: NS3.2
Addition and subtraction strategies (page 6)
Addition and subtraction (page 6)
Split: 325 + 133
Use mental strategies to add pairs of numbers, e.g.
Think: (300 + 100) (20 + 30) (5 + 3)
67 + 28  Think 67 plus 30 minus 2
Bridge: 38 + 37 Think: 38 + 30 = 68 + 2 + 5
(97 – 2 = 95)
Rounding: 82 – 47 becomes 80  50
Round each addend to the nearest 100 to estimate the total,
e.g.
212 + 397  600
Use mental strategies to complete subtractions, e.g.
64  38  Think: 64  40 plus 2
(24 + 2 = 26)
Estimate and solve problems.
Outcome: NS3.4
Outcome: NS3.4
Thirds, sixths and twelfths (page 7)
Fractions and decimals (page 7)
Identify and use terms ‘numerator’ and ‘denominator’.
Shade hundredths grids to represent fractions of 100 and use
decimals to label the grids.
Demonstrate equivalence between fractions, decimals and
percentages.
Use common fractions to describe diagrams.
common
fraction
Shade parts of a shape to represent a fraction.
decimal
%
0.5
50%
Identify fractions of a group.
Identify fractions on number lines.
Use a calculator to convert fractions to decimals, e.g.
= 1  4 = 0.25
Strand: Space and Geometry
Outcome: SGS3.2b
Strand: Space and Geometry
Outcome: SGS3.2b
Angles (page 8)
Measuring angles (page 8)
Recognise and classify angles.
Recognise 6 types of angles:

right angle: is 90° (a square corner)

an acute angle is between 0° and 90°

obtuse angle: is larger than a right angle; greater than
90°

a right angle is 90°


an obtuse angle is between 90° and 180°
acute angle: is smaller than a right angle; less than 90°


a straight angle is 180°
straight angle: can be made from 2 right angles; is 180°


a reflex angle is between 180° and 360°
reflex angle: is larger than a straight angle; greater than
180°

a revolution (full turn) is 360°
Measure angles shown on protractors.
Label angles as: right, obtuse, acute, reflex or straight.
Use a protractor to measure angles.
Use clues to identify shapes. e.g.
I have 1 obtuse angle, 1 acute angle and 2 right angles.
3
Strand: Measurement
Outcome: MS3.2
Strand: Measurement
Outcome: MS3.2
Area (page 9)
Square centimetres and square metres (page 9)
Find the area of a credit card by counting the number of
square centimetres it covers.
Use the area formula to calculate the area of shapes.
Recognise and apply the area formula to calculate the area of
rectangles.
Break shapes into rectangles in order to work out their area,
e.g.
Given a movie ticket calculate the area of:

the large portion

the small portion

the entire ticket
A = (4 cm  3 cm) + (3 cm  2 cm)
= 12 cm2 + 6 cm2

= 18 cm2
Strand: Patterns and Algebra
Strand: Patterns and Algebra
Strand: Chance and Data
Strand: Chance and Data
4
Week 3
Year 5
Year 6
Strand: Number
Outcome: NS3.2
Strand: Number
Outcome: NS3.2
3-digit subtraction (page 10)
4-digit subtraction (page 10)
Link the vertical algorithm to a base 10 model.
Model the subtraction process
Trading in subtraction
Hundreds
–
3
1
1
9
1
2
4
4
Tens
7
8
Ones
1
6
2
9
5
7
3
5
2
9
Step 1
7 from 6 can’t be done. Trade a 10 from the tens
column.
There are now 7 tens in the tens column and 16 ones in
the ones column. 16  7 = 9.
Record 9 on the answer line in the ones column.
Step 1
9 ones from 3 ones can’t be done.
Trade a ten from the tens column to the ones column to
make 13 ones. 4 tens becomes 3 tens. 9 ones from
13 ones equals 4 ones.
Step 2
Subtract 1 ten from 3 tens to give 2 tens.
Step 2
5 tens from 7 tens = 2 tens.
Record 2 on the answer line in the tens column.
Step 3
Subtract 1 hundred from 2 hundreds to give 1 hundred.
Step 3
9 hundreds from 4 hundreds can’t be done. Trade 1000
from the thousands column. There are now 5 thousands
in the thousands column and 14 hundreds in the
hundreds column. 14 – 9 = 5.
Record 5 on the answer line in the hundreds column.
Step 4
2 thousands from 5 thousands = 3 thousands.
Record 3 on the answer line in the thousands column.
Complete examples.
no trading
1
6
1
4
Hund.
5
Ones
3
2
–
Thou.
Tens
trading in 1s
Complete examples.
trading in 10s
879
852
648
– 257
– 434
– 263
Use a combination of addition and subtraction to complete
algorithms with missing numbers.
587
– 259
Use subtraction to crack a code.
3517
Outcome: NS3.3
Outcome: NS3.3
3-digit subtraction (page 11)
3-digit division (page 11)
Complete division facts for 3, 5, 6, 7 and 8.
Model the division process.
Record solutions to divisions with remainders, e.g.
25  4 = 6 r 1
Show how a bag of 33 marbles can be shared.
33  2 = ___ r ___
Share out the
hundreds, with
each school
getting 1.
33  4 = ___ r ___
33  6 = ___ r ___
33  5 = ___ r ___
33  8 = ___ r ___
Trade the 2
hundreds left for
20 tens. Now
share the 26 tens.
Each school
gets 5.
Trade the 1 ten left
over for 10 ones.
Now share the 17
ones. Each school
gets 3 and there is a
remainder of 2.
Investigate how many divisions produce a quotient of 6.
Complete examples.
Solve problems using addition, division and knowledge of
averages.
Create a set of division algorithms that have a remainder of 2.
5
Strand: Chance and Data
Outcome: DS3.1
Strand: Chance and Data
Outcome: DS3.1
Picture graphs (page 12)
Picture graphs (page 12)
Recognise that:
Read and interpret a picture graph whereby 1 computer
symbol represents 10 children.

symbols can represent more than one item

a key shows how many items each symbol represents
Answer questions, e.g. How many more chose Internet over
study?
Read and interpret picture graphs where:

one symbol represents 10 items

one symbol represents 4 items

Create a picture graph to represent tallied data.
Answer questions about graphed data.
Explain how a survey could be made more reflective of the
NSW population.
symbols are used
Strand: Measurement
Outcome: MS3.2
Strand: Measurement
Outcome: MS3.3
Cubic centimetres (page 13)
The cubic centimetre (page 13)
Given a set of 3D shapes, select those that are suitable for
packing and stacking.
Recognise that:

a cubic centimetre is a standard unit for measuring
volume and capacity
Recognise that:

a cubic centimetre is a standard unit for measuring
volume and capacity

a cubic centimetre is a cube that has 1-cm sides, e.g.
a base 10 one

a cubic centimetre is a cube that has 1-cm sides, e.g. a
base 10 one

cm3 is short for cubic centimetre

cm3 is short for cubic centimetre
Build rectangular prisms with centicubes and record their
length, breadth, height and volume in a table.
Given a model’s base, calculate its height so that the shape
has a specific volume.
Build rectangular prisms with centicubes and record the
volume of each shape.
Challenge: Build and sketch a shape with a volume of 24 cm 3
Strand: Patterns and Algebra
Strand: Patterns and Algebra
Strand: Space and Geometry
Strand: Space and Geometry
6
Week 4
Year 5
Year 6
Strand: Number
Outcome: NS3.2
Strand: Number
Outcome: NS3.2
Addition and subtraction strategies (page 14)
4-digit addition (page 14)
Extending: 7 + 8 = 15, so 700 + 800 = 1500
Refer to a chart to calculate the length of journeys, e.g.
Darwin to Gove to Cairns
Jump: 38 + 43
Think: 38 + 40 + 3 = 81
(647 km + 1091 km = 1738 km)
Open-ended investigation to show any flight within Australia
and the distance travelled.
Compensation: 35 + 48
Think: 35 + 50 minus 2
Outcome: NS3.1
Outcome: NS3.1
Place value to 5 digits (page 15)
Place value (page 15)
Use a place-value chart to show how numbers are
structured, e.g.
Use an abacus to represent 6-digit numbers.
Number
Tth
Th
H
T
O
3
6
7
367
Study a place-value chart to see that numbers are read in
groups of hundreds, tens and ones.
Millions
1454
H
T
Thousands
Ones
O
H
T
O
H
T
2
0
6
3
4
1
7
4
0
3
2
8
O
25 309
206 341
87 936
257 403 280
Order numbers from smallest to largest, e.g.
Place numbers up to 8-digits on a place-value chart.
2
5
0
12 335, 12 553, 21 335, 21 553
Make largest/smallest number using 5 digits.
Write numbers in words, e.g. 25 327
Strand: Space and Geometry
Outcome: SGS3.3
Strand: Space and Geometry
Outcome: SGS3.3
Coordinates/compass points (page 16)
Compass points (page 16)
Understand that coordinates:
Read and interpret a map:

show where two lines meet


are read across then up
use compass points to explain directions from one point
to another

calculate distance and direction between points
Give coordinates for places on a map, e.g. Darwin = E7
Create a plan view of the classroom and mark compass
points to identify location of objects, e.g. blackboard = NE.
Recognise cardinal and intercardinal compass points.
Cardinal points: N, E, W, S.
Intercardinal points: NE, SE, SW, NW.
Use compass points to explain directions, e.g.
From Darwin to Bourke is SE.
Follow directions and apply a scale to plot a course on a
map, e.g. Start at Waugh and head north 24 km.
Strand: Measurement
Outcome: MS3.4
Strand: Measurement
Outcome: MS3.4
Mass (page 17)
Mass (page 17)
Estimate and then measure the mass of objects in grams.
Use scales to measure the mass in grams of everyday
objects, e.g. glue-stick = 40 g
Use bathroom scales (kg) to measure and record the mass
of 4 people.
Balance 10 grams with quantities of pencils, paper clips,
coins and centicubes.
Problem: Calculate how many items can be packed into a
box with a capacity of 3 kg, e.g.

250 g glue pots

750 g books

150 g calculator

50 g sticky tape
Calculate how many smaller items are needed to balance
larger masses, e.g.
 600 g calculators = 12 kg
 150 g tea packets = 3 kg
Match objects to suitable measuring devices,
e.g. truck  weighbridge.
Strand: Patterns and Algebra
Strand: Patterns and Algebra
Strand: Chance and Data
Strand: Chance and Data
7
Week 5
Year 5
Year 6
Strand: Number
Outcome: NS3.3
Strand: Number
Outcome: NS3.3
Multiplication strategies (page 18)
3-digit × 1-digit multiplication (page 18)
Recognise that basic facts can be extended, e.g.

3 × 5 = 15, so 3 × 50 = 150

4 × 6 = 24, so 40 × 60 = 2400
Thou.
Hund
Tens Ones
1
1
6
3
5
×
Use mental strategies to solve multiplications, e.g. 6 CDs at
$30 each.
1
3
9
0
5
Model and discuss the process.
Complete examples.
Round to the nearest 10 or 100 to estimate the product, e.g.
3 × 49  Think 3 × 50 = 150
Use multiplication as part of problem solving, e.g.
Maria bought a new stereo. How much did it cost her if she
paid a $100 deposit and made 8 payments of $129?
Outcome: WMS3.2
Outcome: NS3.4
Problem solving (page 19)
Decimals, percentages and fractions (page 19)
Discuss and model problem-solving strategies, e.g.
Express:
What operation will I use? Should I estimate?

decimals as percentages, e.g. 0.09 = 9%
Solve problems:

percentages as decimals, e.g. 125% = 1.25

use own strategies

fractions as decimals and percentages,

check how others solved it

check answer using an alternative strategy
e.g.
= 0.25 and 25%
From a set of fractions, decimals and percentages identify the
largest, e.g.
, 0.89, 90%
Problem solving
Optional Year 6 Student Book Blackline Master, to be used
with page 19 of the Year 5 Student Book.
Solve problems using own strategies.
Share the cost of a restaurant bill two different ways.
Strand: Chance and Data
Outcome: NS3.5
Strand: Chance and Data
Outcome: NS3.5
Chance experiments (page 20)
Chance predictions (page 20)
Investigate probability:

predict the most likely score when two dice are rolled
Create a table using tally marks to show the number and
colour of counters in a bag.

tally results
Red Blue Green Pink

identify most frequent score

explain why 7 has a greater chance of occurring than 12
IIII
identify the most likely colour to be drawn out first

describe the likelihood of one colour being drawn out first,
e.g. 50/50 or even

identify the least likely colour to be drawn out first

decide whether one colour is more or less likely than
another to be drawn first
IIII
Yellow
IIII III II
Make predictions about other bags of counters based on the
data in the table, e.g.
Given a bag of coloured marbles:

I
Altogether 20 bags of counters were filled. How many pink
counters do you think there were?
Given a sample of 10, make predictions about the composition
of a group of 100, e.g.
3 out of 10 are red, therefore, 30 out of 100 should be red.
8
Strand: Space and Geometry
Outcome: SGS3.1
Strand: Space and Geometry
Outcome: SGS3.1
Prisms and pyramids (page 21)
3D objects (page 21)
Review properties of prisms and pyramids.
Match 3D objects to their name and net, e.g.
Prisms have two bases that are the same shape and size. All
other faces on a prism are rectangular. Prisms are named
from their bases.
triangular pyramid


Pyramids have only one base with all other faces being
triangles. The triangular faces meet at a common vertex.
Pyramids are named from their bases.
Match illustrations to names, e.g.

rectangular prism

Classify objects by stating the number of faces, edges and
vertices, e.g.
rectangular pyramid

triangular pyramid = 4 faces 6 edges 4 vertices
square pyramid

triangular pyramid

cube
Strand: Patterns and Algebra
Strand: Patterns and Algebra
Strand: Measurement
Strand: Measurement
9
Week 6
Year 5
Year 6
Strand: Number
Outcome: NS3.3
Strand: Number
Outcome: NS3.3
2-digit division (page 22)
4-digit division (page 22)
Recognise that 12 ÷ 3 = 4 is the same as
Model the division process.
Solve basic division facts recorded in algorithmic form, e.g.
Share 26 hundreds among 5. Each paddock gets 5 hundreds.
Solve division problems that have remainders, e.g.
Solve a transport problem, e.g.
Trade the 1 hundred over for 10 tens. Now share the 17 tens.
Each paddock gets 3 tens.
72 children are being transported to a carnival. How many
trips would a car capable of taking

3 people make?

4 people make?

5 people make?

12 people make?
Trade the 2 tens left over for 20 ones. Now share the 23 ones.
Each paddock gets 4 ones. There is a remainder of 3.
Complete examples.
Read and interpret a map to calculate the average distance
between train stations.
Investigate to find a number that can be divided by 2, 4 and 8.
Strand: Patterns and Algebra
Outcome: PAS3.1a
Strand: Patterns and Algebra
Outcome: PAS3.1a
Number patterns (page 23)
Number patterns (page 23)
Complete sets of counting patterns, e.g.
Solve ‘rate’ type problems by completing tables to show
+ 5: 15, 20, 25, 30 . . . . . . . . .
relationships between numbers, e.g.
× 2: 3, 6, 12, 24 . . . . . . . . .
A car travels 13 km per litre of petrol.
– 7: 198, 191, 184, 177 . . . . . . .
litres
1
2
3
Write a rule to describe a pattern, e.g.
km
13
26
39
3.5, 4, 4.5, 5, 5.5  Add 0.5
4
5
6
Use the table to make predictions, e.g.
Continue a pattern of square numbers on dot paper and as
numbers, e.g.
How far would the car travel on 15 litres of petrol?
Extend the sequence of square numbers to the 12th term.
Strand: Chance and Data
Outcome: DS3.1
Strand: Chance and Data
Outcome: DS3.1
Column graphs (page 24)
Column graphs (page 24)
Make and interpret a column graph based on data presented
in a table, e.g. millimetres of rain per month over a year.
Read and interpret a graph to identify features such as:

city with highest maximum temperature
Represent temperature data on a column graph e.g.

city with lowest minimum temperature
Obtain a weather map of Australia showing the current
temperatures of capital cities. Construct a column graph
representing the temperatures of the capital cities.

city with greatest difference between minimum and
maximum temperatures

average maximum temperatures of Darwin, Sydney and
Melbourne
10
Strand: Measurement
Outcome: MS3.5
Strand: Measurement
Outcome: MS3.5
am and pm time (page 25)
24-hour time (page 25)
Recognise that am is short for ante meridiem (before midday).
Express time on:
Recognise that pm is short for post meridiem (after midday).

analog clocks
Convert analog times to digital.

24-hr digital clocks
Order times from earliest to latest, e.g.
Convert measurements into other units, e.g.
3:00 pm; 3:00 am; 6:00 pm

2 days = 48 hours
Calculate times, e.g.

5 minutes = 300 seconds
25 minutes after 3:10 am
Strand: Space and Geometry
Strand: Space and Geometry
11
Week 7
Year 5
Year 6
Strand: Number
Outcome: NS3.3
Strand: Number
Outcome: NS3.3
2-digit × 1-digit multiplication (page 26)
Multiplication strategies (page 26)
H
T
1
3
×

O
5
of 24  Think 6 × 4 = 24
3
1
0
use multiplication to find a unit fraction, e.g.

5
extend multiplication facts, e.g.
40 × 60 = 4 tens × 6 tens = 24 hundreds = 2400
Model and discuss the process of multiplication.

Complete examples.
multiply the front first, e.g.
35 × 3  Think 3 × 30 (90) + 3 × 5 (15) = 105
Use multiplication as a problem-solving strategy.
Solve mini-problems.
Outcome: NS3.4
Outcome: NS3.4
Fractions of a collection (page 27)
Unit fractions of a collection (page 27)
Recognise that fractions can name part of a group, e.g.
Recognise that:

fractions can name part of a group, e.g.

multiplication and division can be used to find unit
fractions, e.g.
Find unit fractions of numbers, e.g.
Use an array to find fractions of a group of 48, e.g.

Complete examples.
Solve unit fraction problems.
Open-ended investigation to find unit fractions that produce 6
as the answer.
Use knowledge of unit fractions to solve problems, e.g.
of the 96 seats in the restaurant . . .
Use knowledge of unit fractions to solve fractions with
numerators greater than 1, e.g.
If
of a group is worth 5 what would
of the group be
worth?
Strand: Space and Geometry
Outcome: SGS3.2b
Strand: Space and Geometry
Outcome: SGS3.2b
Measuring angles (page 28)
Angles (page 28)
Observe that a 180° protractor can be read from both ends.
Use a protractor to construct:
Label a protractor to show its supplementary angles.

acute angles
Name angle types and size of angles depicted in illustrations,
e.g.

right angles

obtuse angles
obtuse 120°
Use a protractor to measure the size of various angles.
12
Strand: Measurement
Outcome: MS3.1
Strand: Measurement
Outcome: MS3.1
Metres of kilometres (page 29)
Millimetres and centimetres (page 29)
Divide metres by 1000 to convert to kilometres, e.g.
Read a ruler calibrated in millimetres.
1525 m + 1000 m = 1.525 km
Measure lines and record in centimetres and millimetres.
Multiply kilometres by 1000 to convert to metres, e.g.
Measure and record the perimeter of shapes in millimetres.
3.505 km × 1000 = 3505 m
Use 5-mm dot paper to draw two passport-size photos:
Refer to a map with distances marked in metres to:
40 mm × 50 mm

calculate distances from town to town in metres
45 mm × 60 mm

convert metres to kilometres to identify a journey longer
than 13 km
Strand: Patterns and Algebra
Strand: Patterns and Algebra
Strand: Chance and Data
Strand: Chance and Data
13
Week 8
Year 5
Year 6
Strand: Number
Outcome: NS3.2
Strand: Number
Outcome: NS3.2
4-digit addition with trading (page 30)
3-, 4- and 5-digit addition (page 30)
Demonstrate the processes involved in adding 4-digit
numbers.
Find totals for various quantities, e.g.
kilometres
Learning to trade in an addition sum
T
1
+
H
T
218
45667
16508
415
O
1
3
4
3
3
5
9
1
9
9
3
5
2
Use addition or subtraction to find missing numbers.
Step 1
9 ones plus 3 ones equals 12 ones. Exchange 10 ones
for 1 ten. Record 2 in the ones column.
+
3562
2 73
322
Step 2
1 ten plus 3 tens plus 1 ten equals 5 tens. Record 5 in the
tens column.
Use a reverse operation to check solutions, e.g.
5899 
– 3276
Step 3
9 hundreds plus 4 hundreds equals 13 hundreds.
Exchange 10 hundreds for 1 thousand. Record 3 in the
hundreds column.
2623
+ 3276
2623
5899
Use addition as a problem-solving strategy.
Step 4
5 thousands plus 3 thousands plus 1 thousand equals
9 thousands.
Complete examples.
no trading
trading in 1s
trading in 10s and 1s
3242
+ 5447
3064
+ 2306
3560
+ 2074
Explain the error:
5544
4733
+ 9277
Strand: Patterns and Algebra
Outcome: PAS3.1b
Strand: Patterns and Algebra
Outcome: PAS3.1b
Missing numbers (page 31)
Number sentences (page 31)
Discuss how reverse operations can help to find missing
numbers, e.g.
Complete equations by substituting values for missing
numbers, e.g.
25 –  = 13, therefore 13 +  = 25
3 ×  + 6 = 30
Find the missing number in equations, e.g.
3, 4, 5 and 6
3 × 5 +  = 19
Given the value of a symbol to solve equations, e.g.
Use strategies such as ‘trial and error’ to balance equations,
e.g.
If ∆ = 7, solve ∆ +  = 15
99 ÷ 3 = (57 – 24)
Use strategies such as trial and error to solve an equation,
e.g.

Use inverse operations to check whether statements are
correct, e.g.
Substitute numbers
120 ÷ 6 = 20 inverse 20 × 6 = 120
Create and solve own equationS.
14
Strand: Space and Geometry
Outcome: SGS3.1
Strand: Space and Geometry
Outcome: SGS3.1
Prisms and pyramids (page 32)
Drawing 3D objects (page 32)
Demonstrate procedure for drawing prisms and pyramids.
Demonstrate how dotted lines are used to show hidden faces,
edges and vertices.
Make tracings of prisms, cylinders and pyramids.
Add dotted lines to drawings of prisms, cylinders and
pyramids.
Add dotted lines to drawings to show hidden faces, edges
and vertices.
Make sketches of prisms, cylinders and pyramids.
Complete isometric drawings of rectangular prisms on
isometric dot paper.
Make sketches of prisms and pyramids.
Strand: Chance and Data
Outcome: DS3.1
Strand: Chance and Data
Outcome: DS3.1
Picture graphs (page 33)
Picture graphs (page 33)
Read and interpret a picture graph whereby 1 car symbol
represents 100 cars.
Read and interpret a graph whereby 1 picture = 4 children.
Select another scale that could be substituted for one
provided.
How many rode a bike to school?
Answer questions, e.g.
Given a list showing ‘pocket money’ create:
Design a picture graph to represent data presented on
a column graph.
Strand: Measurement

a grouped tally to represent survey data.

a picture graph to represent the data
Amounts
Tally
$0 to $4.99
IIII
$5 to $9.99
IIII IIII I
$10 to $14.99
IIII II
$15 to $19.99
IIII II
$20 to $25
IIII
Strand: Measurement
15
Week 9
Year 5
Year 6
Strand: Number
Outcome: NS3.3
Strand: Number
Outcome: NS3.3
Division strategies (page 34)
Division with fractional remainders (page 34)

Rounding: Round the dividend to the nearest 10 or 100,
e.g. 492 + 5 ≈ 500  5 = 100
Recognise that remainders can be expressed as a fraction of
the divisor.

Extending: 63  7 = 9, so 630  7 = 90
Complete examples.

Halve and halve again to divide by 4.
Use division to:

Halve, halve and halve again to divide by 8.

solve problems

Create own strategies.

complete a number cross
Outcome: NS3.4
Outcome: NS3.4
Equivalent thirds, sixths and twelfths (page 35)
Improper fractions and mixed numerals (page 35)
Equivalent fractions
Recognise that:

improper fractions have numerators larger than their
denominators, e.g.

mixed numerals consist of a whole number and a fraction,
e.g.
Use improper fractions and mixed numerals to describe
models, e.g.
Discuss, model and observe the equivalence between
fractions with denominators of 2, 4, 3, 6 and 12
Use number lines to show equivalence between mixed
numerals and improper fractions.
Supply missing numerator in pairs of equivalent fractions.
Convert improper fractions into mixed numerals.
Use the < less than and > greater than symbols to compare
fractions, e.g.
Solve a sharing problem, e.g.
36 footy cards to be shared like this:

to Tom

to Millie

to Jessica
Strand: Space and Geometry
Outcome: SGS3.1
Strand: Space and Geometry
Outcome: SGS3.3
Classifying 3D objects (page 36)
Coordinates (page 36)
Recognise that the properties used to classify 3D shapes are
its faces, edges and vertices.
Faces: the flat surfaces that make up a 3D object. A cube
has 6.
Refer to the plan of a theatre to:

give the coordinates of pupils’ seats, e.g. Tom = 13J

add items to the plan, e.g. a  at coordinates 17M
Top, front and side views
Edges: where two faces meet or intersect. Edges can be
straight or curved.
Optional Year 6 Student Book Blackline Master, to be used
with page 36 of the Year 5 Student Book.
Vertex: where 2 or more lines meet to form an angle or a
corner. The plural of vertex is vertices.
Build 3D models given the top, front and side views of the
model.
Use the words ‘face’, ‘edge’ and ‘vertex’ to label shapes.
Record the properties of 3D shapes on a chart, e.g.
Sketch the 3D shape built from the three views.
Given pictures of various prisms and pyramids, record their
names, and count the number of faces, edges and vertices on
each shape.
16
Strand: Chance and Data
Outcome: DS3.1
Strand: Chance and Data
Outcome: DS3.1
Column graphs (page 37)
Chance and column graphs (page 37)
Investigate the most common vowel in a paragraph:
Test a conjecture that:

read a paragraph from any source
Six will be the most frequent score when 3 dice are rolled.

make a table to tally the number of times each vowel
appears

make own prediction

roll 3 dice 60 times
present the tallied data as a column graph

record and tally results

display data on a column graph

identify score with highest frequency

Read, interpret and present tabled data as a column graph.
Explain why a score such as 11 is more likely than 3.
Use knowledge of the probability scale of 0 to 1 to decide
whether statements are true or false, e.g. The chance of
rolling an even number is about 0.5  True.
Strand: Patterns and Algebra
Strand: Patterns and Algebra
Strand: Measurement
Strand: Measurement
17
Program Planner: Stage 3
Term 2
Week 1
Year 5
Year 6
Strand: Number
Outcome: NS3.2
Strand: Patterns and Algebra
Outcome: PAS3.1a
4-digit subtraction (page 40)
Geometric patterns (page 40)
Demonstrate the processes involved when carrying out 4-digit
subtractions.

create a pattern of hexagons, e.g.

use a table to record data about the pattern of hexagons,
e.g.
Learning to trade in subtraction
T
5
6
–
H
1
2
T
4
5
O
1
3
2
4
2
4
3
8
2
9
Step 1
4 ones from 3 ones can’t be done. Trade a ten from the
tens column to the ones column to make 13 ones. 5 tens
becomes 4 tens. 4 ones from 13 ones equals 9 ones.
hexagons
1
2
sides
6
12
3
4
5

write a rule to describe the pattern

predict how many sides would be on 12 hexagons

repeat for heptagons, octagons and nonagons
6
Complete similar tables to describe the number of sides for
sequences of pentagons, decagons, dodecagons and
icosahedrons.
Step 2
2 tens from 4 tens equals 2 tens.
Step 3
4 hundreds from 2 hundreds can’t be done. Trade a
thousand from the thousands column to make 12
hundreds. 6 thousands becomes 5 thousands. 4 hundreds
from 12 hundreds equals 8 hundreds.
Optional Year 6 Student Book Blackline Master, to be used
with page 40 of the Year 5 Student Book.
Step 4
2 thousands from 5 thousands equals 3 thousands.
Complete subtraction of 4-digit numbers.
4-digit subtraction
Complete examples.
Calculate the difference in population between towns.
Trading in 1s
Create own algorithm to calculate difference in population.
8933
– 5325
Use own strategies to solve a problem.
Trading in 10s or 1s
8623
– 3464
Use distances provided to calculate the distance between
cities such as Perth and Melbourne, e.g.
3 9 6 7 km
–
8 6 9 km
Strand: Patterns and Algebra
Outcome: NS3.4 and PAS3.1a
Strand: Number
Outcome: NS3.3
Prime and composite numbers (page 41)
Prime and composite numbers (page 41)

Prime numbers only have themselves and 1 as factors.
Understand that:

Composite numbers have more than 2 factors.

prime numbers only have themselves and 1 as factors

composite numbers have more than two factors
List all factors for numbers and identify them as either prime or
composite, e.g.
8 has factors {1, 2, 4, 8} = composite
Apply the ‘rules of divisibility’ to classify numbers as either
prime or composite, e.g.
Explain whether statements are correct or incorrect, e.g.
54 = composite, factors are {1, 2, 3, 6, 9, 18, 27, 54}
All odd numbers are prime numbers.
71 = prime.
Identify numbers that can be classed as ‘square’ and ‘oblong’
numbers, e.g.
Square
Oblong
18
Strand: Space and Geometry
Outcome: SGS3.2a
Strand: Space and Geometry
Outcome: SGS3.2a
Triangles (page 42)
Triangles (page 42)
Recognise that triangles:
Identify properties of triangles:

have 3 sides

equilateral

have 3 angles

scalene

the sum of the angles is 180°

isosceles

right-angle
Triangles can be classified as:
Use a protractor to measure angles in triangles and then
classify each triangle.
Calculate the missing angle in triangles.
Investigate the properties of each type of triangle, e.g.
Which triangle has all sides of equal length?
Identify right-angled triangles.
Sketch examples of each type of triangle.
Strand: Measurement
Outcome: MS3.2
Strand: Measurement
Outcome: MS3.2
Square centimetres (page 43)
Area of triangles (page 43)
Use the area formula to work out the area of rectangles, e.g.
Strategy 1

convert the triangle into a rectangle

calculate the rectangle’s area then halve to give the
triangle’s area
Strategy 2
Use 1-cm grid paper to construct rectangles that have an area
of 24 cm2.

formula: Area =
base × perpendicular height
Establish that area and perimeter are not related by
investigating a statement, e.g.
All shapes with an area of 12 cm2 have a perimeter of 16 cm.
Strand: Chance and Data
Strand: Chance and Data
19
Week 2
Year 5
Year 6
Strand: Number
Outcome: NS3.3
Strand: Number
Outcome: NS3.4
2-digit division (page 44)
Multiplying fractions (page 44)
Model the contracted form of division.
Recognise repeated addition as a strategy to multiply
fractions, e.g.
Mr Cook had 75 stamps to share among his 5 children.
75 shared
among 5
Share out the
tens with each
person getting 1.
Trade the 2 tens left
for 20 ones. Now
share the 25 among 5.
Use repeated addition to multiply fractions expressing
answers as improper fractions and mixed numerals.
Complete examples.
Use own strategies to solve problems.
Write division facts from multiplication facts, e.g.
Division
6 × 4 = 24  24  4 = 6 or 24  6 = 4
Use multiplication and division as problem-solving strategies.
Optional Year 6 Student Book Blackline Master, to be used
with page 44 of the Year 5 Student Book.
Complete 4-digit by 1-digit divisions.
Use multiplication to check answers to divisions.
Complete divisions, recording the remainder as a fraction.
Use rounding as a strategy to estimate quotients, when
dividing by 10 and 100.
Outcome: NS3.4
Outcome: NS3.4
Two-place decimals (page 45)
Decimals to thousandths (page 45)
Use a decimal place-value chart to model and record
decimals.
Model a 7-digit number with decimals to 3 places.
Place decimals in ascending order, e.g.
0.43, 2.57, 0.28, 4.35, 2.50, 8.22, 4.45
Use decimal notation to convert centimetres to metres, e.g.
127 cm = 1.27 m
From a set of heights, name the tallest and shortest. Explain
why 1.90 m is greater than 1.09 m.
State the place value of digits within a number, e.g.
77.498
9 = hundredths
Express fractions and mixed numbers as decimals, e.g.
Express decimals as fractions or mixed numbers.
Place decimals in order from smallest to largest, e.g.
0.65, 0.87, 0.36, 0.75
20
Strand: Chance and Data
Outcome: NS3.5
Strand: Chance and Data
Outcome: NS3.5
Chance—scale (page 46)
Chance from zero to one (page 46)
Chance can be recorded on a scale from 0 to 1.

Events that are certain to happen are given the probability
of 1.

Events that will never happen are given the probability of
0.

Events that could happen are rated between 0 and 1.
0 describes an event that is impossible to happen.
1 describes an event that is certain to happen.
0.5 describes two events with an equal chance of happening.
All other points on the scale are given a numerical value
between 0 and 1.
Rate the likelihood of events happening on a scale of 0 to 1,
e.g.
Match ‘chance’ words to a chance number line, e.g.
A
Impossible
B
Unlikely
C
Even
Chance
D
Unlikely
E
Certain
A person has blue eyes.
Describe events to match probability ratings, e.g. 0.3
Rate the likelihood of one colour being the winning colour on
various spinning wheels.
Use the scale 0 to 1 to rate the likelihood of events happening,
e.g.
It will rain today.  0.1
I’ll watch TV today. 0.8
List events that could happen tomorrow and rate their
probability.
Strand: Space and Geometry
Outcome: SGS3.3
Strand: Space and Geometry
Outcome: SGS3.3
Using a scale (page 47)
Mapping (page 47)
Study a conventional scale as seen in maps and atlases.
Read and interpret a map and its scale to:
Apply a scale to work out the distance being represented by
various lines.

give the compass direction from point to point, e.g. from
pirate to ship  north

plot a path on the map, e.g. north 200 m, east 500 m

write a set of directions to describe a path
Read and interpret a map and its scale to determine distance,
e.g. 1 cm = 20 km
_____________
= 80 km
Strand: Patterns and Algebra
Strand: Patterns and Algebra
Strand: Measurement
Strand: Measurement
21
Week 3
Year 5
Year 6
Strand: Number
Outcome: NS3.2
Strand: Number
Outcome: NS3.2
4-digit addition (page 48)
Adding decimals and money (page 48)
Complete examples with trading, e.g.
Recognise that the decimal point must be kept in a straight
line.
3429
Complete examples, e.g.
+ 4056
$476.92
354.74
Given a map of NSW with distances, calculate the length of
journeys, e.g. Wollongong to Port Macquarie.
4.08
Investigate to find return trips that cover certain distances, e.g.
between 450 and 600 km
Given a set of prices for various items, calculate totals for
different purchases.
Create word problems to match operations, e.g.
$3.24 + $3.75 + $3.06
Strand: Patterns and Algebra
Outcome: NS3.1
Strand: Patterns and Algebra
Outcome: NS3.1
Roman numerals (page 49)
Roman numerals (page 49)
Investigate how Roman numerals are structured.
Investigate how Roman numerals are structured.
Consult a table to convert numbers into Roman numerals, e.g.
Consult a table to convert numbers into Roman numerals, e.g.
33 = XXXIII and 365 = CCCLXV
2 181 = MMCLXXXI
Complete Roman numeral magic squares.
Convert the year landmark buildings were built into Roman
numerals, e.g.
Sydney Opera House, 1973 = MCMLXXIII
Strand: Chance and Data
Outcome: DS3.1
Strand: Chance and Data
Outcome: DS3.1
Line graphs (page 50)
Line graphs (page 50)
Understand that meaning can be attached to any point along
the line of a line graph.
Read and interpret a line graph, e.g.
Express data presented in a table as a line graph, e.g.
L
6
12
18
24
30
36
42
Km
50
100
150
200
250
300
350
How long was their stop?
Given three line graphs, select the one that accurately
represents the data in a table.
Interpret the line graph, e.g.
How many litres would the car use on a 400 kilometre trip?
Represent data about time and distance on a line graph.
Make meaningful judgements about:

data lying on the line

data beyond the line, that is, if the line graph was to be
extended to a point not included in the table of presented
data
22
Strand: Measurement
Outcome: MS3.3
Strand: Measurement
Outcome: MS3.3
Cubic centimetres (page 51)
Volume (page 51)
Construct prisms and record:
Apply formula to calculate volume of rectangular prisms.

the length, breadth and height of each in a table
Solve packaging problem:

the volume of each by counting the number of cubes used

how many small boxes will fit in a container

how many large boxes will fit in a container
Use centicubes to construct cubes of given dimensions:

tally the number of cubes used

record the volume of each shape
Strand: Space and Geometry
Strand: Space and Geometry
23
Week 4
Year 5
Year 6
Strand: Number
Outcome: NS3.3
Strand: Number
Outcome: NS3.3
3-digit x 1-digit multiplication (page 52)
4-digit multiplication (page 52)
H
1
2
T
1
4
×
Model the multiplication process.
O
5
Th
3
7
3
H
1
1
2
5
6
T
O
1
4
×
Model and discuss the process.
3
7
Complete examples.
5
9
3
5
Step 1
3 × 5 = 15. Trade the ten ones for one 10. Write the 5 in
the ones column.
Use multiplication as a problem-solving strategy.
Step 2
3 × 4 tens = 12 tens plus 1 ten = 13 tens. Trade the 10 tens
for one hundred. Write the 3 in the tens column.
Step 3
3 × 6 hundreds = 18 hundreds plus 1 hundred = 19
hundreds. Trade the 10 hundreds for one thousand. Write
the 9 in the hundreds column.
Step 4
3 × 2 thousands = 6 thousands plus 1 thousand equals
7 thousands. Write the 7 in the thousands column.
Complete examples.
Solve problems.
Create and solve 4-digit x 1-digit multiplications.
Strand: Patterns and Algebra
Outcome: PAS3.1b
Strand: Patterns and Algebra
Outcome: PAS3.1b
Constructing number sentences (page 53)
Number sentences (page 53)
Find the missing number in equations, e.g.
Supply missing numbers in equations, e.g.
4 × 7 =  – 22

35 ÷ 5 ×  = 28
Play ‘Celebrity Heads’, e.g.

54 ÷  = 21 – 12
If you add 2 and multiply by 4 the answer is 36.
Create own equivalent number sentences.
Create number sentences to solve problems, e.g.
Solve missing number equations in order to solve a number
cross.
Double the number and add 6 to get 14 becomes
 × 2 + 6 = 14
Create clues for someone to find the ‘celebrity number’.
Strand: Space and Geometry
Outcome: SGS3.2a
Strand: Space and Geometry
Outcome: SGS3.2a
Drawing shapes (page 54)
Drawing rectangles/squares (page 54)
Use a protractor and ruler to construct:
Use geometric tools to construct:

a 7 cm × 4 cm rectangle

a 10 cm × 6 cm rectangle

a 6 cm × 6 cm square

a 6 cm × 6 cm square
Create an irregular octagon on 5-mm grid paper by following
directions, e.g.
Identify lines of symmetry on both shapes.

forward 60 mm
Observe that each shape’s diagonals are equal.

right 90°

forward 30 mm
Identify sets of parallel lines on both shapes.
24
Strand: Measurement
Outcome: MS3.5
Strand: Measurement
Outcome: MS3.5
24-hour time (page 55)
24-hour time (page 55)
Investigate conventions used when recording time.
Recognise and express time:
Convert 12-hr time

using 12 hr-form (am/pm)
into 24-hr time, e.g.

using 24-hr form
7:30 pm = 19:30
Convert times on a timetable into 24-hr form, e.g.
3:25 pm = 15:25
Show how time can be expressed in analog, digital and
24-hr form.
Add and subtract minutes using the 24-hr form, e.g.
12 minutes after 14:54?
Interpret a TV guide expressed using 12-hr time.
Read and interpret a TV guide:
Strand: Chance and Data

start time

finish time

duration
Strand: Chance and Data
25
Week 5
Year 5
Year 6
Strand: Number
Outcome: NS3.2
Strand: Number
Outcome: NS3.2
4-digit subtraction (page 56)
4- and 5-digit subtraction (page 56)
Complete examples with trading in the 100s.
Complete examples.
Complete examples with trading in the 100s, 10s and 1s.
Complete examples with missing digits.
Given a table of motor vehicle production over 6 months,
calculate differences between months e.g. April (2506) and
January (932).
Solve problems.
Use rounding to estimate answers before calculating exact
answers to problems.
Outcome: NS3.3
Outcome: NS3.4
2-digit division (page 57)
Comparing and ordering fractions (page 57)
Model the division process involving remainders.
Match mixed numerals to positions on a number line, e.g.
Demonstrate how sometimes divisions don’t work out equally
and have ‘remainders’. Let’s see how Mrs King shared 83
cakes among 5 groups.
83 shared
among 5
Share out the
tens with each
person getting 1.
Trade the 3 tens left for
30 ones. Now share
the 33 among 5.
Order fractions from smallest to largest, e.g.
Division
Answer: 16
remainder 3
Optional Year 6 Student Book Blackline Master, to be used
with page 57 of the Year 5 Student Book.
Complete examples involving remainders.
Extend basic division facts to divide by numbers up to 6-digits,
e.g.
Use division to identify numbers contained on a bingo card.
35  5, 350  5, 3500  5
Open-ended investigation to find divisions that produce a
remainder of 2.
Calculate the average price of various shopping items.
Use a calculator to solve travel problem, e.g.
How long would a 1200 km trip from Sydney to Adelaide take
at an average speed of 60 km/h?
Strand: Space and Geometry
Outcome: SGS3.1
Strand: Space and Geometry
Outcome: SGS3.1
Describing objects (page 58)
Top, front and side views (page 58)
Match models of prisms to their descriptions and names, e.g.
Sketch a shape given its top, front and side views.
For the descriptions, include the number of vertices, edges
and faces, as well as other clues. A hexagonal prism might be
identified from the description ‘I have 12 vertices and 18
edges. 2 of my 8 faces are hexagonal whilst the others are
rectangular.’
Describe the similarities and differences between two 3D
objects, e.g. a rectangular pyramid and a pentagonal prism.
List similarities and differences between shapes, e.g. a square
pyramid and a pentagonal prism.
26
Strand: Measurement
Outcome: MS3.1
Strand: Measurement
Outcome: MS3.1
Perimeter (page 59)
Metres, centimetres and millimetres (page 59)
Calculate the perimeter of various shapes after measuring and
recording the shapes’ dimensions.
Measure a distance of 10 m in the playground and count the
number of steps equal to 10 m.
Create staircase shapes on 5-mm dot paper that have
perimeters of 12 cm and 16 cm.
Use above knowledge to estimate familiar distances, e.g.
length of netball court.
Calculate the perimeter of three gardens given their
dimensions.
Use knowledge of metric units to convert measurements into
other units, e.g.
6 cm =  mm
9250 m =  km
Order units from shortest to longest, e.g. 19 cm, 9 m, 250 mm
Solve problems, e.g.
How wide is the room if 8 strips of wallpaper each 500 mm
wide were needed . . .?
Perimeter
Optional Year 6 Student Book Blackline Master, to be used
with page 59 of the Year 5 Student Book.
Calculate the perimeter of various ‘letter’ shapes, e.g. L, C, F, E
Complete a chart to show relationship between length,
breadth and perimeter.
Measure and record the perimeter of various polygons in
millimetres.
Strand: Patterns and Algebra
Strand: Patterns and Algebra
Strand: Chance and Data
Strand: Chance and Data
27
Week 6
Year 5
Year 6
Strand: Number
Outcome: NS3.3
Strand: Number
Outcome: NS3.3
3-digit x 1-digit multiplication (page 60)
4-digit multiplication (page 60)
Complete examples, e.g.
Complete examples.
Find the missing numbers in worked examples.
326
× 4
2 33 35 
6
2
×
Use multiplication as a problem-solving strategy.
1 4130
Write a problem to suit an algorithm.

Use data about an office block to solve problems, e.g.
125
× 5
If a building has 8 floors, 298 lights per floor, how many lights
altogether?
Strand: Patterns and Algebra
Outcome: NS3.4
Strand: Patterns and Algebra
Outcome: NS3.4
Adding and subtracting fractions (page 61)
Adding and subtracting fractions (page 61)
Use shapes to model addition of fractions, e.g.
Subtract fractions with the same denominator, e.g.
Model addition of fractions with diagrams and record the total
as an improper fraction and as a mixed numeral,
e.g.
Complete addition sentences, e.g.
Complete subtractions, e.g.
Use a number line to add fractions with the same
denominator, e.g.
Identify pairs of fractions that can be either added or
subtracted to produce
Strand: Chance and Data
Outcome: DS3.1
Strand: Chance and Data
Outcome: DS3.1
Databases (page 62)
Spreadsheet data (page 62)
Examine how data can be organised into a database.
A
B
C
Add data to an existing database.
1
Date
Deposit
Subtotal
Create subsets of data from a database, e.g. Friends who live
in Kensington.
2
31 Jan
$319.50
(= C2) $319.50
3
28 Feb
$116.30
(= C2 + B3) $435.80
4
31 Mar
$121.40
(= C3 + B4) $557.20
5
30 Apr
$213.70
(= C4 + B5) $770.90
6
31 May
$118.05
(= C5 + B6) $888.95
7
30 June
$214.90
(= C6 + B7) $1103.85
8
31 July
$325.50
(= C7 + B8) $1429.35
9
31 Aug
$124.50
(= C8 + B9) $1553.85
Observe the spreadsheet and recognise that:

cell references (e.g. C2) refer to a particular cell in the
spreadsheet

the = sign indicates a formula (e.g. C4 is the value of cell
C3 added to the value in cell B4)
Complete two spreadsheets adding extra entries.
28
Strand: Measurement
Outcome: MS3.2
Strand: Measurement
Outcome: MS3.2
Square metres (page 63)
Using a scale (page 63)
Apply the area formula to calculate the area of rectangles.
Read and interpret the plan view of a house drawn to scale in
order to calculate costs associated with:
Apply a simple scale, e.g. 1 cm = 1 m, in order to calculate the
area of rectangles.

carpeting some areas
Solve area problems e.g.

tiling some areas
What would it cost to carpet a room 4 m long and 3 m wide if
the carpet is $20 per m2?

fencing the perimeter
Strand: Space and Geometry
Strand: Space and Geometry
Add other costs such as the initial purchase price, a pool and
a garage to find the total cost of building the house.
29
Week 7
Year 5
Year 6
Strand: Number
Outcome: NS3.3
Strand: Number
Outcome: NS3.3
3-digit division (page 64)
Extended multiplication (page 64)
Model the division process.
Model and discuss extended multiplication.
Share 426 sheep among three paddocks.
Share out the
hundreds. Each
paddock
gets 1.
Trade the 1 hundred
left over for 10 tens.
Now share the 12 tens.
Each paddock gets 4.
Share out the
6 ones. Each
paddock
gets 2.
Complete examples.
Use multiplication as a problem-solving strategy.
Complete examples without trading but with remainders.
Division

Complete examples with trading.

Optional Year 6 Student Book Blackline Master, to be used
with page 64 of the Year 5 Student Book.
Employ division as a problem-solving strategy.
Complete 4-digit by 1-digit divisions.
Investigate to find divisions that have a quotient between 150
and 200.
Solve rent problems, e.g.
$621 rent shared among 9; $1 840 shared among 10.
Solve problems.
Outcome: NS3.1
Outcome: NS3.1
Place value to 6 digits (page 65)
Expanding numbers (page 65)
Convert numbers expressed as words into numerals, e.g.
Expand numbers, e.g.
Fifty thousand, two hundred and four = 50 204
227 386 = 200 000 + 20 000 + 7000 + 300 + 80 + 6
State the place value of particular numerals, e.g.
Write numbers in words, e.g. 356 257
56 873  8’s place value = 8 hundreds
Identify numbers from clues, e.g.
Expand numbers to show place value, e.g.
I have a 6 in the tens of thousands, 7 in the hundreds of...
235 240 = 200 000 + 30 000 + 5000 + 200 + 40
Read clues to identify a mystery number, e.g. I am an odd
number between 5000 and 5999. The number in the
thousands ...
30
Strand: Patterns and Algebra
Outcome: PAS3.1a
Strand: Measurement
Outcome: MS3.4
Geometric patterns (page 66)
Mass and capacity (page 66)
Use matches to create a pattern of triangles, e.g.
Experiment 1
What is the mass of 1 litre of water?
Use a table to record data about the pattern of triangles, e.g.
Triangles
1
2
Matches
3
6
3
4
5
6
Follow instructions to reach the conclusion that 1 litre of water
has a mass of 1 kilogram.
7
Experiment 2
What is the mass of 1 millilitre of water?

create a rule to describe the pattern

apply the rule to predict number of matches needed for 15
triangles

repeat for pentagons and squares
Follow instructions to reach the conclusion that 1 mL of water
has a mass of 1 gram.
Complete a table to show the relationship between the mass,
volume and capacity of water, e.g.
Capacity
Volume
Mass
1 mL
1 cm3
1g
3
20 mL
20 cm
200 mL
200 cm3
20 g
200 g
Geometric patterns (page 66)
Optional Year 6 Student Book Blackline Master, to be used
with page 66 of the Year 5 Student Book.
Recognise the sequence of matches needed to create a
pattern of houses.
Complete a table to represent the pattern of houses and
matches.
Complete a table to show the number of matches needed to
make a sequence of 6-point stars.
Recognise that triangular numbers can be displayed in the
shape of a triangle.
Construct the 5th term in the pattern of triangular numbers.
Identify the next two triangular numbers after 15.
Strand: Space and Geometry
Outcome: SGS3.2a
Strand: Space and Geometry
Outcome: SGS3.2a
Rotational symmetry (page 67)
Symmetry (page 67)
Define rotational symmetry.
Recognise that a shape has:
Make tracings of shapes to test for rotational symmetry, e.g.

line symmetry if both parts match when folded along a line

rotational symmetry if it matches the original shape more
than once through a full rotation
Identify how many lines of symmetry shapes have.
Given a shape butted against a line of symmetry, draw the
other half.
Continue a tessellating pattern.
Make tracings of shapes to test for rotational symmetry, e.g.
Strand: Chance and Data
Strand: Chance and Data
31
Week 8
Year 5
Year 6
Strand: Patterns and Algebra
Outcome: NS3.3
Strand: Patterns and Algebra
Outcome: NS3.3
Order of operations (page 68)
Order of operations (page 68)
Read, discuss and model the rules for the order of operations:
Read, discuss and model the rules for the order of operations:

brackets first, e.g. (3 × 6) × 7 = 126

brackets first, e.g. (3 + 6) × 7 = 63

left to right, e.g. 3 × 8 ÷ 2 = 12


multiplication and division before addition and subtraction,
e.g. 6 + 8 × 3 = 30
multiplication and division before addition and subtraction,
e.g. 6 + 8 × 3 = 30

left to right, e.g. 3 × 8 ÷ 2 = 12
Complete a variety of examples employing all the order of
operations rules, e.g.
Complete a variety of examples employing all the order of
operations rules, e.g.

6 + (3 × 7) = 

(9 – 4) × 5 = 

8×7÷2=

72 + 88 ÷ 4 = 

7 + 64 ÷ 8 = 

4.2 × 4 + 3 = 

3 + 99 ÷ 3 = 
Strand: Number
Outcome: NS3.4
Strand: Number
Outcome: NS3.4
Subtracting fractions from wholes (page 69)
Add and subtract fractions (page 69)
Use shapes to model subtraction of fractions, e.g.
Use number lines to add and subtract fractions.
Add and subtract 2 or 3 fractions with the same denominator,
e.g.
Model how fractions can be subtracted from more than one
whole number, e.g.
Add fractions and express the answers as improper fractions
and as mixed numerals, e.g.
Use diagrams to complete subtractions, e.g.
Use number lines to complete subtractions.
Strand: Chance and Data
Outcome: NS3.5
Strand: Chance and Data
Outcome: NS3.5
Chance (page 70)
Chance from zero to one (page 70)
Examine a series of spinners to determine the likelihood of a
particular colour being the winning colour.
Use the range of 0 to 1 to rate the likelihood of events
happening, e.g.
Use terms such as ‘50% chance’ and ‘1 in 4 chance’ to
compare the likelihood of a particular colour being the winning
colour.
Use a scale of 0 to 1 to rate the likelihood of colours on a
spinner being the winning colour.
32

it will rain today

a red counter will be selected first from a group
Strand: Space and Geometry
Outcome: SGS3.1
Strand: Space and Geometry
Outcome: SGS3.1
Top, front and side views (page 71)
Top, front and side views (page 71)
Understand that 3D objects can be represented by drawings
of their views from the top, front and side.
Make models of 3D shapes then draw their top, front and side
views on grid paper.
Locate prisms, pyramids and cones and draw their views from
the top, front and side.
Observe 3D models and draw their three views, e.g.
Build 3D shapes given their top, front and side views.
Strand: Measurement
Strand: Measurement
33
Week 9
Year 5
Year 6
Strand: Number
Outcome: NS3.2
Strand: Number
Outcome: NS3.4
5-digit addition (page 72)
Subtracting decimals/money (page 72)
Complete examples, e.g.
Read and interpret a bank statement to:
35974

determine the balance at given times
20607

find the total amount deposited
+ 30708

add extra entries including the cheque number, amount in
debit column and progressive balance
Refer to a map of Australia with distances marked and
calculate the length of journeys, e.g.
Discuss alternative methods of payment other than by cash or
cheque.
Hobart to Sydney via Melbourne = 610 km + 706 km = 1316 km
Outcome: NS3.1
Outcome: NS3.1
Roman numerals (page 73)
Rounding (page 73)
Investigate how Roman numerals are structured.

to the nearest 10
Consult a table to convert numbers into Roman numeral, e.g.
724 = DCCXXIV

to the nearest 100

to the nearest 1000
Name the next term in a sequence, e.g.

V VI VII ____

XXIV XXIII XXII ____

LXXV LXXX LXXXV ____
Recognise K as a symbol for 1000, e.g.
23 000 = 23K
Estimate totals and express thousands using the K symbol,
e.g. 1249 + 1958 = 3K
Using a signpost featuring Roman numerals, calculate
distances between towns, e.g.
Roman numerals
Optional Year 6 Student Book Blackline Master, to be used
with page 73 of the Year 5 Student Book.
Convert Roman numerals into Hindu-Arabic numerals.
Match Roman numerals to positions along a number line.
Calculate distances between towns given data in Roman
numerals.
Oberon
200 km
Blackheath
130 km
70 km
Write any 5 numbers between 100 and 300 in Roman
numerals.
34
Strand: Chance and Data
Outcome: DS3.1
Strand: Chance and Data
Outcome: DS3.1
Line graphs (page 74)
Line graphs (page 74)
Read and interpret a line graph showing temperature over a
period of time.
Plot data onto a line graph to show different jogging rates of
two people.
Recognise an emerging pattern in a table and use this data to
create a line graph, e.g.
Plot the data in the table below onto a graph, with seconds on
the horizontal axis and litres on the vertical axis.
Sec. 10 20
30
40
50
60
70
L
6
8
10
12
14
2
4
Interpret data from completed graph, e.g.
How far has Lisa walked after 7 minutes?
Complete a table to show the rate at which water is filling a
tank. Represent the data on a line graph.
Strand: Measurement
Outcome: MS3.3
Strand: Measurement
Outcome: MS3.3
Cubic centimetres and millimetres (page 75)
Volume and capacity (page 75)
Recognise that 1000 mL = 1 L
Immerse a 50 cm3 model into a jug of water to measure how
much water is displaced, e.g.
Estimate and measure the capacity of containers in mL e.g.
teacup = 200 mL
Construct a shape comprising 50 centicubes and submerse it
in a measuring jug. Note the amount by which the water level
is raised.
Experiment: Does 1 cm3 displace 1 mL?

place centicubes (5, 10, 15) into 3 medicine glasses and
observe amount of displaced water

conclude that each cubic centimetre does displace 1 mL
Submerge a base 10 cube into a saucepan to measure the
amount of overflow.
Predict how much water various centicube models would
displace, e.g.
36 cm3 ≈ 36 mL
Strand: Patterns and Algebra
Strand: Patterns and Algebra
Strand: Space and Geometry
Strand: Space and Geometry
35
Program Planner: Stage 3
Term 3
Strand: Number
Outcome: NS3.3
Strand: Number
Outcome: NS3.3
3-digit division (page 78)
Dividing 5-digit numbers (page 78)
Demonstrate the division process.
Complete operations and record remainders as fractions.
Share 573 books among four schools.
Share out the
hundreds.
Each school
gets 1. One
hundred is
left over.
Trade the 1
hundred left over
for 10 tens. Now
share the 17 tens.
Each school gets
4.
Trade the 1 ten left
over for 10 ones.
Share out the 13
ones. Each school
gets 3. There is a
remainder of 1.
Use division to:

solve problems

crack a code
Complete examples, e.g.
Write a problem to suit an algorithm, e.g.
Outcome: NS3.4
Outcome: NS3.4
Percentages (page 79)
Percentages (page 79)
Understand that a percentage is one way of recording a
fraction with a denominator of 100.
Recognise that a simple way to find a percentage of an
amount is to think of it as a fraction, e.g.
Use the % sign to record percentages.
10% of $20 =
Use fractions, decimals and percentages to show equivalence
between fractions, e.g.
Visual
Fraction
Hundredths
Decimal
Percentage
0.1
10%
of $20 = $2
Match percentages to fractions, e.g. 25% =
Calculate discounts, e.g. 20% of $60
Complete a chart to calculate the number of goals scored e.g.
Name
Attempts
%
Goals
Sam
20
25%
5
Open-ended investigation.
Strand: Space and Geometry
Outcome: SGS3.3
Strand: Space and Geometry
Outcome: SGS3.3
Plan views (page 80)
Distance and direction (page 80)
Interpret the plan view of a flat in order to calculate the length
and breadth of the rooms.
Read and interpret a map and its scale to:

plot an ‘orienteering course’, e.g.
Travel south 300 metres then north-east 500 metres.

On 1-cm dot paper, draw the plan view of a room given:

a scale of 2 cm = 1 m

the position of objects in the room

the dimensions of objects in the room
36
give directions and distances to explain how to move
between one point and another
Strand: Measurement
Outcome: MS3.4
Strand: Measurement
Outcome: MS3.4
The tonne (page 81)
Tonnes (page 81)
Recognise that:
Recognise that:

1 tonne = 1 000 kilograms

1000 kilograms = 1 tonne

‘t’ is the symbol for tonne

a Toyota Corolla ≈ 1 tonne
Explain times when it would be more convenient to use tonnes
rather than kilograms.
Refer to a table to:

convert mass of 5 cars from kilograms into tonnes using
decimal notation

place cars in order of mass from lightest to heaviest

calculate difference in mass between cars
Given the mass of various ships and vehicles:



place them in order from lightest to heaviest, e.g.
4788 t, 4 t, 2456 t, 3921
solve problems based on the total mass and difference in
mass between vehicles
Convert tonnes into kilograms, e.g. 3.5 t = 3500 kg
Calculate how many smaller masses (200 kg, 500 kg, 50 kg,
400 kg and 10 kg) equal 2 tonnes.
Convert measurements into smaller units, e.g.
5 t = 5000 kg
Strand: Patterns and Algebra
Strand: Patterns and Algebra
Strand: Chance and Data
Strand: Chance and Data
37
Week 2
Year 5
Year 6
Strand: Number
Outcome: NS3.2
Strand: Number
Outcome: NS3.2
Addition (page 82)
5- and 6- digit subtraction (page 82)
Complete additions with a variety of addends.
Complete subtractions by:
Examine a series of estimated sums to see if they are
reasonable or unreasonable, e.g.

rounding to the nearest 1000 to estimate the difference

calculating the exact answer

149 + 52 ≈ 250 is unreasonable

331 + 71 ≈ 400 is reasonable
Write a word problem to match a solution.
Refer to a chart to compare navy ships, e.g.
Given the prices of airline tickets to London offered by
different companies, calculate the best option for a family.

How much longer is HMAS Perth than HMAS Otway?
(134.34 m – 91.40 m)

What is the difference in mass between a destroyer and a
patrol boat? (4 846 t – 247 t)
Outcome: NS3.3
Outcome: NS3.3
Averages (page 83)
Dividing by 10s/Averages (page 83)
Model and demonstrate the strategy used to calculate the
‘average’ (mean).
Develop a strategy to divide by multiples of 10 
480  80 = 
Calculate the average for sets of scores, e.g.
Think
40, 36, 32 = 108  3 = 36
480  10 = 48
48  8 = 6
Solve problems based on averages.
Complete examples.
Recall that averages are found by adding all scores in a group
and dividing by the number of scores.
Find the average of sets of numbers.
Solve ‘average’ problems.
Strand: Space and Geometry
Outcome: SGS3.2a
Strand: Space and Geometry
Outcome: SGS3.2a
Enlargements (page 84)
Enlargements (page 84)
Enlarge polygons by doubling their dimensions.
Plot coordinates onto a grid to create the shape of a house.
Given a diagram of a boat on 4-mm grid paper, create an
enlarged version on a larger grid.
Make sketches on grid paper of another student’s face smaller
than and larger than the original.
Repeat the process plotting onto a larger and distorted grid.
Copy an intricate design onto a smaller grid.
38
Strand: Chance and Data
Outcome: DS3.1
Strand: Chance and Data
Outcome: DS3.1
Sector graphs (page 85)
Sector graphs (page 85)
Recognise that sector graphs show how a total is divided.
Recognise that sector graphs show how a total is divided.
Read and interpret a sector graph, e.g.
Read and interpret a sector graph whereby each sector
Of the 96 people in the survey about how many chose peach?
represents a fraction of the total, e.g.
Interpret a graph divided into 24 sectors to determine time
spent on activities such as TV, sport, study, sleep and eating.
Conduct a ‘hair colour’ survey and construct a sector graph to
represent this.
Record time spent on daily activities in a table and then as a
sector graph.
Interpret a graph representing the population of Australia’s
states and territories.
Strand: Patterns and Algebra
Strand: Patterns and Algebra
Strand: Measurement
Strand: Measurement
39
have brown hair.
Week 3
Year 5
Year 6
Strand: Number
Outcome: NS3.3
Strand: Number
Outcome: NS3.3
3-digit multiplication (page 86)
Extended multiplication (page 86)
Demonstrate a mental strategy, e.g. 543 × 6
Complete examples and explain why the second line always
has a zero in the ones column.
Think: 500 × 6 = 3000
Use multiplication to solve a problem.
40 × 6 = 240
3×6=
Use multiplication to solve a number cross.
18
3258
Use mental and written strategies to solve examples, e.g.
854 × 6 = 
Use multiplication to complete a wages table, e.g.
Name
Days
Rate
Erica
5
$125
Total
Write a problem to suit this working.
300 × 5 = 1 500
60 × 5 =
300
5×5=
25
Outcome: NS3.1
Outcome: NS3.1
Reading large numbers (page 87)
Place value (page 87)
Recognise that numbers are read in groups of hundreds, tens
and ones.
Order sets of numbers from smallest to largest, e.g. 182 321,
821 321 000, 281 321, 1 218 321.
Convert numbers expressed in words into numerals, e.g.
Place numbers recorded as words on a place-value chart.
Two hundred and sixteen thousand, four hundred and twentysix becomes 216 426.
Show the place value and total value of certain digits within a
number, e.g. 357 291
Refer to a table showing area of Australian states:
7 is in the thousands place, its value is 7000.

place them in order of size

make comparisons between the states, e.g. Western
Australia is more than double the size of New South Wales
Strand: Chance and Data
Outcome: DS3.1
Strand: Chance and Data
Outcome: DS3.1
Divided bar graphs (page 88)
Divided bar graphs (page 88)
Read and interpret a divided bar graph, e.g.
Read and interpret a divided bar graph.
Do more students like bananas than apples?
Create a divided bar graph to represent tallied data about
favourite colours.
Conduct a survey about hair colour; record the data in a table
and as a divided bar graph.
Interpret a graph that uses more than one bar, e.g.
Which year has the most fair-haired students?
Construct a graph to show how an amount of $600 was spent.
Strand: Measurement
Outcome: MS3.5
Strand: Measurement
Outcome: MS3.5
24-hour timetables (page 89)
Elapsed time/timetables (page 89)
Refer to a Brisbane–Melbourne bus timetable to find:
Given starting times and finishing times for various workers
calculate the time spent at work, e.g.

the duration of sections, e.g. Moree–Dubbo

the length of rest stops

the duration of the entire trip
Nurse: 9:00 pm – 6:30 am = 
Solve problems.
Make a timetable for a typical day at school.
Prepare a timetable of daily events, e.g.
Time
Activity
0700 to 0800
0800 to 0900
1000 to 1100
Strand: Patterns and Algebra
Strand: Patterns and Algebra
Strand: Space and Geometry
Strand: Space and Geometry
40
Week 4
Year 5
Year 6
Strand: Number
Outcome: NS3.2
Strand: Number
Outcome: NS3.2
5-digit subtraction (page 90)
5- and 6-digit subtraction (page 90)
Complete examples with random trading.
Complete examples using measurement units,
e.g.  tonnes
Given a population table, calculate differences between cities
such as Wagga Wagga (42 848) and Dubbo (30 102).
795286
– 347275
Refer to a table to calculate differences in price between
Australia’s most expensive cars, e.g. Mercedes ($366 999)
and BMW ($263 999).
Complete details on a ‘log book’ to calculate the distance
travelled per trip.
Outcome: NS3.4
Outcome: NS3.4
Percentages (page 91)
Equivalent fractions (page 91)
Demonstrate how a calculator can be used to find a
percentage of a collection, e.g.
10% of 40  40 × 10% = 4
Convert percentages to common fractions, e.g.
25% of 60 becomes
of 60 or 60 ÷ 4 = 15
Calculate percentage discounts on clothing, e.g. 10% of $80.
Refer to a fractions chart to select fractions of equivalent
value, e.g.
Use symbols <, = and > to compare fractions, e.g.
Create equivalent fractions by multiplying a fraction’s
numerator and denominator by the same number, e.g.
Fractions, decimals and percentages
Optional Year 6 Student Book Blackline Master, to be used
with page 91 of the Year 5 Student Book.
Complete a chart to express amounts as fractions, decimals
and percentages, e.g.
, 0.75, 75%
Calculate the number of coloured marbles given the
percentage of the total, e.g. 15% of the 20 marbles are purple.
Calculate percentages of amounts of money.
41
Strand: Patterns and Algebra
Outcome: PAS3.1a
Strand: Measurement
Outcome: MS3.5
Geometric patterns (page 92)
Timetables (page 92)
Read and interpret a bus timetable, e.g.
Use a table to record data about the pattern of hexagons, e.g.
hexagons
1
2
3
4
5
6
Construct or obtain a bus timetable and schedule of bus fares.
Use the tables to answer questions such as ‘What bus would
Fred need to catch on Wednesday to be at Harris St by
10:47 am?’
Refer to a bus-fare table to solve problems.
7
sides
Geometric patterns

create a rule to describe the pattern

apply the rule to predict number of sides there would be on
9 hexagons

repeat for octagons, decagons and dodecagons
Optional Year 6 Student Book Blackline Master, to be used
with page 92 of the Year 5 Student Book.
Recognise the relationship between the number of matches
and the size of the shape.
Complete tables to express the relationship between the
shape and the number of matches.
Recognise that square numbers can be displayed in the shape
of a square.
octagon
decagon
Construct the 4th term in the pattern of square numbers.
dodecagon
Strand: Space and Geometry
Outcome: SGS3.1
Strand: Space and Geometry
Outcome: SGS3.1
Constructing objects (page 93)
Drawing 3D shapes (page 93)
Match 3D objects to their top, front and side views, e.g.
Demonstrate the process for constructing an oblique drawing.

front view = exact size

side and top are drawn at an angle of 45°

side and top =

Construct diagrams of shapes on grid paper to represent
shapes, e.g. 3 cm × 2 cm × 2 cm rectangle
size
Given an object’s views, make and sketch that shape.
Strand: Chance and Data
Strand: Chance and Data
42
Week 5
Year 5
Year 6
Strand: Number
Outcome: NS3.3
Strand: Number
Outcome: NS3.4
3-digit × 1-digit multiplication (page 94)
Multiplying decimals/money (page 94)
Complete examples, e.g. 236 × 5 = 

model the process of multiplying decimals
Refer to a map marked with distances to calculate the length
of journeys, e.g.

emphasise the role of the decimal point
Complete examples, e.g.
5 trips between Carey and Stuart: 265 m × 5 = 
$256.48
×
8
Use rounding to estimate products, e.g.
6 × 213 becomes 6 × 200 = 1200
Solve problems, e.g.
7 boxes each with a mass of 2.75 kg.
What is the total mass . . . ?
Use knowledge of multiplication of decimals and a calculator’s
memory function to solve shopping problems.
Investigate combinations of shopping problems that total
between $26 and $29.
Outcome: NS3.4
Outcome: NS3.4
Improper fractions (page 95)
Add and subtract fractions (page 95)
Recognise that improper fractions have a numerator larger
than the denominator, e.g.
Add fractions with related denominators, e.g.
Complete examples using an equivalence chart if necessary.
Write improper fractions to describe diagrams.
Subtract fractions with related denominators, e.g.
=
Solve problems, e.g.
Use number lines to identify improper fractions.
If she ate
and her friend ate
, how much was left?
Solve problems.
Strand: Chance and Data
Outcome: NS3.5
Strand: Chance and Data
Outcome: NS3.5
Chance—Tree diagrams (page 96)
Chance—Tree diagrams (page 96)
Recognise that tree diagrams display all possible outcomes
from a chance investigation.
Recognise that tree diagrams display all possible outcomes
from a chance investigation.
Complete a tree diagram to show all possible combinations
that can be made when buying a car, e.g.
Use a tree diagram to show all possible disguises a man could
have.
Choices that will provide forks in the tree might include:

Red or black?

Convertible or hard top?

Automatic or manual?

V6 or four cylinder?
Construct a tree diagram to show all possible combinations
when making a sandwich.
Use a tree diagram to work out the sex of four children in a
family and their order of birth, e.g. boy, boy, boy, girl.
43
Strand: Space and Geometry
Outcome: SGS3.3
Strand: Space and Geometry
Outcome: SGS3.3
Scale, direction, coordinates (page 97)
Coordinates (page 97)
Read and interpret a street map and its scale to:
Refer to a city map to:

name streets found at coordinate points

give the coordinates of people, e.g. Joe = P3

name the coordinates for points on the map

add items to the map, e.g. a + at coordinates G5

plot courses on the map, e.g. Start at B and travel
west 600 m. . .
Use the scale, coordinates and compass directions to plot a
course, e.g. Start at J4 then head east for 100 m

find the shortest distance between points
Strand: Patterns and Algebra
Strand: Patterns and Algebra
Strand: Measurement
Strand: Measurement
44
Week 6
Year 5
Year 6
Strand: Number
Outcome: NS3.3
Strand: Number
Outcome: NS3.3
Division by ten (page 98)
Dividing large numbers (page 98)
Model and discuss the process.
Model the division process. 
575 nails were shared among 10 carpenters.
Divide 57 tens by
10. Each carpenter
gets 5.
Trade the 7 tens left for 70 ones.
Now share the 75. Each gets 7
with a remainder of 5.
Complete examples.
Use a calculator to divide large numbers.
Use own strategies to complete problems.
Answer: 57 remainder 5
Examine a series of estimates to divisions to see if they are
reasonable or unreasonable, e.g.
388 ÷ 4  100 is reasonable.
Solve ‘average’ problems.
Outcome: NS3.4
Outcome: NS3.4
Mixed numerals (page 99)
Equivalent fractions (page 99)
Recognise that a mixed numeral consists of a whole number
Create equivalent fractions by multiplying a fraction’s
numerator and denominator by the same number, e.g.
and a fraction, e.g.
Write mixed numerals to describe diagrams, e.g.
Shapes
Improper fraction
Identify relationship between fractions with related
denominators in order to make equivalent fractions, e.g.
Mixed number
 Multiply numerator and denominator by 6.
Investigate to find as many fractions as possible that are
Use number lines to show equivalence between mixed
numbers and improper fractions.
equivalent to
Continue equivalent fraction patterns, e.g.
Strand: Space and Geometry
Outcome: SGS3.2b
Strand: Space and Geometry
Outcome: SGS3.2b
Angles in triangles (page 100)
Angles (page 100)
Use a protractor to measure the angles in equilateral, scalene
and isosceles triangles.
Estimate then use a protractor to measure angles.
Observe that:

an equilateral triangle’s angles are all equal

a scalene triangle’s angles are all different
Calculate the size of reflex angles by measuring the smaller
angle then subtracting that from 360°.
Use a compass to construct an isosceles triangle.
Measure and label the angles made when two lines intersect.
45
Strand: Measurement
Outcome: MS3.1
Strand: Measurement
Outcome: MS3.1
Perimeter (page 101)
Perimeter (page 101)
Calculate the perimeter of various shapes after measuring and
recording the shape’s dimensions in millimetres.
Discover that the perimeter of regular polygons can be
calculated this way:
Examine short cuts for calculating the perimeter of regular
polygons.
length of one side × N° of sides
Calculate perimeter of regular and irregular shapes.
Given a floor plan, calculate the perimeter of each room.
Use decimal notation to record perimeters of shapes.
Calculate perimeter given a description of a shape, e.g.
An equilateral triangle with sides of 5 centimetres.
Strand: Patterns and Algebra
Strand: Patterns and Algebra
Strand: Chance and Data
Strand: Chance and Data
46
Week 7
Year 5
Year 6
Strand: Number
Outcome: NS3.2
Strand: Number
Outcome: NS3.2
5-digit addition (page 102)
4-, 5- and 6-digit addition (page 102)
Complete examples with 2 addends.
Complete examples with up to four addends.
Choose between addition and subtraction as strategies to find
missing numbers in algorithms.
Use data presented in a table to calculate the area of each
state and territory, e.g.
+
5
2

3
4
Queensland is 362 000 km2 larger than the Northern Territory
2

7
2
4
(1 346 000 km2).
1
4
0
2
5
8
7
8
8

Solve problems based on prices of motor vehicles.
Outcome: NS3.3
Outcome: NS3.3
Multiplication by tens (page 103)
Multiplication by tens (page 103)
Complete grids for × 10, × 100 and × 1000.
Complete a multiplication chart for ×10, ×100 and ×1000.
Round the multiplicand to the nearest 10 or 100 to
approximate answers, e.g. 813 × 8 ≈ 6400.
Model the process for multiplication by tens.
Model the written algorithm.
Th
H
T
2
×
1
8
O
4
5
4
0
0
0
Complete examples, e.g.
126
Step 1
Put the 0 down because you are multiplying by 10.
× 30
Step 2
Multiply by 4 using the shortened method.
Complete multiplications by:

rounding the larger number to the nearest 100 or 1000 to
estimate the product

calculating the exact answer
Complete examples.
47
Strand: Patterns and Algebra
Outcome: PAS3.1a
Strand: Space and Geometry
Outcome: SGS3.2a
Number patterns (page 104)
Enlargements/reductions (page 104)

identify patterns
Observe a 2-cm square:

continue patterns

note its area is 4 cm2

describe patterns


predict the 10th term
predict what the area of the shape would be if its
dimensions were doubled

draw a 4 cm × 4 cm square

observe that the area has increased 4 times
e.g.
1st number
2nd number
1
2
3
4
9
10
11
12
5
6
Double the dimensions of a rectangle to test whether its area
also increases 4 times.
Write a rule to describe how a rectangle’s area increases 4
times when its sides are doubled.
Halve the dimensions of a rectangle to observe how its area
decreases 4 times.
Double and halve the dimensions of modelled shapes to
create new shapes.
Number patterns
Optional Year 6 Student Book Blackline Master, to be used
with page 104 of the Year 5 Student Book.
Apply rules to create the second number in various
sequences.
Follow a rule to identify numbers on function machines, e.g.
Rule: ● × 2 + 5
Input
Output
2
9
4
13
6
17
8
21
Use a table to show how many items a machine can produce
in a number of minutes.
Strand: Chance and Data
Outcome: DS3.1
Strand: Chance and Data
Outcome: DS3.1
Divided bar graphs (page 105)
Line graphs (page 105)
Read and interpret divided bar graphs to:
Conduct an investigation to see how water temperature may
change over time:

identify areas of least/most expenditure

compare expenditure

identify most popular items

estimate size of groups
Create a divided bar graph to represent tallied data about
shoe sizes.
Strand: Measurement

fill a saucepan with hot water

use an immersion thermometer to measure the
temperature at 5-minute intervals

represent the data on a line graph

read and interpret the line graph to estimate temperatures
for positions along the line, e.g. after 7 minutes
Strand: Measurement
48
Week 8
Year 5
Year 6
Strand: Number
Outcome: NS3.3
Strand: Number
Outcome: NS3.3
2-digit x 2-digit multiplication (Page 106)
Multiplication by 2 digits (page 106)
Model and discuss long multiplication.

review multiplication process
Long multiplication by 2 digits:

explain why there is always a zero in the units column of
the second row of working
2
7
×
2
5
1
3
5
27 × 5 = 135
5
4
0
27 × 20 = 540
6
7
5
(27 × 5) + (27 × 20) = 675
Complete examples, e.g. 4 5 2
× 45
Use ‘guess and check’ strategies to match multipliers to
worked examples, e.g. 
(135 + 540)
Complete examples.
Solve a volume problem given the number of soup tins
contained in a carton and the number of cartons per pallet.
9
6
×


4
8
0
3
8
4
0
4
3
2
0
Refer to a map with distances marked to calculate distance
flown on various flights, e.g.
34 trips from Sydney to Brisbane (752 km × 34).
Outcome: NS3.4
Outcome: NS3.4
Decimals to thousandths (page 107)
Dividing decimals/money (page 107)
Recognise that metric measurements are frequently recorded
in thousandths, e.g.

model the process of dividing decimals

emphasise the role of the decimal point
1 kg and 256 grams = 1.256 kg
Complete examples, e.g.
Record the place value of digits, e.g.
256.73  7 represents 7 tenths
Use decimal notation to convert measurements into one unit,
e.g. 4 L and 649 mL = 4.649 L
Solve shopping problems, e.g.
If 3 tomato sauce bottles cost $1.86, how much would 1 bottle
cost?
Recognise that zero can be used as a place holder, e.g.
Check worked examples for correctness, e.g.
Place decimals in ascending order, e.g.
3.555, 4.098, 4.077, 5.006
Strand: Space and Geometry
Outcome: SGS3.1
Strand: Space and Geometry
Outcome: SGS3.1
Making objects and nets (page 108)
Faces, vertices and edges (page 108)
Make skeletal models of prisms and pyramids.
Investigate Euler’s rule, e.g.
Fold nets to create 3D shapes.
Faces + Vertices – 2 = Edges
Investigate the nets of shapes to test Euler’s rule:

tetrahedron

square pyramid

rectangular prism

pentagonal prism

hexagonal pyramid

octagonal prism
Shape
Create the net of a rectangular prism.
49
Faces
Vertices
Edges
Tetrahedron
4
4
6
Square pyramid
5
5
8
Rectangular prism
6
8
12
Pentagonal prism
7
10
15
Hexagonal pyramid
7
7
12
Octagonal prism
10
16
24
Strand: Chance and Data
Outcome: DS3.1
Strand: Chance and Data
Outcome: DS3.1
Data survey (page 109)
Data survey (page 109)
Survey students to establish how they use computers:
Conduct a survey to find the most popular form of electronic
entertainment.

create survey questions

identify target group

make own prediction

conduct survey

record data in a table

represent data as a column graph

comment on prediction at conclusion of survey

create survey questions

conduct survey

write report

design a column graph to represent data
Strand: Patterns and Algebra
Strand: Patterns and Algebra
Strand: Measurement
Strand: Measurement
50
Week 9
Year 5
Year 6
Strand: Number
Outcome: NS3.3
Strand: Number
Outcome: NS3.3
Division with zero as a place holder (page 110)
Decimal remainders (page 110)
Model and discuss how zero sometimes holds a place in the
quotient.
Review strategy of expressing remainders as a fraction of the
divisor.
5 students shared 515 blocks. How many blocks did each
student receive?
Divide the hundreds You cannot
by 5, with each
divide 1 by 5 so
put a zero.
student getting 1.
Trade the 1 ten for
10 ones. Now divide
the 15 ones by 5.
Complete examples.
Complete divisions on a calculator to observe that remainders
are expressed as decimals.
Use a calculator to convert remainders into decimals, e.g.
Solve problems and round decimals to 3 places.
Calculate an average problem.
Recognise that the keys on a calculator will allow percentages
to be found easily, e.g.
$400 × 25% = $100
Examine a ‘Water usage’ diagram to calculate how water is
used in a household, e.g.
Laundry: 5500 L × 15% = 
Read and interpret a table to:

find the size of each group, e.g. Netball: 480 × 30% = 

solve problems, e.g. How many players play baseball if
they represent 50% of the group?
Outcome: NS3.1
Outcome: NS3.1
Negative numbers (page 111)
Negative numbers (page 111)
Discuss and brainstorm instances where and when negative
numbers are used.
Recognise that negative numbers:

have a value less than zero
Define negative numbers as numbers with a value less than
zero.

have a minus sign (–) placed in front of them, e.g.
Mt Kosciuszko’s temperature was –7°C.
Recognise that a minus sign (–) is used to identify negative
numbers, e.g.
Read and interpret a diagram showing distances above sea
level and distances below sea level, e.g.
The temperature at Thredbo was –5°C.
shipwreck = –700 m
Read and record temperatures on thermometers.
Read and interpret a cross-sectional drawing showing heights
above and below sea-level.
51
Use number lines to solve equations, e.g.

5+2–4–6=
Strand: Chance and Data
Outcome: DS3.1
Strand: Chance and Data
Outcome: DS3.1
Interpreting graphs (page 112)
Graphs (page 112)
Read and interpret 3 graphs showing similar data.
Read and interpret 4 graphs showing the same data.
Hilltop Primary School
Greenway Primary School
Binga Primary School
Sample questions:

Which activity raised the most money at Hilltop?

Were pony rides the least successful at all schools?

Is it reasonable to say that the raffle raised $350 at Hilltop?
Make judgements about which graph:

gives the most accurate information

gives a good overall picture of the data
Name instances when column graphs, picture graphs, sector
graphs and divided bar graphs are used.
52
Strand: Measurement
Outcome: MS3.2
Strand: Measurement
Outcome: MS3.2
Hectares (page 113)
Hectares/square kilometres (page 113)
Recognise that:
Recognise that:

10 000 m2 = 1 hectare

10 000m2 = 1 hectare

2 soccer fields ≈ 1 hectare

2 soccer fields ≈ 1 hectare

‘ha’ is the symbol for hectare

‘ha’ is the symbol for hectare
Investigate whether the school is more, less or about a
hectare:

100 ha = 1 km2

measure the school’s length and breadth with a trundle
wheel

less than 1 ha

use a calculator to find the area in square metres, e.g.
length × breadth = area

about 1 ha

greater than 1 ha

compare the school’s area to a hectare (10 000m )
Mark out an area of 1 hectare then classify local areas as:
Measure and mark out the area of the school to the nearest
hectare.
2
Identify local areas that are one hectare or more, e.g.
shopping centre, swimming pool complex.
Refer to a table with areas recorded in km 2 to calculate
differences and combined size of countries.
Strand: Patterns and Algebra
Strand: Patterns and Algebra
Strand: Space and Geometry
Strand: Space and Geometry
53
Program Planner: Stage 3
Term 4
Week 1
Year 5
Year 6
Strand: Number
Outcome: NS3.4
Strand: Number
Outcome: NS3.4
Adding decimals (page 116)
Multiplying fractions (page 116)
Demonstrate the addition of two 2-place decimals, e.g.
Explore strategies:
6.74 + 2.16

repeated addition e.g.

multiply numerator by whole number and divide that
product by denominator, e.g.

multiply numerators and multiply denominators, e.g.

using base 10 to model the process so that the trading
becomes a concrete operation

as a vertical algorithm
Complete examples with three addends and various numbers
of decimal places.

4.53
2.496
+ 9.9
Adding and subtracting decimals
Interpret a map with distances marked in kilometres to
calculate the shortest distance between towns such as Graf
and Goolagong.
Optional Year 6 Student Book Blackline Master, to be used
with page 116 of the Year 5 Student Book.
(44.521 km + 17.362 km = 61.883 km)
Add columns of decimal numbers up to 3-digits.
Complete subtraction algorithms, e.g.
tonnes
67.986
– 24.354
Complete a bank statement using addition and subtraction
strategies.
Outcome: NS3.3
Outcome: NS3.3
Calculator memory (page 117)
Multiplication and division on a calculator (page 117)
Recognise the purpose and function of the M+ and MR keys
on a calculator.
Demonstrate how the M+ and MR keys on a calculator can
be used to solve a problem.
Complete an example.
Using the memory function
Solve shopping problems based on data provided.
Socks
Stapler
Magazine
Ball
Felt-tip pen
$4.55
$5.50
$4.75
$8.50
$7.35
Write and solve a problem using a calculator’s memory
function.
Solve equations using the M+, M-and MR functions, e.g.
(100 – 57) – (80 ÷ 16) = 
Sue bought 3 pairs of socks, 2 staplers and 3 balls. How
much did she spend?
Step 1
Enter $4.55 × 3 on your calculator and press M+
Step 2
Enter $5.50 × 2 on your calculator and press M+
Step 3
Enter $8.50 × 3 on your calculator and press M+
Step 4
Press MR on your calculator to find the total of $50.15
Use the memory function to calculate the total costs for a
series of purchases.
54
Strand: Space and Geometry
Outcome: SGS3.3
Strand: Space and Geometry
Outcome: SGS3.3
Street directories (page 118)
Street directories (page 118)
Read and interpret a street directory to:
Read and interpret a street map to:

identify streets found at particular coordinates

identify streets found at coordinates

give the coordinates of certain streets

mark points at particular coordinates

write directions on how to travel from one location to
another

follow directions to find a ‘secret’ location, e.g. Start at
Northbridge Plaza (N3), head north along...

draw a path from one location to another

follow directions to plot a path, e.g. (O9) to (D3)
Apply a scale to give the approximate length of streets.
Strand: Measurement
Outcome: MS3.5
Strand: Measurement
Outcome: MS3.5
Timelines (page 119)
Timelines (page 119)
Make a personal timeline from year of birth to now.
Match events to a place on a horizontal timeline.
Match significant world events to a timeline.
Match events to a place on a vertical timeline.
Strand: Patterns and Algebra
Strand: Patterns and Algebra
Strand: Chance and Data
Strand: Chance and Data
55
Week 2
Year 5
Year 6
Strand: Number
Outcome: NS3.3
Strand: Number
Outcome: NS3.3
2-digit × 2-digit multiplication (page 120)
Multiplication by 2 digits (page 120)
Complete examples, e.g.
Complete examples, e.g.

446
28
×15
× 35
Calculate costs involved in buying lots of office equipment, e.g.
18 copiers @ $5460 each.
Use multiplication to solve problems.
Use rounding as a strategy for checking multiplications.
Outcome: NS3.4
Outcome: NS3.4
Subtracting decimals (page 121)
Percentages (page 121)
Demonstrate subtraction of 2-place decimals:
Recognise that a simple way to find a percentage of an amount
is to think of it as a fraction, e.g.

use base 10 to model the process so that the trading
becomes a concrete operation

as a vertical algorithm
Complete examples, e.g.
20% of $20 =
of $20 = $4
Convert percentages to fractions to find quantity.
7. 3 4
Calculate value of discount and adjusted cost, e.g. $48 less
25% discount ($12) = $36
– 5. 1 6
Given a table of heights recorded as decimal fractions
calculate differences, e.g.
Calculate and compare prices after discounting, e.g.
Sam and Alexis (1.57 m – 1.49 m = 0.08 m)
$120 with 25% discount
Use knowledge of decimal place value and subtraction to solve
problems.
$100 with 20% discount
Decimals
Optional Year 6 Student Book Blackline Master, to be used with
page 121 of the Year 5 Student Book.
Supply the missing numbers in 5-digit addition algorithms, e.g.
kilometres
2 3 5 . __ 4
1 2 1 . 3 __
+ 2 2 2. 2 2
5 __ 8 . 7 8
Solve problems using own strategies.
Strand: Chance and Data
Outcome: NS3.5
Strand: Chance and Data
Outcome: NS3.5
Chance (page 122)
Describing likelihood (page 122)
Given the letters and numbers on a number plate, examine all
possible combinations of numerals, e.g.
Read and interpret a column graph displaying data about ‘Pulse
Rates.’
TR-123, TR-132, TR-321
Answer True or False statements, e.g.
Investigate the number of handshakes that would occur at the
end of a doubles tennis match if each player shook hands with
the other three players.
It is more likely that a child has a pulse rate of 64 than 67.
Use a tree diagram to show all possible combinations that
could occur when a spinner with two colours is spun three
times.
56
Use the language of chance to describe everyday events,
e.g. The Sydney Swans win the premiership.  unlikely
Strand: Space and Geometry
Outcome: SGS3.1
Strand: Space and Geometry
Outcome: SGS3.1
Nets (page 123)
Nets (page 123)
Match drawings of objects to their nets, e.g. cone, cylinder,
rectangular prism, triangular prism, octagonal pyramid and
triangular pyramid.
Identify the 6 faces of a box and its net.
Match the top, front and side views of a rectangular prism to
those surfaces on its net, e.g.
Make an identical copy of a triangular pyramid’s net and fold it to
make the shape.
Identify faces on a cube given its net, e.g.
Strand: Patterns and Algebra
Strand: Patterns and Algebra
Strand: Measurement
Strand: Measurement
57
Week 3
Year 5
Year 6
Strand: Number
Outcome: NS3.2
Strand: Number
Outcome: NS3.2
5-digit subtraction (page 124)
4-, 5- and 6-digit subtraction (page 124)
Complete examples that include money.
Complete examples, e.g.
Solve problems.
$452796
Complete a spreadsheet to show how to balance after a
series of purchases have been made, e.g.
–348249
A
B
C
D
1
Date
Item
Cost
Balance
2
May 3
Opening
3
May 7
Balls
$126.00
(D2-C3)
4
May 9
Shirts
$120.32
(D3-C4)
5
May 12 Shorts
$144.22
(D4-C5)
6
May 18 Socks
$35.28
(D5-C6)
7
May 22 Pads
$34.65
(D6-C7)

Refer to a ‘Length of Australian coastline’ table to calculate
differences, e.g.
Victoria (2512 km) and New South Wales (2137 km)
$987.90
Refer to a population chart to calculate differences.
$861.90
Strand: Number
Outcome: NS3.1
Strand: Number
Negative numbers (page 125)
Negative numbers (page 125)
Complete a number line to show negative numbers.
Use number line to solve equations,
Outcome: NS3.1
e.g. 7 + 4–10 – 8 = 
Show how vertical movement can be described using positive
and negative numbers, e.g.
Write a number sentence and show its solution on a number
line.
A side profile of a flight of stairs, where steps above the
landing are positive and steps below the landing are negative.
Calculate differences in temperature when positive and
negative numbers are used, e.g.
What is the difference between Moscow’s highest (7°C) and
lowest temperature (–3°C)?
Strand: Measurement
Outcome: MS3.1–3.4
Strand: Measurement
Outcome: MS3.1–3.4
Length units (page 126)
Measuring units/devices (page 126)
Select the most suitable unit to measure various items, e.g.
Select the most suitable unit to measure various items, e.g.
mm  thickness of mouse pad
kg  my mass
m  length of a swimming pool
m2  area of a room
Select appropriate measuring device, e.g.
km  Brisbane to Cairns
30 cm ruler  length of pencil
Match measuring instruments to measurements, e.g.
Convert units into other units, e.g.
medicine glass  5 mL
m = 850 cm
Estimate the length of a knife in millimetres.
Convert units into other units, e.g. 4 357 m = 4.357 km
Strand: Chance and Data
Outcome: DS3.1
Strand: Chance and Data
Outcome: DS3.1
Mean scores (page 127)
Jason’s spelling scores
The mean (page 127)
Show how a column graph built
with blocks can be manipulated
to determine the mean.
Understand that the mean can be calculated by adding all the
scores and dividing by the number of scores.
Understand that the mean can
be calculated by adding all the
scores and dividing by the
number of scores.
0, 3, 4, 2, 1, 6, 4, 4
Calculate the mean for sets of scores, e.g.
Calculate the mean price for a set of five bicycles.
Investigate ways of finding a missing score if all other scores
and the mean are known.
Calculate the mean for sets of
scores, e.g.
30 kg, 30 kg, 40 kg, 35 kg and 35 kg.
Strand: Patterns and Algebra
Strand: Patterns and Algebra
Strand: Space and Geometry
Strand: Space and Geometry
58
Week 4
Year 5
Year 6
Strand: Number
Outcome: NS3.4
Strand: Number
Outcome: NS3.4
Multiplication of decimals (page 128)
Multiply and divide decimals (page 128)
Model the multiplication process.
Use a calculator to:
Tenths

2
3
4
multiply decimals by 10, 100 and 1000, e.g.
8.46 × 10, 8.46 × 100 and 8.46 × 1000

explain how the decimal point moves when carrying out
such multiplications
9
2

Step 1
Multiply 3 tenths by 4, which equals 12 tenths.
divide decimals by 10, 100 and 1000, e.g.
23.1 ÷ 10, 23.1 ÷ 100 and 23.1 ÷ 1000

explain how the decimal point moves when carrying out
such divisions
Ones
1
×
Step 2
12 tenths is equal to 1 whole and 2 tenths. Trade the
1 whole to the ones column and record the 2 tenths in the
tenths column.
Use mental strategies to multiply decimals by 10, 100 and
1000.
Create own 3-place decimal number and multiply by 10, 100
and 1000.
Step 3
Multiply 2 ones by 4 which gives 8, then add the 1 that has
been traded to give 9. Record 9 in the ones column.
Complete examples.
Calculate shopping subtotals, e.g. 5 calculators at $7.65 each?
Strand: Patterns and Algebra
Outcome: PAS3.1a
Strand: Patterns and Algebra
Outcome: PAS3.1a
Number patterns (page 129)
Number patterns (page 129)

identify patterns

continue patterns
Complete tables that show the relationship between the first
and second number, e.g.

write a rule to describe the pattern e.g.
st
1 number
nd
2
number
35
32
23
29
26
17
23
19
1st number
11
2nd number
27
12
13
14
15
29
16
32
Investigate triangular numbers by:
11
Write a rule to describe the function of a ‘function machine’,
e.g.

drawing a sequence of triangular numbers on dot paper

creating a table to show the relationship between the
number of triangles and the number of dots

predict the ‘nth’ term, e.g. the 7th triangular number
Strand: Space and Geometry
Outcome: SGS3.2a
Strand: Space and Geometry
Outcome: SGS3.2a
Circles (page 130)
Circles (page 130)
Recognise, understand and use the terms ‘radius’, ‘diameter’
and ‘circumference’.
Use a compass to construct circles with:

specific radii (3 cm, 25 mm, 2 cm)
Use a compass to construct circles with a 3 cm radius and a
35-mm radius.

labels for radius, diameter and circumference
Draw and label each circle’s radius, diameter and
circumference.
59
Strand: Measurement
Outcome: MS3.2
Strand: Measurement
Outcome: NS1.1
Square metres (page 131)
Kilometres (page 131)
Recognise that:
Refer to a chart to calculate differences in distance by road
and by air between cities, e.g.

km2 is short for square kilometre

100 hectares = 1 km2

1000 m × 1000 m = 1 km
Sydney–Adelaide
2
Refer to a map to list the Australian states and territories in
order of size, e.g. WA = 2 525 500 km 2
Qld. = 1 727 200 km
Road:
1412 km
Air:
1165 km
247 km
Solve problems.
2
Square kilometres
Apply a scale of 1 cm = 200 m to mark an area of 1 km 2 on a
street directory.
Select the best area unit to measure areas, e.g.
Recognise that 1 square kilometre is a square with
dimensions of 1 km
tennis court = m2
Canberra = km
Optional Year 6 Student Book Blackline Master, to be used
with page 131 of the Year 5 Student Book.
2
Given the size of Australia’s states and territories, calculate
the difference in size between them, e.g.
cricket oval = ha
Qld.
NSW
1 727 200 km2
801 600 km2
Recognise that:
10 000m2 = 1 hectare
Convert hectares into square kilometres.
Strand: Chance and Data
Strand: Chance and Data
60
Week 5
Year 5
Year 6
Strand: Number
Outcome: NS3.3
Strand: Patterns and Algebra
Outcome: PAS3.1a
Multiplication methods (page 132)
Number patterns (page 132)

mental strategies, e.g. 23 × 4 think 4 × 20 (80) plus 4 × 3
(12) = 92

Identify a pattern in a table that relates quantity to price.

Write a rule to describe the pattern.
written  2 4 2

Predict the ‘nth’ term, e.g. the price of 8 T-shirts

represent the data as a line graph

×

4
front end, e.g. multiply the hundreds, then the tens and
then the ones, 235 × 6 =   200 × 6 = 1200
Complete a table that relates to the amount of water pouring
into a bath each minute:
30 × 6 = 180
5×6=
30

represent the data as a line graph

predict the ‘nth’ term, e.g. How many litres will be in the
bath after 20 minutes?
1410
Multiplication is commutative
Optional Year 6 Student Book Blackline Master, to be used
with page 132 of the Year 5 Student Book.
Recognise that multiplication is commutative and that it is
sometimes easier to multiply in any order.
Test to see whether division is commutative.
Change the order to make multiplication easier, e.g.
25 × 16 × 4 = 25 × 4 × 16 = 1600
Outcome: NS3.1
Outcome: NS3.4
Rounding (page 133)
Fractions of a collection (page 133)
Round numbers less than 100 to the nearest 10.
Explore different methods, e.g.
of 20
Round numbers less than 1000 to the nearest 100.
Estimate totals by rounding each addend, e.g. two tennis
racquets and a CD player.

Find
of 20 = 4, then
Investigate to show totals between $1600 and $1700.

Find
of 20 = 4, then multiply 4 by the numerator (3) =
= 4 + 4 + 4 = 12
12

Find
× 20 =
60 ÷ 5 =12
Complete examples.
Use own strategies to solve ‘fractions of a collection’
problems.
Rounding
Optional Year 6 Student Book Blackline Master, to be used
with page 133 of the Year 5 Student Book.
Employ rounding to:

add numbers, e.g. 581 + 316 ≈ 

multiply numbers, e.g.
4998 × 6 ≈ 
3.89 × 7 ≈ 
Recognise and use the abbreviation K in place of zeros when
recording thousands, e.g. 7000 = 7K
Strand: Space and Geometry
Outcome: SGS3.3
Strand: Space and Geometry
Outcome: SGS3.3
Making a map (page 134)
Making a map (page 134)
Use a school plan to:
Add details to a map:

create a coordinate grid

use letters A to P to label the horizontal axis

label the coordinates

use numbers 1 to 11 to label the vertical axis

join coordinates to create shapes, e.g. canteen

use coordinates to locate towns, e.g. Orange = F4

identify features at particular coordinates

add transport routes by plotting and joining coordinates

create a scale, e.g. 1 cm = 3 m

design a scale to suit the map
61
Strand: Measurement
Outcome: MS3.4
Strand: Measurement
Outcome: MS3.4
Tonnes, kilograms and grams (page 135)
Mass (page 135)
Investigate strategy of multiplying tonnes by 1000 to convert
tonnes to kilograms, e.g. 4.259 t = 4259 kg
Select from grams, kilograms and tonnes to measure the
mass of items such as a ship, toothpaste and a chicken.
Place the mass of 6 children in order from lightest to heaviest,
e.g. 32 kg, 29.8 kg, 30.5 kg
Convert kilograms into tonnes using decimal notation, e.g.
3563 kg = 3.563 t
Select the most suitable unit to measure various items, e.g.
Investigation
grams
Calculate the value of different piles of coins given the total
mass of the pile and the average mass of each coin.
 matchbox
kilograms  dog
tonnes
Solve problems.
 whale
Solve mass problems, e.g. Eve weighed 29.5 kg last year and
is now 2.4 kg heavier. What is her mass now?
Strand: Chance and Data
Strand: Chance and Data
62
Week 6
Year 5
Year 6
Strand: Number
Outcome: NS3.4
Strand: Number
Outcome: NS3.4
Division of decimals (page 136)
Decimal remainders (page 136)
Model the division process.
Review strategy of expressing remainders as a fraction of the
divisor.
Share 85.8 among 6.
Complete divisions on a calculator to observe that remainders
are expressed as decimals.
Step 1
The 8 tens are shared 6 ways with each person receiving
1 ten. The remaining 2 tens are traded to 20 ones.
Use a calculator to convert remainders into decimals, e.g.
Step 2
There are now 25 ones divided by 6, which gives each
person 4 with a remainder of 1. The remainder is traded to
become 10 tenths.
Solve problems and round decimals to 3 places.
Division of decimals
Step 3
There are now 18 tenths to be divided by 6 which gives
3 tenths.
Optional Year 6 Student Book Blackline Master, to be used
with page 136 of the Year 5 Student Book.
Complete examples.
Complete division of 2-digit decimals by a 1-digit divisor.
Solve average problems based around long-jump scores, e.g.
Use mental strategies to multiply decimals by 10, 100 and
1000.
24.69 m ÷ 3 = 
Calculate individual restaurant bills if amounts such as $96.55
are shared among 5 people.
Use mental strategies to divide decimals by 10, 100 and
1000.
Use mental strategies to determine the best value.
Outcome: NS3.1
Outcome: NS3.1
Negative numbers (page 137)
Negative numbers (page 137)
Complete number sentences by modelling the operations on
a number line, e.g.
Read and interpret a thermometer to calculate differences in
temperature where one temperature is a negative number,
e.g.
10° C and – 5° C = 
Solve problems with the assistance of a number line, e.g.
Frank scored 3 points, lost 7 points and scored 3 points, what
was his final score?
Read and interpret an ‘Indoor Cricket’ scorecard featuring
negative numbers.
Strand: Chance and Data
Outcome: DS3.1
Strand: Space and Geometry
Outcome: SGS3.2a
Collecting data (page 138)
Triangles (page 138)
Conduct a survey which could be used to improve the school
canteen:
Use geometric tools to construct:


an equilateral triangle
create survey questions


an isosceles triangle
identify target group


a scalene triangle
report on responses to survey questions


identify lines of symmetry
write summary statement

analyse survey in terms whether enough people were
surveyed to make the survey reasonable
Strand: Chance and Data
Outcome: DS3.1
Conduct a trial to answer the question, Does the oldest
person run the fastest?
Collecting and presenting data

gather 8 people

record date of birth from youngest to oldest
Optional Year 6 Student Book Blackline Master, to be used
with page 138 of the Year 5 Student Book.

time each person over 50m
Design survey questions to determine new school sports.

answer ‘trial’ question
Survey students and present results in a table.
Create a column graph to represent data.
Write a statement about the data collected.
63
Strand: Measurement
Outcome: MS3.3
Strand: Measurement
Outcome: MS3.3
Cubic metres/centimetres (page 139)
The cubic metre (page 139)
Discuss how the volume of 3 packets or boxes of different
dimensions can be compared when packed with cubic
centimetres.
Construct a cubic metre using available materials.
Follow a set of directions to make a cubic metre out of
cardboard.
Identify objects that are:

less than 1 m3

about 1 m3

greater than 1 m3
Use the ‘homemade’ cubic metre to classify items as:

less than 1 m3 e.g. TV

about 1 m3 e.g. BBQ

greater than 1 m3 e.g. fridge
Use formula volume = length × breadth × height to calculate
the volume of buildings, e.g.
Bank = 40 m × 30 m × 40 m = 48 000 m 3
Strand: Patterns and Algebra
Strand: Patterns and Algebra
64
Week 7
Year 5
Year 6
Strand: Number
Outcome: WMS3.2
Strand: Patterns and Algebra
Outcome: PAS3.1a
Calculator problems (page 140)
Number patterns (page 140)
Use the memory function on a calculator to calculate
shopping bills.
Apply a rule to complete number sequences, e.g.
■ + 17 = ●
Create and solve problems that incorporate the use of a
calculator’s memory function.
■
Match problems with number sentences that are the solutions
to the problems.
1
2
3
4
5
6
●
Write rules to describe patterns
e.g.
27 41 55 69 83  + 14
Create own rule and show relationship between 1st and
2nd numbers in a table.
Shopping problems
Optional Year 6 Student Book Blackline Master, to be used
with page 140 of the Year 5 Student Book.
Apply knowledge from all strands to solve shopping
problems, e.g.
kg of mushrooms at $5.50/kg and 5 kg of potatoes at
$5.50/kg?
Open-ended investigation to find quantities of goods that
match a total.
Solve problems.
Outcome: NS3.4
Outcome: NS3.4
Multiplying and dividing decimals (page 141)
Reducing fractions (page 141)
Multiply 2-place decimals by 1, 10, 100 and 1000, e.g.
Understand that sometimes a fraction’s numerator and
denominator can be divided by the same number to make an
equivalent fraction.

0.45 × 1 = 

0.45 × 10 = 

0.45 × 100 = 

0.45 × 1 000 = 
Complete examples.
Explain how the decimal point moves when carrying out a
series of multiplications like these.
Reduce fractions of $60 into their lowest form, e.g.
Divide decimals by 1, 10, 100 and 1 000, e.g.
Food: $30/$60 =

0.47 ÷ 1 = 
Add fractions then reduce to lowest terms, e.g.

0.47 ÷ 10 = 

0.47 ÷ 100 = 

0.47 ÷ 1 000 = 
Fractions, decimals and percentages
Explain how the decimal point moves when carrying out a
series of divisions like these.
Optional Year 6 Student Book Blackline Master, to be used
with page 141 of the Year 5 Student Book.
Find parts of a group, e.g.
13 of 48 = 
0.25 of 48 = 
50% of 48 = 
Apply knowledge of fractions, decimals and percentages to
divide a bill, e.g. 10% of $240
Solve problems.
65
Strand: Space and Geometry
Outcome: SGS3.1
Strand: Space and Geometry
Outcome: SGS3.1
Cross-sections (page 142)
Cross-sections (page 142)
Create cross-sections:
Create cross-sections:

create 3D shapes using playdough

Use playdough to create a 3D shape.

cut cross-sections with a plastic knife

Use a knife to cut a cross section

draw the exposed face

Sketch the cross-section.
Identify 3D shapes that would have a square, circle, triangle
and rectangle as their cross-section.
Examine a series of shapes and draw what the cross-section
would look like.
Strand: Chance and Data
Outcome: DS3.1
Strand: Chance and Data
Outcome: DS3.1
Mean scores (page 143)
Sector graphs (page 143)
Understand that the mean can be calculated by adding all the
scores and dividing by the number of scores.
Read and interpret a graph,
e.g. Do more students play rugby than Australian Rules?
Find the mean for groups of cricket batting scores, e.g. Sam:
3, 7, 8, 2 becomes (3 + 7 + 8 + 2) ÷ 4 = 5
Find the mean price for 5 pairs of shoes.
Interpret a set of test results to:

calculate the mean

identify scores below the mean
Interpret a column graph to:

identify highest/lowest temperature

mean temperature

days where temperature was below the mean
Conduct own survey to compare with presented data.
Read and interpret a sector graph broken into 36 sectors,
each representing 10 people.
Complete a sector graph with 36 sectors each representing
100 people.
Data investigation
Optional Year 6 Student Book Blackline Master, to be used
with page 143 of the Year 5 Student Book.
Calculate the mean for sets of scores, e.g.
185, 105, 140, 150 mean = 145
Investigate the worldwide price of hamburgers:
Strand: Measurement

rank countries by price

calculate the mean

graph data
Strand: Measurement
66
Week 8
Year 5
Year 6
Strand: Patterns and Algebra
Outcome: PAS3.1b
Strand: Patterns and Algebra
Outcome: PAS3.1b
Inverse operations (page 144)
Equivalent number sentences (page 144)
Use multiplication to check that the quotient in a number
sentence is correct, e.g.
Solve equations by calculating the value of missing numbers,
e.g.
12 ÷ 4 = 3 check  3 × 4=12
If ■ = 5, solve 3 × ■ = ▲
Use multiplication to check that division algorithms are
correct.
Work backwards to supply the missing decimal in number
sentences, e.g. 5 × =  3.5
Create number sentences to solve problems, e.g.

If you multiply me by 3 and add 4 the answer is 19
1
4
×
4
5
6
  × 3 + 4 = 19
Inverse operations
Optional Year 6 Student Book Blackline Master, to be used
with page 144 of the Year 5 Student Book.
Use rounding to estimate the quotient when dividing.
Use inverse operations, such as multiplication and division to
check answers, e.g.
5 3 7 6
×
3
316128
16128
Work backwards through number sentences to identify the
1st number.
Work backwards through the volume formula to determine
dimensions of a shape.
Strand: Number
Outcome: NS3.3
Strand: Number
Outcome: WMS3.4
Division (page 145)
Justifying a solution (page 145)
Use a calculator to convert fractions to decimals, e.g.
Solve problems and give valid reasons to support the
solution.
becomes 27 ÷ 100 = 0.27
Strategies could include:
Solve divisions as traditional algorithms and check using a
calculator.
Solve divisions on a calculator and note repeating decimals,
e.g.

rounding

operations (+, –, ×,÷)

tree diagrams

diagrams
Use a calculator to solve problems.
Calculator multiplication and division
Optional Year 6 Student Book Blackline Master, to be used
with page 145 of the Year 5 Student Book.
Apply exchange rates to convert foreign currency into A$,
e.g. NZ$410 ÷ 1.21 = A$338.84
67
Strand: Space and Geometry
Outcome: SGS3.2a
Strand: Space and Geometry
Outcome: SGS3.2a
Diagonals (page 146)
Diagonals (page 146)
Recognise that a diagonal joins two non-adjacent vertices of
a polygon.
Recognise that a diagonal joins two non-adjacent vertices of
a polygon, e.g. a rectangle has two diagonals.
Add diagonals to:

quadrilaterals

a pentagon

a hexagon
Add diagonals to polygons, e.g. square, rectangle, trapezium,
pentagon, hexagon, heptagon
Recognise that there is a pattern that relates the number of
sides a polygon has to the number of diagonals.
Explain why the number of diagonals increases as the
number of vertices increases.
Strand: Measurement
Outcome: MS3.5
Strand: Measurement
Outcome: MS3.5
Time zones (page 147)
Time zones (page 147)
Recognise Australia’s time zones and the differences
between them.
Recognise that Australia has 3 time zones.
Refer to a map of Australia with the time zones marked in
order to complete a time-zone grid.
Complete time zone tables expressed in 24-hour time.
Western
standard time
Central
standard time
Refer to a world map to:
Eastern
standard time
1600
1630
1800

observe meridians of longitude

recognise that each meridian represents 15° or one hour

locate Greenwich

recognise that places west of Greenwich are behind GMT,
places east of Greenwich are ahead of GMT

calculate times around the world
1900
Draw hands on clocks to show corresponding time in
Australia’s capital cities.
Examine daylight savings. Show the time in other states
when daylight savings is operating in NSW.
Strand: Chance and Data
Strand: Chance and Data
68
Week 9
Year 5
Year 6
Review all outcomes
Review all outcomes
Diagnose strengths and weaknesses.
Diagnose strengths and weaknesses.
Provide remedial and extension activities where necessary.
Provide remedial and extension activities where necessary.
69