MATHS OVERVIEW-YEAR 5 SEMESTER 2
CONTENT DESCRIPTORS
Number & Algebra
YEAR LEVEL
Year 5
DURATION
Semester 2
LINKS TO OTHER LA’s
ARTs
ACMNA291 Use efficient mental and written strategies and apply appropriate digital technologies to solve problems
ACMNA099 Use estimation and rounding to check the reasonableness of answers to calculations
ACMNA106 Create simple financial plans
ACMNA107 Describe, continue and create patterns with fractions, decimals and whole numbers resulting from addition and subtraction
ACMNA102 Compare and order common unit fractions and locate and represent them on a number lin
Measurement & Geometry
ACMMG112 Estimate, measure and compare angles using degrees. Construct angles using a protractor
ACMMG111 Connect three-dimensional objects with their nets and other two-dimensional representations
ACMMG108 Choose appropriate units of measurement for length, area, volume, capacity and mass
Statistics & Probability
ACMSP116 List outcomes of chance experiments involvingequally likely outcomes and represent probabilities of those outcomes using fractions
ACMSP117 Recognise that probabilities range from 0 to 1
By the end of Year 5, students solve simple problems involving the four operations using a range of strategies. They check the reasonableness of answers using estimation and rounding.
Students identify and describe factors and multiples. They explain plans for simple budgets. Students connect three-dimensional objects with their two-dimensional representations.
They describe transformations of two-dimensional shapes and identify line and rotational symmetry. Students compare and interpret different data sets.
Students order decimals and unit fractions and locate them on number lines. They add and subtract fractions with the same denominator. Students continue patterns by adding and
subtracting fractions and decimals. They find unknown quantities in number sentences. They use appropriate units of measurement for length, area, volume, capacity and mass,
and calculate perimeter and area of rectangles. They convert between 12 and 24 hour time. Students use a grid reference system to locate landmarks. They measure and construct different
angles. Students list outcomes of chance experiments with equally likely outcomes and assign probabilities between 0 and 1. Students pose questions to gather data, and construct data
displays appropriate for the data.
MAG Planning Semester 1 Year 5
TOPIC
5.2.21-1
Learning
journal
TOPIC
CONTENT
DESCRIPTOR
Applicable to all
content descriptors
CONTENT
DESCRIPTOR
KEY IDEA
The proficiency strands
Understanding, Fluency, Problem
Solving and Reasoning are an
integral part of mathematics
content across the three content
strands:
KEY IDEA
ASSESSMENT
Various examples
ASSESSMENT
INVESTIGATION
STUDENT
JOURNAL
Frayer Model
Beach Ball Activities
INVESTIGATION
RESOURCES
Maths learning journal
STUDENT
JOURNAL
RESOURCES
1
Applicable to all
content descriptors
5.2.21-2
TOPIC
5.2.22
TOPIC
CONTENT
DESCRIPTOR
ACMNA291 - Use
efficient mental and
written strategies
and apply
appropriate digital
technologies to
solve problems.
CONTENT
DESCRIPTOR
ACMMG112
Estimate, measure
and compare angles
using degrees.
Construct angles
using a protractor
The proficiency strands
Understanding, Fluency, Problem
Solving and Reasoning are an
integral part of mathematics
content across the three content
strands:
KEY IDEA
It is important to explicitly teach
thinking skills as a means of
equipping all students with
important strategies that will assist
students to be life-long learners.
Various examples with
Inspiration
ASSESSMENT
Indicators on progression
chart
KEY IDEA
Pre-ASSESS
ASSESSMENT
How do you
measure and
draw angles with
accuracy and
precision?
What’s a Line.
Re-engage
with concepts
of line
Focus students’ attention on
the use of shapes in the
environment.
Ask students to recall the
different geometric shapes
(Quadrilaterial family) and
list the properties they have
studied in previous lessons.
Ask them to also describe
the different types of lines
(parallel, perpendicular,
intersecting).
5.2.23
TOPIC
CONTENT
DESCRIPTOR
KEY IDEA
Pre-ASSESS
ASSESSMENT
5.2.24
ACMMG111
connect threedimensional objects
with their nets and
Identify
quadrilaterals by
attributes.
Distinguish
The purpose of
this activity is
to relate the
term
Building Bridges:
Quadrilaterals.
http://www.scootle.e
du.au/ec/viewing/L1924/ind
Frayer Model
Beach Ball Activities
INVESTIGATION
iPad or digital device
Maths learning journal
STUDENT
JOURNAL
Various
INVESTIGATION
FISH
FISH pockets (optional)
Learning Journal
QR code reader
STUDENT
JOURNAL
Ask learners to identify the
subject of this picture and
the 3D objects used by
Picasso.
RESOURCES
FISH Problem Solving
http://www.mrbartonmaths.com
/resources/Treasure%20Hunts%2
0pdf/Measuring%20Angles%20Tr
easure%20Hunt.pdf
Links to Kandinsky images
http://www.artchive.com/artchiv
e/K/kandinsky.html
Body language vocab
http://www.youtube.com/watch
?v=THhMqLWdcV8
IWB protractor
Thinking ladder http://www.tes.co.uk/ResourceD
etail.aspx?storyCode=6351709
TLF MO17691 This is a free iPad
app for measuring with a 180
degree protractor
Do all shapes have angles
which add up to 3600?
INVESTIGATION
RESOURCES
STUDENT
JOURNAL
RESOURCES
FISH Problem Solving
grid paper
Ruler
individual whiteboards (with grid)
2
other twodimensional
representations
TOPIC
5.2.25
CONTENT
DESCRIPTOR
Connect threedimensional objects
with their nets and
other twodimensional
representations
ACMMG111
quadrilaterals
from nonquadrilaterals.
Analyze
quadrilaterals to
identify specific
members
(square,
rectangle,
trapezoid,
parallelogram
and rhombus) of
the group.
relate common
3D shapes and
their nets to
quadrilaterals
quadrilaterals
to ‘4’ - 4 sides,
4 corners.
Introduce the
term
quadrilateral
using
http://goo.gl/q
zjvOQ
on the
Interactive
Whiteboard.
ex.html
Investigates properties of
simple quadrilaterals used
to make a bridge. Links with
graphing, number patterns
and multiples.
and pens
iPad Apps - Dictionary.com,
Kahoot.it
2D shape cut outs (pictures of
various 2d shapes to sort)
chart paper and pens
geoboards and dot paper
rubber bands
3d shapes
3D nets
KEY IDEA
Pre-ASSESS
ASSESSMENT
INVESTIGATION
triangles are part
of the polygon
family of shapes
triangles can be
classified by
their interior
angles, as right,
acute obtuse
and all interior
angles add to
1800
triangles can be
classified by the
length of their
sides as
equilateral,
isosceles, and
scalene
identifying the
relationship
between plane
triangles and
solid 3D shapes
To assess
learners' prior
knowledge,
read aloud The
Greedy
Triangle by
Marilyn Burns.
Option 1
Choose any 2 net solid from
the 9 possible, and
assemble. (two pieces are
needed to complete one 3D
shape) Display with it name.
Option 2
Choose a triangular net solid
from the 9 possible,
assemble and name. (two
pieces are needed to
complete one 3D shape)
Display with its attributes
listed
The different side lengths in
triangles.
Using the website (National
Library of Virtual
Manipulatives – 3-5 Grade
Geometry – Geoboards) the
teacher will model making
different types of triangles.
http://nlvm.usu.edu/en/nav
/frames_asid_172_g_2_t_3.
html?open=activities&from
=topic_t_3.html
STUDENT
JOURNAL
RESOURCES
SH problem solving
rgrid paper
protractors
string
geoboards
dot paper
rubber bands
Frayer Model Template
paddlepop or match sticks
page of triangles (different sizes
and types)
Scootle-Shape Sorter activity
The Greedy Triangle by Marilyn
Burns.
3
TOPIC
5.2.26
CONTENT
DESCRIPTOR
Use estimation and
rounding to check
the reasonableness
of answers to
calculations
ACMNA099
KEY IDEA
Recognising the
usefulness of
estimation to
check
calculations
applying mental
strategies to
estimate the
result of
calculations,
such as
estimating the
cost of a
supermarket
trolley load
engaging
students in
reasoning and
thinking about
solutions to
problems and
the strategies
needed to find
these solutions
are core parts of
the Mathematics
curriculum.
Purposefully
creating the a
classroom
culture where
mathematical
thinking is part
of the daily
routine
Pre-ASSESS
Estimation as
a skill for life
ASSESSMENT
INVESTIGATION
Option 1-Estitmating the
Cost
The learner selects a
supermarket catalogue
page.
Three items are chosen to
be purchased and the price
is rounded to the nearest
dollar and then given an
estimated cost of their
shopping trip.
Option 2
The learner selects a
supermarket catalogue
Four items are chosen to be
purchased for school lunch
on two days of the week and
the price is rounded to the
nearest dollar. The amount
of change
Option 3
The learner selects a budget
for school lunches for a
week including one day of
tuckshop. The amount is
written down and given to
the teacher. This amount
cannot be changed.
The leaner will: estimate the
amount your groceries are
going to cost
purchase and calculate the
cost of items rounded to the
nearest dollar
produce a menu for 4 school
lunches and 1 tuckshop day
calculate total cost exactly
and whether the original
estimation was under or
Rounding numbers for
newspaper headlines. The
government reports
spending $33,883,641.31 on
law inforcement in the past
financial year. Draw a
number line to illustrate.
STUDENT
JOURNAL
RESOURCES
•
•
•
•
•
•
FISH
Scootle
Number lines
Number expanders
Supermarket brochures
Maths Charts app
4
over estimated
give an example of when
under and over estimating
might be inappropriate
TOPIC
CONTENT
DESCRIPTOR
Choose appropriate
units of
measurement for
length, area,
volume, capacity
and mass
(ACMMG108)
5.2.27
TOPIC
CONTENT
DESCRIPTOR
Create simple
financial plans
(ACMNA106
5.2.28
TOPIC
CONTENT
KEY IDEA
Pre-ASSESS
ASSESSMENT
INVESTIGATION
choose
appropriately
from a range of
strategies
including
estimation, and
knowledge of
standards
measures to
approach various
measuring tasks
with confidence
and accuracy.
Volume or
Capacity?
The purpose of
this activity is
to clarify the
difference
between
capacity and
volume.
Option 1
What is the volume of a
rectangular prism that has
the following dimension.
Option 2
Provide students with the
following task:
Figure out which number
goes in which spot.
Complete the puzzle.
What is the volume of the
cereal box?
Option 3
Build a tower of snap cubes.
Make the first five shapes
into a pattern. Use between
10 to 20 cubes. What will
your pattern look like?
What is the volume of your
tower?
KEY IDEA
Pre-ASSESS
ASSESSMENT
INVESTIGATION
simple
calculations of
percentage
select and use
connections
between key
percentages and
fractions to
assist in solving
problems
Out of a
hundred
We meet and
use percentage
in many
aspects of our
lives. The word
percent comes
from the Latin
per centum
meaning ‘for
each hundred’.
Learners are introduced to
the abstract art of Dutch
painter Piet Mondrian. They
use his characteristic style.
To create their own artwork.
KEY IDEA
Pre-ASSESS
here are 100 squares in a
grid. Colour the grid
• 6% red
• 10% blue
• 25% green
• 1% black
• 9% yellow
• 3% navy
• 17.5 pink
• 2.5% orange
• 9% dark green
What percentage of the grid
remains white?
ASSESSMENT
STUDENT
JOURNAL
•
•
•
•
•
•
Option 3
Build a tower of snap cubes.
Make the first five shapes
into a pattern. Use between
10 to 20 cubes. What will
your pattern look like?
What is the volume of your
tower?
INVESTIGATION
RESOURCES
STUDENT
JOURNAL
FISH
Scootle
Variety of containers
Measuring cups and jugs
MABS
Maths glossary
RESOURCES
FISH
* 100 grids (large and small grids
on a sheet)
* maths pads
* activity worksheets
* collection of catalogues
* online resources
• Essential Facts and tables (text)
STUDENT
RESOURCES
5
DESCRIPTOR
ACMSP116 List
outcomes of chance
experiments
involving equally
likely outcomes and
represent
probabilities of
those outcomes
using fractions
ACMSP117
Recognise that
probabilities range
from 0 to 1
5.2.29
JOURNAL
The likelihood of
winning simple
games of chance
by considering
the number of
possible
outcomes and
the consequent
chance of
winning.
Investigate the
probabilities of
all outcomes for
a simple chance
experiment and
verifying that
their sum equals
1.
Talking about
Probability
Learners need
to be able to
describe the
probability of
different
events using
words. Words
like probable,
improbable,
likely and
unlikely are
needed to do
this clearly.
Make up a
probability
scale with the
students,
clearly showing
where the
words might
fit.
Option 1
Looking at examples.
Learners play a number of
games which have been
devised by someone else,
discover faults and shortcomings and suggest
improvements. (This
involves the strategic skills
of 'understanding a
situation' and 'identifying
relevant factors in it'.)
Option 2
Developing your own ideas.
Learners share their ideas
within groups, then decide
on a rough plan for their
own game. (This involves
'listing alternatives',
'estimating resources
required', 'making decisions'
and ’planning'.)
Making your game. Each
group of learners produces a
design, then makes it up and
checks the finished version.
(This involves 'implementing
a plan', 'selecting and using
appropriate mathematical
techniques' and 'checking
and testing'.)
Option 3
Testing and Evaluating. The
groups exchange games and
test them. When they are
returned, each group reassesses its own game in the
light of another group's
comments. (This involves
'evaluating the outcome of a
plan in action'.)
Learners then are told there
are 12 counters in the sock
and have to estimate how
many of each colour there
are. Points can be awarded
for every colour correct.
The difficulty can be altered
by changing the number of
colours or the number of
counters.
•
•
•
FISH
A Very Improbable Story
by Edward Einhorn
socks (either paper cut
outs or real ones)
6
TOPIC
5.2.30
CONTENT
DESCRIPTOR
Describe, continue
and create patterns
with fractions,
decimals and whole
numbers resulting
from addition and
subtraction
ACMNA107
Compare and order
common unit
fractions and locate
and represent them
on a number line
ACMNA102
KEY IDEA
Pre-ASSESS
ASSESSMENT
INVESTIGATION
how to identify
simple, common
and mixed
number
fractions.
- comparing,
ordering and
simplifying
different
combinations of
parts of a whole
- identifying links
between
different parts of
a whole and how
this can be
represented.
It would be a
good idea for
teachers to
revise/look
over the
previous MAG
5.1.7 and
discuss what
has been
covered and
could be used
for introducing
mixed number.
Option 1
Learners to sort fraction
cards on a number line
Option 2
Learners are asked to shade
in the correct amount on
these shapes and sort the
fractions in descending
order.
Option 3
‘The National History
Museum has collected 125
dinosaurs. George has
collected 3/5 of this amount.
How many dinosaurs has
George collected? Prove
your answer using a
numberline
Option 1
“Kate’s Kitchen sells pizza
pieces. Each pizza is cut into
4 equal pieces. At the end of
the day, the computer
shows Kate has sold 13
pieces of pizza. How much
pizza has she sold?”
Option 2
“Imagine 19 pieces of pizza
where each piece is a fifth of
a pizza. How many pizzas is
this?” What other fraction
pieces could the pizza be cut
into and how would this
change the answer. Give
one example.
Option 3
Complete the diagra
STUDENT
JOURNAL
RESOURCES
FISH
calculators
grid paper
coloured brenex squares
fraction strips/cards/pieces
(school box)
counters
toothpicks
http://eisforexplore.blogspot.com.
au/search/label/fractions
Shaped accordian book idea
7