02
Volume 24 Term 2 2009
ISSN 0816 9349 Registered by Australia Post Publication Number VBG 2502
PrimeNumber
In this issue
Feature Article
'Orchestrating the End' of Mathematics Lessons by Jill Cheeseman
Lesson Starters
Whiz Kid by Jaclyn Osborne
This Works for Me
A Chest of Maths Treasures by Julie Austin
In this issue
02
Feature Article
3 ‘Orchestrating the End’ of Mathematics Lessons
Jill Cheeseman
Teacher Talk
7 The Real Cost of a Day at Footy
Meridith McKinnon
Lesson Starters
8 Whiz Kid
Jaclyn Osborne
Poster
10 Food Maths
Photograph courtesy Peter Henzel
Resource Review
Editor
Suzanne Gunningham
Editorial Board
Jill Brown
John Gough
Marj Horne
David Leigh-Lancaster
David Shallcross
Design
Patricia Tsiatsias
Cover photograph
Courtesy of Barry Johnston
13 Global Food and Maths
Ian Lowe
This Works For Me
14 A Chest of Maths Treasures
Julie Austin
Feature Article
16 Ideas for Teaching Place Value
Prof. Peter Sullivan and Julie Millsom
Production
Publishing Solutions Pty Ltd
www.publishing-solutions.com.au
Resource Review
Contributions and
Correspondence
The Editor, Suzanne Gunningham
Email: [email protected]
Membership and Journal
Subscriptions
The Executive Officer
Simon Pryor
MAV
Email: [email protected]
The Mathematical Association
of Victoria
Cliveden
61 Blyth Street
Brunswick VIC 3056
Tel: +613 9380 2399
Fax: +613 9389 0399
Email: [email protected]
Web: www.mav.vic.edu.au
ABN: 34 004 892 755
18 Making Sense of Consumer and Financial Literacy
Fiona May
Teacher Talk
20 Maths Talent Quest – Diary of a Year Six Student
James Hogan
Answers
IBCAnswers to Back Cover puzzles from Term 1,
2009 edition (inside back cover)
Prime Number may contain paid advertisements for third party products and
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For more information about advertising in Prime Number, please contact the
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Prime Number Volume 24, Term 2 2009
1
Editorial
Sue Gunningham
In this editorial I mourn the passing of my long-term partner and best friend Barry Johnston,
who perished in the Kinglake bushfires during February 2009. Barry had contributed many of
the cover and centrefold photos used in Prime Number since I became editor. He provided me
with ideas, proof-read my work and gave me focus. My onward journey will be much harder
without him beside me.
This edition of Prime Number once again contains a smorgasbord of ideas and activities for
use in the primary classroom. The feature article by Jill Cheeseman serves as a reminder
of the need to think about and plan for an effective conclusion to each mathematics lesson.
Jill explains why the term ‘share time’ underplays the complexity and importance of this
part of the session.
Peter Sullivan and Julie Millsom build on their previous article by providing further
suggestions for teaching place value and Julie Austin describes an innovative way of
engaging students in mathematics while at the same time developing home–school links.
The rise in consumerism and an increasingly complex global economic environment has
focused attention on how to better equip consumers to make informed decisions regarding
money and to manage their money effectively. An article by Fiona May explains some
funding initiatives aimed at supporting consumer and financial literacy in schools.
Some insight into the true cost of living is found in a delightful article about a day at the
footy, while the centrefold provides a stimulus for cross-curricula investigations involving
mathematics and food.
As always, I hope that you find this edition of Prime Number a valuable support to
your teaching. I would be very pleased to receive your contributions of articles, photos,
suggestions or letters of support.
Sue Gunningham
Editor
Using the front cover to stimulate mathematical thinking
1.How many holes are on the entire Chinese Checker game-board?
2.Describe any relationship between the number of game-pieces and the number of
empty spaces.
3.What percentage of all the game-pieces shown are the black game-pieces?
4.Design a similar game-board where each player has 6 game-pieces rather than 10.
2
Prime Number Volume 24, Term 2 2009
Jill Cheeseman lectures in primary
mathematics education at Monash
Univeristy.
‘Orchestrating
the End’ of
Mathematics Lessons
Drawing mathematics lessons to a close
is important with current approaches to
mathematics education. This is difficult
to do well because it involves much more
than simply restating the mathematics
addressed. Children are often encouraged
to reflect on their learning and to explain
or describe their strategic thinking.
The end of the session also offers the
opportunity for teaching after children have
had some experience of the mathematics
concept. Ideas can be drawn together
explicitly to help children see the purpose
of the session.
Why focus on lesson endings?
Mathematics teaching and learning has
changed. In recent times mathematics
lessons have become more complex in
character and diverse in style. When I was a
child the style was quite straightforward and
usually the same each day. My mathematics
teacher explained some mathematics to the
class and demonstrated a technique which
students then used to complete a set of
exercises. The answers were corrected and
more examples were set as homework.
Today there is much less expository
teaching and children are expected to
behave as young mathematicians. Teachers
set up learning opportunities with ‘rich
tasks’ and expect students to grapple with
the mathematical ideas that are presented
in these tasks. Individual children respond
differently to problems and teachers
encourage a range of strategic thinking by
students. Teachers know that solution paths
to the same task are often different. Often
the teacher moves around the classroom
questioning individuals and groups about
their thinking and engaging students in
mathematical discussion. There is a need
to bring the whole session together at some
stage. With younger children this usually
happens at the end of the lesson.
Feature
Article
Jill Cheeseman
Focusing on the end of the
lesson
Most teachers are very skilled at
introducing a task and having children
engage with the mathematics they have
selected for the day. They are also very
skilled at monitoring, questioning,
explaining and generally teaching children
by supporting their thinking as they engage
with the task. However when it comes to
pulling the mathematics lesson together at
the end of the session, some teachers feel
less than confident about their skills.
As part of the Early Numeracy Research
Project (ENRP) (Clarke, et al., 2002)
professional development program, an
anecdote from a classroom was used to
stimulate discussion about the purpose
and essential features of the ‘the end of
the lesson’. The anecdote appears on the
following page.
After a conversation about the lesson two
additional questions were used to focus
further discussion. These were: “Why do we
get the children together at the end of the
mathematics lesson?” and “What are some of
the features of a good ending to a lesson?”
Ideas from the teacher-participants are
summarised below:
Purposes: Why do we get the
children together at the end of
the mathematics lesson?
• Gather evidence for a general finding,
conclusion or solution
• Summarise the work of the session
• Illustrate the central idea with work
samples
• Return to the lesson’s purpose and
clarify the aim
• Raise a general point from different
activities
• Raise possibilities for future
mathematical thinking
Prime Number Volume 24, Term 2 2009
3
•
•
•
•
•
•
•
•
•
•
Share common discoveries
Celebrate children’s learning
Summarise
Learn from each other
Use children’s natural language to
explain the mathematics
Have children think and analyse the
mathematics of the session
Have children think about and articulate
how they work things out
Take ideas further to extend thinking
Provide opportunity to assess student
learning
Allow for teacher evaluation of session
effectiveness
Features of a good ending
• Focus on the mathematics learning
and may explicitly address the ‘big
mathematical idea’ of the session
• Develop with students a sense of
completion
• Short and targeted
• Challenge and raise new challenges
• Address different mathematical learning
needs within the class
• Offer insights
• Reiterate the purpose of the mathematics
session
• Give positive feedback for good ideas
A Story From The Classroom
How many chocolates?
The teacher constructed some boxes which could hold 24 ‘chocolates’.
The teacher held up a box in one hand and a sample chocolate in the other. The students were
asked to estimate how many chocolates would be in the box and write it down.
The students were told, “Soon I will give you an empty box and three chocolates. How could you
work out how many chocolates would be needed to fill the box?” The students in groups then
discussed how they would go about solving the task.
The groups of students were then given their box and three chocolates and invited to implement
their method.
The point of the activity is basically to illustrate the multiplicative nature of the problem. In other
words, even though it is possible to solve the problem by an additive method, by simply estimating
and counting up the chocolates, a more efficient way is to work out the number of rows and the
number in each row and to multiply.
During the conduct of the activity the teacher noted a particular child who was using a calculator
to work out the answer. The reason for choosing that student was to focus discussion on the
mathematical point.
The student was then asked to explain to the class how she went about solving the problem. She
explained how she had worked out there were four in each row and how she worked out there were
six rows, and that she then multiplied using the calculator.
The teachers asked her why she chose to multiply. She said that there are four groups of six.
Another student volunteered the information that it could also be thought of as six groups of four.
There were other students who said there are two ways of doing the same thing.
The teacher then explained to the students that one way to work out the answer was to consider
the number of rows and the number in each row and think of them as groups and so the answer
can be found by multiplying.
Ideas for discussion:
Why did the teacher select only one student to report back?
Why was the work of only one student focused on in the lesson discussion?
4
Prime Number Volume 24, Term 2 2009
Some useful teaching strategies
to ‘cut to the chase’
phrase clearly underplays the complexity
and importance of this part of the session.
Two strategies were presented to the ENRP
participants for general consideration. The
two strategies were:
Sharing implies everyone contributing
something. This may not be the case,
certainly at the end of the lesson where it
would be unwieldy for every child in the
class to report.
1.As a preliminary statement to a sharing
session one project teacher said “I don’t
want you to tell us what you did today,
because we all saw that – tell us what
you learned today.”
2.Another project teacher kept a book.
It was plain paper bound together.
After reporting results of the morning’s
findings, the children decided which few
‘important ideas’ they wanted to write
in their book. The teacher modelled the
first important idea then wrote a couple
of others suggested by her children.
A variety of closure techniques was thought
to be more interesting than using the same
strategy every day.
Sharing time or plenary or
what?
I think we must be careful in referring to the
end of the mathematics lesson as a ‘sharing
time’ even in casual conversation, as the
Fleetingly children may share their work by
simultaneously showing it to each other in
a ‘sitting circle’ or forming work pages into
the pages of a class book. The book is then
read to the whole class as a summary of the
session. However it is rare for every child to
have the chance to ‘share’ on a single day.
Often teachers select individuals to describe
their mathematical thinking so that with
two or three speakers a range of strategic
approaches to a task can be covered.
Maybe the end should be called ‘selected
report back’.
Sharing also has the sense of children
recounting what they did during the lesson.
This is of much less interest than the
mathematical learning that has taken place.
The shaping and modelling of reflections
is far more complex and is best described
Prime Number Volume 24, Term 2 2009
5
by such words as ‘explaining’, ‘showing’,
‘justifying’ and ‘demonstrating’. Maybe
this part of the lesson should be called
‘explaining time’.
In conclusion
Whichever way it is expressed, the critical
issue is to think about drawing mathematics
lessons to a close in the most effective
and interesting manner. It is difficult to
do well and quite complicated because it
involves much more than simply restating
the mathematics. It encourages children
to reflect on their learning and to explain
or describe their strategic thinking. The
end of the session gives the opportunity
for teaching after children have had some
experience with a mathematical concept. It
can draw ideas together and help children to
see the purpose of the session.
Deciding how to conclude the lesson
requires forethought and planning but it
also requires some last minute modifications
6
Prime Number Volume 24, Term 2 2009
during the lesson. These adjustments are
made after watching children and listening
to their mathematical thinking so that
their ideas can be incorporated into the
wrap-up. It involves using elements of
the children’s thinking to focus on the
intended mathematical learning of the
session. Bringing mathematics sessions to
a conclusion is an important, complex and
creative teaching skill.
Reference
Clarke, D. M., Cheeseman, J., Gervasoni,
A., Gronn, D., Horne, M., McDonough, A.,
et al. (2002). Early Numeracy Research Project:
Final report, February 2002. Fitzroy, Victoria:
Australian Catholic University, Mathematics
Teaching and Learning Centre.
NOTE: A transcript of the complete article
‘Orchestrating the End’ of Mathematics
Lessons is available via the MAV website at
http://www.mav.vic.edu.au/pd/confs/2003/
index.html
The Real Cost of a
Day at Footy
Meridith McKinnon is an Education
student at Deakin University.
Engaging students in real-life class
scenarios for learning maths can often
bring unprecedented outcomes into the
classroom. In a classroom with a broad
range of learning abilities and socioeconomic backgrounds, teaching the
concept of ‘Money’ can lead to a lengthy
student discussions as I found during my
teaching practicum. I planned the following
lesson as a re-introduction to the concept
of Money and related it to the pending AFL
Football Finals where students would be
contemplating what a day at the football
would cost them.
This lesson not only had students adding,
subtracting, multiplying and estimating
costs, but possibly even more importantly,
it raised these students’ awareness of
budgeting, and an even deeper concept
of where money comes from. The class
consisted mostly of fiercely competitive boys,
situated in a rural school where football is
prominent in their sporting and school life.
This is a story of how the lesson went.
With Football Finals approaching the class
discussed the pending games and where they
were going to be played. We discussed the
crowds, car parking and food stalls. I asked:
— How much does a day at the footy cost
your family?
I initially prompted discussions based
on a certain amount of money that their
parents might have for the day. As a class,
Teacher
Talk
Meridith McKinnon
we listed how this money could be divided
up for different purchases. The children’s
perception of their parent’s wallet was very
interesting, as most saw it as bottomless.
No budgeting; just what they wanted, when
they wanted it.
But one boy quietly sat and listened as most
of the class spouted about how many pies,
cokes, lollies they had, or didn’t have. When
I asked him to contribute he had this to say:
— He had considered the entry fee for the
family car, the cost per person entry fee,
the raffle at the gate, the cost of fuel to get
to the game, the fact that his mother took
the Saturday off work (no wages) to watch
his older brother play in the finals and then
considered how his family packed their
lunch, but allowed a treat.
It took some prompting for him to divulge
all this information, but there was silence
from his peers while he did. As I prompted
him to go further I praised him for his detail
and we listed his expenses on the board.
The rest of the class then began to revise
their original thinking and added some
of the extra items mentioned to their own
lists. They were eventually amazed at how
much the day REALLY cost.
Lateral thinking had spread throughout the
class and enabled the students to see the
bigger picture. I was impressed with their
depth of engagement stemming from the
use of a real-life issue involving maths.
Prime Number Volume 24, Term 2 2009
7
Lesson
Starters
Whiz Kid
Jaclyn Osborne
This is an interactive game that is similar to
the letter-spelling game “Hang the Butcher”,
the number-game “Guess My Number”, the
word-guessing game “Dictionary”, or the codeguessing game “Mastermind”. One player
makes a secret rule (equivalent to an algebraic
formula), and the other players take turns to
ask number-based questions that each generate
an answer based on the secret rule. The
pattern of the answers will eventually reveal
the rule, through simple problem solving.
The game is suitable for Year 4 students but
could be adapted for students at other levels.
Players
Three or more players
Materials
One 12-sided die or a spinner numbered
1 to 12 or a pack of 52 cards with Ace = 1,
J = 11, Q = 12, K = 12.
Pencils, paper and a calculator (optional).
Playing
Students form groups of five or six and sit
in a circle.
One player is nominated as the ‘Whiz Kid’
for the first round.
He or she sits in the middle of the circle
with a dice and calculator.
The Whiz Kid rolls the dice. Using the
number rolled, the Whiz Kid must apply
two different arithmetic processes on the
number and tell the other players the
resulting number.
For example, when the number 10 is rolled;
the Whiz Kid can multiply 10 by 3 and
then add 4 so the number becomes 34.
That is, the (secret) process is: Multiply the
Called Number by 3, then add 4, and state
the result or Answer.
The Whiz Kid tells the other players that
10 has become the number 34.
8
Prime Number Volume 24, Term 2 2009
Jaclyn Osborne is an Education
student at Deakin University.
The process must involve two different
mathematics operations and only use the
numbers 1-12. (The Whiz Kid may use a
calculator to check the calculations with the
input numbers, and must also secretly write
down the two secret processes on a hidden
piece of paper so they are not forgotten).
Game play starts when a player from the
circle gives the Whiz Kid a Called Number
between 1 and 12 to process. The Whiz Kid
works out what the resulting answer will
be using the two secret processes on the
Called Number and reports: “Your number
was turned into … by the secret rule”.
As playing proceeds, a player may
nominate to become a ‘Would-Be-Guesser’.
The Whiz Kid then asks the ‘WouldBe-Guesser’ to say what the number …
becomes, using the Whiz Kid’s secret rule.
If the ‘Would-Be-Guesser’ player is correct,
the final stage is for the Would-Be Guesser
to state what he or she thinks the two secret
processes (the rule) must be. If the Would-BeGuesser does this correctly, he or she is the
winner and becomes the next Whiz Kid.
If the Would-Be-Guesser is not correct, the
game continues until the secret process is
worked out, OR ALL the (whole) numbers
between 1 and 12 have been used.
Scoring one game
The successful Would-Be-Guesser scores
5 points.
The Whiz Kid scores the number of
numbers (from 1 to 12) used to work out
the secret rule, with a maximum possible
score of 12 points.
Winning
Play continues until ALL players have been
a Whiz Kid, or one player reaches a score
of 100, and wins the whole game, or the
highest score after an agreed time wins the
whole game.
Food Maths
The picture shows a family in Germany. In front of them is all the food they
buy, and eat, in a typical week. This family spends about $700 (Australian)
per week on food. Their favourite foods are fried potatoes with onions,
bacon & herring, fried noodles with eggs & cheese, pizza and vanilla pudding.
1.
What do you see?
How many people? Guess their ages.
Describe the type of house and furnishings.
Does the family seem well-off or poor?
Compare the amounts of meat, ‘starchy foods’, fruit and vegetables.
What food groups are shown in the picture?
2. Where is Germany?
Use an atlas to find Germany’s latitude and longitude.
Compare the area of Germany with the area of Australia.
3.
Your own family
Compare the people in your family to this one.
What food does your family eat in one week?
For your family’s food, compare the amounts of meat, ‘starchy foods’, fruit and vegetables.
4. Your own class
Find an average family size for your class.
For different foods, find the average amount eaten (or drunk) by families in your class in
one week.
Compare your family’s food (amounts of meat, ‘starchy foods’, fruit and vegetables) with
that for other families in your class.
PROJECT POTENTIAL
Students can use the internet to learn more about how people in many other countries
live. One valuable site with material designed for primary school is the educational section
of the World Vision website www.worldvision.com.au/learn/schoolResources/index.asp.
For each country students could learn where it is in the world (including latitude and
longitude if able), compare the country area to Australia and compare the population size
to that of Australia. Data like average family income is available on several websites.
This
family in
Germany spends about
$700 Australian per week
on food.
The Prime Number team is always on the lookout for mathematically stimulating photos for use
as a centrefold. Please contact the Editor if you have a suggestion or photo that we could use.
Photo: courtesy of Peter Henzel
THE UNIVERSITY OF NEW SOUTH WALES
moremore
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Q:
A:
A film produces the illusion of movement by showing many pictures very quickly.
Each of these pictures is called a frame. There are 16 frames in every 30
centimetres of film. Films are shown at a rate of 24 frames per second.
How many minutes would it take to watch a film that was 3.24 kilometres long?
Go to www.eaa.unsw.edu.au/primenumber and win an ICAS USB flash drive.
The most effective diagnostic tool for
teachers, parents and students
ICAS-MATHEMATICS
Wednesday 19 August 2009
T: (02) 8344 1010
E: [email protected]
Image Copyright Liv friis-larsen, 2009 Used under licence from Shutterstock.com
Global Food and
Maths
Ian Lowe
Ian Lowe is an MAV project officer.
The photo on the centrefold for this
edition of Prime Number comes from
a book called Hungry Planet: what the
world eats (2006). It is one of four books
by Peter Menzel and Faith D’Alusio; the
others being Material World: a global
family portrait (1994), Women in the
Material World (1996) and What the World
Eats (2008). This review will consider the
set of four.
As a group they manage to provide a very
stimulating picture of the entire world,
but also in a very personal way. They
show the rich-poor divide very clearly,
but each reader can identify with much
of the story of every family. Living in
families is what unites us all.
Material World shows statistically typical
families from 30 countries, covering
the full range of areas and populations
(China to Samoa) and wealth (Bhutan
to United States). For each family their
complete material possessions are shown
spread out before them and carefully
identified. Menzel says he did the book
in response to Madonna’s ‘Material Girl’;
he says the world needed a ‘reality check’.
Stories about each family’s life style are
well illustrated. As with this centrefold,
each picture offers the opportunity to ask
many mathematical questions, and the
potential for interesting comparisons is
enormous.
Women in the Material World, written by
Peter’s wife Faith, focuses on the stories
of how women live in 20 of the countries.
These stories are also richly illustrated by
Peter’s photos.
Hungry Planet takes a typical family in
each of 25 countries and lays out their
weekly food. The food is analysed and
favourite recipes are given. Statistics
Resource
Review
for each country (such as Number of
McDonalds and life expectancy) allow
for interesting comparison, using both
numbers and graphs. There are two
Australian families, one indigenous and
one from middle-class Brisbane.
What the World Eats is similar to Hungry
Planet (30 families from 24 countries), and
contains some of the same photos, but the
statistics are presented in vivid graphs to
highlight their meaning.
You may have seen 15 photos by
Peter Menzel in Time magazine in
the last 12 months. You can see
them on-line at www.time.com/time/
photogallery/0,29307,1626519,00.html.
MAV has secured permission to use these
same 15 photos for education purposes. The
centrefold of this edition of Prime Number
and its questions are one example of this.
Another is to make the photos available to
teachers electronically in high resolution
on a CD. In this way they can be projected
onto an electronic whiteboard for class
discussion. The CD will include questions
and links to websites for statistics and
further information. It will be called Global
food and maths and made available through
the MAV on-line bookshop www.mav.vic.
edu.au/shop.
References
D’Alusio, F. & Menzel, P. (1996) Women in the
material world, Sierra Club Books
Menzel, P. & D’Alusio, F. (1994) Material world,
Sierra Club Books
Menzel, P. & D’Alusio, F. (2006) Hungry Planet:
What the World Eats, Tricycle Press
Menzel, P. & D’Alusio, F. (2008) What the
World Eats, Tricycle Press
Prime Number Volume 24, Term 2 2009
13
This
works
for me
A Chest of Maths
Treasures
Julie Austin
‘Couldn’t ask for a better idea, FUN and
LEARNING together!’
them to spend time sharing these activities
with their children.
‘Our family had a lot of fun going through the
various activities with our daughter. She had
a blast with the tape measure and measured
everyone and everything in sight, even our two
dogs.’
Each child takes the Treasure Chest home
for several days each term and all students
eagerly await their turn. The Treasure Chest
contains a list of ‘suggested activities’ as
well as ‘task’ and ‘discussion’ cards. Several
of the activities and materials change each
term, others remain throughout the year.
‘The timer was a brilliant idea, our son took
it as a challenge to ‘beat the time’ when doing
the various activities. Thank you for making
learning so much fun for all the kids!’
‘The Treasure Chest is a great idea and has us
doing lots of Maths at home.’
These are just some of the comments
written by parents in ‘feedback’ booklets
when the Year 1 teachers at Watsonia North
Primary School each sent home a class
Treasure Chest of Maths activities.
Parents are usually confident when helping
their children with Literacy at home but
don’t feel as confident when dealing with
Mathematics. We want to give parents an
idea of some of the tasks and games we use
at school, hoping that this will encourage
14
Julie Austin is a Year 1 teacher at
Watsonia North Primary School.
Prime Number Volume 24, Term 2 2009
The Treasure Chest contains items such as:
a large pack of cards
a calculator
textas
a ruler and tape measure
coloured paper, glue and scissors
a stop watch
an egg timer
dice and counters
dominoes
tens frames
laminated number cards
unifix
icy-pole sticks grouped as tens and ones
a small clock face
plastic money
tangrams
pattern blocks
2D and 3D shapes
a mirror
streamers
game boards
laminated days of the week and months.
Parents and children are given ideas if
they wish to use them, otherwise they
are encouraged to freely explore and
experiment with these materials. The
response has been overwhelming, as is
evident in the many positive comments
written by parents in our ‘feedback’ books.
Parents and students measure, time,
calculate, draw, sort, order, design and
play. Families are encouraged to estimate
answers and prove their findings, and most
importantly, to have FUN participating in
these activities together. Several families
have made their own Treasure Chest to
keep at home permanently.
excitement. They listen to others chat about
the activities and games they have enjoyed
and wait with great anticipation for their
turn to experience this. The parents marvel
at the students’ excitement and enjoy seeing
them walk out of the classroom carrying the
Treasure Chest and smiling broadly. They
also appreciate the many suggestions and
tasks to enable them to participate in a range
of Mathematics activities with their children.
It gives them greater confidence to help their
children with Mathematics at home.
The idea for this activity came from Ann
Gervasoni (Australian Catholic University,
Ballarat Campus). During my EMU
(Extending Mathematics Understanding)
training, I received a copy of an article
written by Ann about the Treasure Chest
and thought it would be good to try with
the Year 1 students at our school. In fact,
this would be suitable for students in any
year level and is definitely a valuable link
between home and school.
The Treasure Chest has had a positive effect
on the attitude of our students and parents
towards Mathematics. The students view
the Treasure Chest as a box full of fun and
Prime Number Volume 24, Term 2 2009
15
Feature
Article
Ideas for Teaching
Place Value
Prof. Peter Sullivan & Julie Millsom
Peter Sullivan is the Professor of
Science, Mathematics and Technology
Education at Monash University.
Julie Millsom teaches at St Anne’s
Primary School in East Kew.
This article presents some activities that might
assist students to learn about place value. It
builds on the article titled ‘Linking Research
results on Place Value and Teaching’ that
appeared in the first edition of Prime Number
for 2009. The authors underscored the fact that:
units”, plus the two diagrams below (a total
of 16 cards in all).
• Learning place value is much more
than making models of numbers using
structured materials.
• Even though development of
understandings of place value is
important at all levels, the transition from
1-digit to 2-digit numbers is perhaps the
most critical.
• Students have only learnt two digit
numbers when they have adaptable
mental models of the patterns and
relationships in two digit numbers.
So you might have four different cards
representing 23 including the numeral,
the number in words, a representation
using base 10 blocks, and a set of objects
arranged in groups of 10. You might have
similar cards for the number 32, 53 and 35.
Place value grid
Have a blank board like this:
Players, in turn, place one card on the
board to organise the shuffled cards into
rows that represent each number. One
suggestion is to make a rule that there
should be no talking and players can only
touch and place or move one card when it
is their turn. This has the effect of making
it a co-operative activity.
One in each row
Players take turns to throw two ten-sided
dice, making a 2-digit number, (2 and 3
makes either 23 or 32), and placing a
marker on that number on a hundreds
chart. The winner is the first to place at
least one counter in every row.
and have sets of cards that contain four
different representations of each of four
different numbers like “23”, “2 tens and 3
43
16
Prime Number Volume 24, Term 2 2009
Jigsaw pieces
Make up some pieces like these (see below)
from a hundreds jigsaw. Students are asked
to write in the missing numbers.
77
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
Number grid with some missing
Make up some number grids with some
numbers missing. Some can be completely
blank. Students are asked to fill in the blanks.
Open ended place value
activities
There are some specific teacher actions
that can contribute to the effectiveness of
open-ended questions. For example, it is
important to emphasise that there are many
possible answers to such questions, that
we are just as interested in the way that
the student explores the possibilities as we
are in the correctness of their responses,
that the process of communicating their
answers is important, that we expect
that the student will learn by working
on the questions, and that everyone will
be able to give at least one answer. Some
other features are that the open-ended
questions are often easier for the students
experiencing difficulty learning that aspect
of mathematics, the students can learn from
each other, and because there are many
possible answers students do not have to
worry about getting the “right answer”.
1
2
11
12
31
32
3
4
5
6
10
15
23
24
18
19
20
68
69
70
88
89
27
41
60
64
65
66
74
81
92
76
77
86
87
93
111
80
99
114
115
116
120
Add to 100
Players in turn roll a die (ideally, it can
be a 10-sided die, but a 6-sided die also
works), and write the number in one of the
squares.
+
= 100
The aim is to make the answer to the two
digit addition as close as possible to 100.
Once the number has been written, it
cannot be erased or rewritten.
Prime Number Volume 24, Term 2 2009
17
Resource
Review
Making Sense of
Consumer and
Financial Literacy
Fiona May
“Young people today are participants in a
dynamic consumer world characterised by an
extraordinary expansion of choice and ever
increasing complexity. Reaping the benefits
on offer requires confident and competent
participation” Grahame Crough (Financial
Literacy Foundation).
In an increasingly complex global, social
and economic environment, it is critical
that young people are equipped with
the knowledge, understandings, skills
and values to make informed decisions
regarding the use and management of
money.1 A 2007 study of the financial
literacy attitudes and behaviours of
young Australians revealed that an
overwhelming majority of students are
interested in learning more about how to
budget, save and plan for their financial
futures. Many young people feel they
lack the basic knowledge, skills and
confidence to deal with a range of moneyrelated matters, with most indicating that
Fiona May is a Senior Project Officer
in the Department of Education and
Early Childhood Development.
it would be beneficial to learn more about
money at school.2
Research has demonstrated that effective
decision-making related to consumer
behaviours and the management of
personal financial matters can be achieved
by improving consumer and financial
literacy.3 In addition to improving outcomes
for the individual, increasing the consumer
and financial literacy of young people
has been demonstrated to have economic
benefits for the entire community.4
In May 2005 the Ministerial Council on
Education, Employment, Training and
Youth Affairs (MCEETYA) developed
the National Consumer and Financial
Literacy Framework to further articulate
the learning needed to fulfil the National
Goals for Schooling in the Twenty-first
Century.5 The Framework outlines
the knowledge, understandings, skills
and values in consumer and financial
education that young people should
acquire at school. To support the
implementation of the Framework in
schools, the Consumer and Financial
Literacy Professional Learning Program
for teachers was released in 2008 by the
Financial Literacy Foundation. The aim
of the program is to support teachers
to integrate and embed consumer and
financial literacy across the curriculum
from Prep to Year 10.
1 National Consumer and Financial Literacy Framework at
http://www.mceetya.edu.au/mceetya/default.asp?id=14429
2 Financial Literacy: Australians Understanding Money at
www.understandingmoney.gov.au/documents/Australiansunderstandingmoneyweb.pdf
3 ANZ Survey of Adult Financial Literacy in Australia: Final Report at
http://www.anz.com.au/australia/support/library/MediaRelease/MR20030502a.pdf
4 Improving financial literacy in Australia: benefits for the individual and the nation,
Commonwealth Bank Foundation at
http://www.commbank.com.au/about-us/download-printed-forms/FinancialLiteracy_Report2004.pdf
5 The Adelaide Declaration on National Goals for Schooling in the Twenty-first Century
http://www.dest.gov.au/sectors/school_education/policy_initiatives_reviews/national_goals_for_
schooling_in_the_twenty_first_century.htm
18
Prime Number Volume 24, Term 2 2009
Funding has been provided to each state
and territory through the Australian
Government Quality Teacher Programme
(AGQTP) to deliver the professional learning
program for teachers of primary, secondary
and special schools from the Department
of Education and Early Childhood
Development (DEECD), the Catholic
Education Commission of Victoria (CECV)
and the Association of Independent Schools
of Victoria (AISV). Cross-sectoral Consumer
and Financial Literacy workshops for
primary and secondary teachers commenced
in October 2008. The workshops, facilitated
by Social Education Victoria (SEV), aim
to build the capacity of teachers to engage
students in consumer and financial literacy.
The program supports and encourages
teachers to look broadly at the curriculum
and identify opportunities across four areas
of study:
•
•
•
•
Understanding money
Consumer education
Personal finance
Money management
curriculum. The program highlights the links
to the Victorian Essential Learning Standards
(VELS) curriculum and provides hands‑on
opportunities for teachers to explore
strategies and resources to develop their own
financial literacy programs. Participants are
supported to consider strategies for sharing
their learning back at school and developing
programs for the classroom to ensure that
consumer and financial literacy is firmly
embedded in the curriculum.
The program continues in a range of
locations across Victoria in Semester 1,
2009. In addition to day workshops, twohour after school sessions and an online
delivery module will be available to teachers
across the Government, Catholic and
Independent sectors. For further information
about the program, please contact Liz Aird
at Social Education Victoria – Telephone:
(03) 9349 4957 Mobile: 0414 876 568 or
Email: [email protected].
The professional learning is supported
through the associated website:
www.financialliteracy.edu.au.
Teachers are encouraged to add value to
quality teaching and learning by building
on existing knowledge and skills, and
providing further information regarding
available resources to incorporate across the
Prime Number Volume 24, Term 2 2009
19
Teacher
Talk
Maths Talent Quest
– Diary of a Year Six
Student
James Hogan
2nd February
Dear Diary
Today was the first day back at school,
and we started with Maths (ew!). Our
teacher told us that we were going to
do some sort of weird project called the
Maths Talent Quest. It’s a project where
we have to investigate something and
use maths to work out stuff. She also
told us that we had to do a logbook or
something. It sounds boring, but at least
we can work on it during class with a
partner.
James Hogan currently attends
Camberwell Grammar. He is a past
entrant in MTQ
2nd March
Dear Diary
We’ve started! Today our teacher gave us
time in class to work on it, and we found
out how much energy a light bulb uses
every second. We also did some work in
our logbook which is just like a diary.
My partner is writing the project on his
computer and I’m doing the maths work.
I’m actually having fun with this!
23rd March
Dear Diary
11th
February
Dear Diary
Our teacher told us more about the
Maths Talent Quest. She said that we
could do it on anything, not just about
boring stuff like fractions. She showed
us some old projects about things like
football or the Olympics, and how we
can find maths in anything. She also told
us that it was a competition against other
schools around Australia, with prizes for
the best projects. We’re going to do it on
electricity around the house and work
out how much electricity is wasted from
leaving on electrical stuff like light bulbs.
We’ve almost finished! We worked out
how much energy is wasted by leaving
stuff around the house on, and we
worked out ways to use less energy. We
also compared our information to other
houses, and worked out the amount
wasted in Australia every year. Our
teacher told us that she has entered our
project to be a part, and that she will
send it off soon. I can’t wait to see if we
win… I really like this! I’m definitely
going to try again next year!
IMPORTANT 2009 MTQ DATES:
Registration start of Term Two – Monday 20 April 2009
Registration closes – Monday 20 July 2009
Delivery of entries Latrobe Thursday 6 August and Friday 7 August
Judging Sunday 9 August – Saturday 15 August 2009
Display of entries Monday 17 August 2009 and Tuesday 18 August 2009
Entry Pick Up Tuesday 18 August
20
Prime Number Volume 24, Term 2 2009
Answers to back cover puzzles Edition 1 2009
Level 1
Multiple answers possible; combinations of two whole numbers that total seven
(1 + 6) (2 + 5) (3 + 4)
Level 2
Multiple answers possible;
Hundreds column may be 3, 2 or 1
Tens column must be 7
Units column cannot be 7 and cannot be the same as hundreds column
Level 3
(9 × 4) + (2 × 3) = 42 (6 + 8) – (2 × 5) = 4
Level 4
= $7 = $9 = $11
Fun Maths Puzzles
Volume 24 Term 2 2009
Level 1
Level 2
One nose on a face
Two socks in a pair
List objects for all the numbers 1 to 10
Find someone’s age:
Ask the person to multiply the first digit
of their age by 5.
Tell them to add 3.
Ask them to double this number.
Finally, ask them to add the second digit
of their age to the number and then tell
you their answer.
Subtract 6 and you will have their age.
Level 3
Level 4
I have some pencils and some jars.
If I put 9 pencils into each jar I will have
two jars left over.
If I put 6 pencils into each jar I will have
three pencils left over.
How many pencils and how many jars?
TWO
THREE
+ SEVEN
TWELVE
Replace the letters with numbers to make
the sum true.
Same letter, same value.