Term 1-2 - Year 4 Independent Inquiry
Big Idea
Numeracy capabilities are needed in our personal,
work and civic lives.
Enduring
Students will be confident, creative users and
Understandings
communicators of mathematics, who are able to
investigate, represent and interpret situations in
personal and work lives and as active citizens.
Essential
How does number help us understand our world
Questions
further?
How is mathematics used? How can number add
another dimension to our understanding of our
world?
Unit design Term 1 & 2
Content Strands: Mathematics /
Year Level: 4
Civics & Citizenship/ Personal
Learning
Proficiency Strands: Ethical Behaviour
/ ICT
Unit summary
Students will work independently or in small groups to inquire around an
interest that matters to them and create data for their class so to
investigate further. The students will model problem-solving techniques to
their peers during the investigation. They will design a presentation to
inform their peers of their learning’s and new questions the investigation
has presented.
Goals & Standards
What is important to learn?
How do we determine this?
See curriculum frameworks
Understandings
Focusing Questions
What do we want the students to
Mathematics
understand as a result of this unit? Where is mathematics in our world?
Mathematics
Where isn’t it?
Data can be organize into different
How do we organize data to support
forms to help with analysis
interpretation and analysis? Are there
Mathematicians choose from a
errors in the collecting of data? What
range of strategies to problem
impact does this have on results and
solving
conclusions?
What operations or strategies do a
Civics & Citizenship
mathematician use with solving the
We all can contribute to the
problem?
functions of a fair and caring world.
Civics & Citizenship
What issue does this data present
and therefore how can we act?
Personal Learning
What does it mean to be an active
Seeking support, asking new
and informed citizen?
questions and persisting when faced
Personal Learning
with difficulties are characteristics
What strategies support problem
of an effective learner.
solving?
What do effective learners do?
Knowledge and skills required to support development of understandings
(explicit teaching)

Skills in collection and presentation of data

Knows how to input data into excel spreadsheets

Able to select simple functions on spreadsheet / excel program to
help explore numbers

Knows how to identify and clarify thoughts, questions and issues
using a thinking routine think puzzle, explore and an online concept
map

Able to create a question to guide inquiry

Knowledge of ways to monitor and manage goal getting

Able to identify relevant and reliable sources of information to
explore inquiry

With scaffolding, knows an inquiry process to explore the idea further

With scaffolding, knows a problem solving framework and strategies
to support

Able to use a rubric to progress and evaluate own achievements

Knows basic mathematical properties and processes related to
personal goal and the needs of inquiry
Assessment Design
How will we know what learners have learned and how well they have
progressed?
Entry level assessments
 Mathematics Assessment Interview
 Collated list of where is number in the games
 Concept map around goal
 Questions around interest area
 Developing a rubric for effective mathematicians characteristics
Formative Assessment
 Students, parents and teachers create a portfolio based on student
selected goal and progress towards achieving
 Retest questions from Mathematics Assessment Interview in June
 Concept map around goal –post
 New questions around interest area – post
 Rubric - self assessment - output – presentation
Components to be incorporated into Learning Sequence
Learning Sequence is translation of a unit design into learning, teaching &
assessment experiences for students.
Learning Sequence goals is to progress the understandings, knowledge and
skills, essential standards ( state & national expectations of learners)
Assess the needs of each cohort -Interests, experiences, aspirations, ways
of learning What do the students bring to the learning? Therefore how can
we progress these learners? Where is the difference so to meet the
learning needs of a particular class?
1. Participate in simulation games on the iPad. As a group create a list
of where number is in the game. Collate the results.
2. Students predict where number will be present at camp. Students
begin investigation based on the predictions.
3. Following camp, begin collection, collation and input of data. (explicit
teaching – collection of data process and excel spreadsheet input and
auto-sum) Students share another function they have learnt on excel
to the rest of the group.
4. Students reflect on collected data: identify and clarify thoughts,
questions and issues using a thinking routine think puzzle, explore.
Create new questions around the data and areas of interest.
Term 2
5. What do you already know about your goal? How will you know you
have achieved it?
6. Continue to explore excel features and teach one another.
7. Students unpack an area of interest leading to creating a question/
focus for inquiry. Scaffold using an inquiry planner.
8. Introduce drafted likert scale so students are aware of the criteria
and a tool to support the managing and monitoring of their own
learning
9. Explicitly teach problem solving framework & a strategy
10. Students demonstrate to a group of students by thinking aloud
when exploring a problem. Other students using metacognitive cards
to track students thoughts while problem solving
11. Students independently explore their area of interest and create
opportunities to explore and practice their goal. Explicit teaching is
provided based on goal and needs of inquiry. Resources - Khan
Academy
Resources
iPad game – tiny towers
Excel program
Small meta cognitive cards – laminated - Appendix 1
Inquiry planner – Appendix 2
Where maths? – Appendix 3
Goal and concept map – Appendix 4
What makes a good inquiry question proforma – Appendix 5
Problem solving strategies & framework – Appendix 6
Mathematical processes & rules / terminology page eg brackets –Appendix 7
Drafted likert scale - Appendix 8
Reflection tools/ web cam / flip camera / wiki
Appendix 1 – Cognitive Cards
I tried to
remember if I
had ever done
a problem like
this before or
similar
I acted it out
I made a list
I looked for a
pattern
I made a plan
to start the
problem
I worked
backwards
I tried all
possibilities
I subtracted
I guessed then
checked and if
needed to I
improved my
plan
I broke the
problem into
smaller parts
I looked for an I thought
exception and I about what I
found one
would do next
I tried a
simpler
problem
I created a
diagram
I tried one way I counted
and it didn’t
work so I just
started again
another way
I wrote an
equation
I multiplied
I thought
about what I
already knew
I thought 'I
know what to
do'
I thought 'I
know this sort
of problem'
I thought
about a
different way
to solve the
problem
I changed the
way I was
working
I divided
I added
I thought ' is
this right?'
I thought 'I
can't do it' but
kept going
I thought
about how I
was going
I checked my
result as I was
working
I thought
about
something I
had done
another time
that had been
helpful
I made a guess
then checked it
I read the
question again
so to
understand the
problem
I thought
about whether
what I was
doing was
working
I noticed a
pattern
I made a table
I drew a
picture
I made a model I thought this
isn’t working
so I started
again another
way
I drew a graph
I collected and I carried out a
organised data plan
about the
problem
I discussed my I recorded
ideas with
some notes
some else
I found
connections in
the organised
data
I looked for
problem
solving
strategies
which could
help
I made and
tested
hypotheses
based on
patterns and
connections I
found
I thought
about what
else can be
learnt from
this
I published my I asked myself I asked what
results
can I check this would happen
another way
if …..
I asked how
many solutions
are there
I asked myself I was curious
how do I know
I have found all
the solutions
I enjoyed the
challenge
I was excited
to get into the
problem
I thought ‘ let’s I let my mind
see what
float freely to
happens if I do help get ideas
this’
I was
frustrated but
stuck to it
I knew I’d get
it eventually
I used my
strengths
I preferred to
work on my
own this time
I was confused
but knew that
is part of
learning and
made myself
feel better
I trusted my
guess
I asked
questions
I came up with I found an area I listened to
an idea that
that I can learn what others
was a bit crazy more about
have to say
I thought
I found a way
I took notice of I had to think
about how this that no-one
how I felt
hard
relates to my
else thought of
life
Appendix 2
What is possible for
taking action that
matters?
How can I share my
learning so that
others learn from
me?
What resources are
available to help
explore my
question?
How does my
personal goal relate
to my research?
What would I like
to know more
about?
What does my topic
make me think,
make me wonder
about and want to
explore?
Reflection : What is
going well? What
will I do next?
Our big question
...
.... how does
number help us
understand our
world further?
How does my
research help
answer big
question?
Appendix 3
Maths is everywhere – Resource : Australian Curriculum

In science understanding sources of error and their impact on the
confidence of conclusions is vital, as is the use of mathematical models in
other disciplines. Interpret data and make informed judgments about events
involving chance

In geography, interpretation of data underpins the study of human
populations and their physical environments;

In history, students need to be able to imagine timelines and time
frames to reconcile related events

In English, deriving quantitative and spatial information is an important
aspect of making meaning of texts.

Ethical behavior - through analysing data and statistics; seeking
intentional and accidental distortions; finding inappropriate comparisons and
misleading scales when exploring the importance of fair comparison; and
interrogating financial claims and sources. Financial mathematics, time
management, budgeting and financial management, and understanding
statistics in everyday contexts.

In Literacy - interpret and use learn vocabulary /language - synonyms-
Minus/subtract, technical terminology, -lowest common denominator, create
and interpret texts – calendars & maps / data displays

In ICT-investigate, create and communicate mathematical ideas and
concepts using fast, automated, interactive and multimodal technologies.
They employ their ICT capability to perform calculations, draw graphs,
collect, manage, analyse and interpret data; share and exchange information
and ideas and investigate and model concepts and relationships.

Intercultural – range of cultural traditions, understand that
mathematical expressions use universal symbols, while mathematical
knowledge has its origin in many cultures
Appendix 4
Goals
Students Specific Goals
Ellie – By the end of June I would like to explore adding two fractions
together when they have different denominators
Lincoln - By the end of June I would like to explore the properties of
negative numbers
Charlie - By the end of June I would like to explore patterns in
number equations
Alyssa - By the end of June I would like to explore adding two
fractions together when they have different denominators
Aidan - By the end of June I would like to investigate other strategies
to problem solve
Jack - By the end of June I would like to discover patterns so to
make problem solving simpler
Nicholas - By the end of June I would like to reflect by talking my
idea through after finding a possible answer
Nicholas – By the end of June I would like to use the language to
order and write decimals
Yin - By the end of June I would like to investigate other strategies
to problem solve
Digby - By the end of June I would like to discover patterns so to
make problem solving simpler
Siena– By the end of June I would like to order and add fractions
Inspiration
Appendix 5
Making a good inquiry question
What makes a good inquiry question?
 There are lots of possible answers.
 The answer means lots of exploring and more questions.
 They help clarify and extend your ideas or explore other possibilities.
 The answer can’t just be found in a search on the Internet.
 The answer is more than a yes or no.
Sentence starters might be …
Is it possible that ….?
What might ….?
What if ….?
How could ….?
What evidence supports that view…?
Why does this happen?
What could cause that?
What else is possible?
What makes a good inquiry answer?
 The person experiments and has evidence to prove a position.
 There is deep exploration of the area. The person looks at all possibilities
and perspectives.
 There may not be an answer.
Appendix 6
Mathematical Problem solving framework
1.
2.
3.
4.
5.
Play with the problems to collect and organize data about it
Discuss and record notes and diagrams
Seek and see patterns or connections in the organized data
Make and test hypotheses based on the patterns or connections
Look in the strategy toolbox for problem solving strategies which could
help
6. Look in their skill toolbox for mathematical which could help
7. Check answers and think about what else can be learnt from it
8. Share the results
Strategy Toolbox for problem solving
Thinking about your thinking
Make a plan to start the problem
Try and remember if you have ever done a problem like this before, what was
helpful?
Make a guess then check it
Try one way and if it doesn’t work start again another way
Check your result as you work
Make a plan
Read the question again so to understand the problem and find the important
information
Check in to see whether what you are doing is working
Possible methods
Record the ideas/thoughts
Collect and organise data about the problem
Make a table
Draw a picture
Act it out
Make a model
Make a list
Create a diagram
Draw a graph
Find connections in the organised data
Write an equation
Look for a pattern
Work backwards
Break the problem into smaller parts
Try a simpler problem
Appendix 7
Exploring words in the mathematics world
Terminology
Example
BRACKETS The signs ( ) { } & [ ] are used for grouping things or numbers
Definition
together. Brackets are used to indicate the order of operations
Example
12 = 3 x (2 +2)
Rule
related
Order of operation …..
Brackets first, of sign, division, multiplication addition subtraction
BODMAS
Definition
Example
Rule
related
Appendix 8
Self -Assessment tool – Likert Scale – mark on the scale of 1-4 how you are
progressing towards the statement in the box. Mark in different colours each
time and date the mark
Name :
I can contribute an idea or evidence
1
2
3
4
1
2
3
4
1
2
3
4
1
2
3
4
1
2
3
4
1
2
3
4
of our questions:
How does number help us understand
our world further?
How is mathematics used?
Mathematics I understand that data can be
organize into different forms to help
with analysis
I understand that mathematicians
choose from a range of strategies to
problem solving
Civics &
I demonstrate that I can contribute
Citizenship
to the functions of a fair and caring
world.
Personal
I demonstrate that I can seek
Learning
support, ask new questions and
persist when faced with difficulties
I demonstrate that I can monitor
and manage goal getting.
Knowledge I can ….
and skills
Collect and present data. Input data
into excel spreadsheets. Select simple
functions on spreadsheet / excel
program to help explore numbers.
1
2
3
4
I can ….
Identify and clarify thoughts,
1
2
3
4
1
2
3
4
1
2
3
4
questions and issues using a thinking
routines like - think puzzle, explore
and an online concept map. Create a
question to guide inquiry.
Use an inquiry process to explore the
idea further. Identify relevant and
reliable sources of information to
explore inquiry.
I can …
Use a mathematics problem solving
framework and strategies to support.
Select basic mathematical properties
and processes related to personal goal
and the needs of inquiry
I can …
Use a monitoring tool to progress and
evaluate own achievements