MATHEMATICS UNIT PLANNER
Topic: Probability
Year Level: 4
Term: 3
Week: 1
Date: 21/9/2012
Learning focus:
Students will develop skills in describing and interpreting different
data sets in order to challenge their subjective probability views and
develop probabilistic reasoning through experimental contexts.
Key mathematical understandings
Key AusVELS documentation (taken directly from AusVELS documents):
(2-4 understandings only):

Fairness
Content strand(s):

Data collection
Sub-strand(s):

Probabilistic reasoning
Level descriptions:

Probabilistic language
Describe possible everyday events and order their chances of occurring.
Number and Algebra
Measurement and Geometry
Statistics and Probability
Identify everyday events where one cannot happen if the other happens.
Identify events where the chance of one will not be affected by the occurrence of the other.
Proficiency strand(s):
Understanding
Fluency
Problem Solving
Reasoning
Understanding includes making connections between representations of numbers
Fluency includes collecting and recording data
Problem Solving includes formulating, modelling and recording authentic situations
Reasoning includes using generalising from results of calculations, and communicating information using
graphical displays
Key skills to develop and practise (including strategies, ways of working
Key equipment / resources:
Key vocabulary:
mathematically, language goals, etc.):
Refer to appendices

Sample space

Probabilistic reasoning

Fairness

Probabilistic language

Prediction

Experimental probability

Problem solving

Experiment

Results

Data representations

Analysis

Justifications

Probability/likelihood
Overview of assessment
Key probing questions (focus questions that will be used to
Links to other contexts (if applicable, e.g., inquiry unit focus,

develop understanding to be used during the sequence of lessons):
current events, literature, etc.)

“how can you justify this?

Literacy

“why do you believe so?”

Fractions/percentages

“what have you learned?”

Number
Teacher assessment – strong use of teacher
assessment throughout, mainly through work
samples and observations.

Peer assessment – through many discussions and
justifications students evaluated each-others’ work 

and provided constructive criticism for future

learning.

“how do you know?”
“what do you notice about..?”
“can you apply this to another situation?”
Self-assessment – at the end of this learning
sequence students have the opportunity to selfassess, whereby they evaluate what they have
skills
Learning strategies/
learnt.
Analysing
Estimating
Listening
Performing
Reading
Seeing patterns
Testing
Checking
Explaining
Locating information
Persuading
Recognising bias
Selecting information
Viewing
Classifying
Generalising
Making choices
Planning
Reflecting
Self-assessing
Visually representing
Co-operating
Hypothesising
Note taking
Predicting
Reporting
Sharing ideas
Working independently
Working to a timetable
Considering options
Inferring
Observing
Presenting
Responding
Summarising
Designing
Interpreting
Ordering events
Providing feedback
Restating
Synthesising
Elaborating
Justifying
Organising
Questioning
Revising
MATHEMATICAL
FOCUS
‘TUNING IN’
‘INVESTIGATIONS
‘REFLECTION & MAKING
(WHOLE CLASS FOCUS)
SESSION’
CONNECTIONS
(a short, sharp task relating to the
(what you want the children
focus of the lesson; sets the scene/
to come to understand as a
context for what students do in the
work in pairs, small groups or
result of this lesson – short,
independent aspect. e.g., It may be a
individually. Time for teacher to probe
problem posed, spider diagram, an
children’s thinking or work with a small
succinct statement)
open-ended question, game, or
reading a story)
SESSION’
(INDEPENDENT LEARNING)
(extended opportunity for students to
group for part of the time and to also
conduct roving conferences)
ADAPTATIONS
ASSESSMENT
STRATEGIES
- Enabling prompt
(to allow those experiencing difficulty to
(WHOLE CLASS FOCUS)
engage in active experiences related to
(focused teacher questions and
the initial goal task)
summary to draw out the mathematics
- Extending prompt
and assist children to make links. NB.
(questions that extend students’
This may occur at particular points
thinking on the initial task)
during a lesson. Use of spotlight,
(should relate to objective. Includes
what the teacher will listen for,
observe, note or analyse; what
evidence of learning will be collected
and what criteria will be used to
analyse the evidence)
strategy, gallery walk, etc.)
Session 1
‘Language Line’ (refer to
Students individually write
The class discussion and
Enabling prompt:
The class response to
Students will
appendix 1)
4 sentences which each
writing activity involves
In order for students who
‘language line’
develop an
include one word or phrase
critical thinking and
may be struggling with
specifically their
understanding of
from the number line and
justifications in order for
understanding the language
justification of
the language used
are contextualised through
students to develop a clear
of probability, the teacher
word/phrase placement
to describe the
being linked with an
understanding of the
provides real life examples
can be used as
probability of
everyday event.
difference between words
of an event and asks “is
documentation of
everyday events,
(See appendix 2)
and phrases within
this event likely to occur”?
learning.
and will be able to
probability of everyday
The students respond and
order them based
events.
order each events based on
Students’ probability
how likely they are to
sentences are evaluated
occur. They can then link
based on accuracy of
these ordered events to a
likelihood as well as
specific word along the
justifications to show
Language Line.
students’ thinking and
on likelihood of
occurrence.
Questions: see appendix 2
understanding of
Extending prompt:
probability language
The students create their
meanings.
own language line which
has 10 words along it, and
link each word with an
event.
Session 2
Class reads “It’s probably
‘Spinners activity’ (refer to
Throughout the lesson,
Enabling prompt:
Teacher observation and
Students will
Penny” and is involved in
appendix 4)
teacher helps students to
instead of differentiating
anecdotal notes drawn
identify various
discussion of the book and
make connections between
between all the words on
from discussion,
events within
prior learning (see
students’ predictions and
the number line, the
including students’ prior
everyday life
appendix 3)
interpretations of
teacher allocates them
knowledge of probability,
which have
probability with
words from the line to look
their understanding and
different
appropriate language
at, and the students then
use of language,
probabilities and be
through questioning (refer
have to find the spinner
predictions, outcome
able to order their
to italics, see appendix 4).
within the group which
interpretations
matches with the given
justifications,
words.
explanations and
likelihood of
occurrence along a
Students will be
continuum of
encouraged to link
probabilistic
probability with everyday
Extending prompt:
language.
events through teacher’s
Create a mix-n-match sheet
providence of clear
for partner, whereby you
examples (refer to italics,
will draw a certain number
see appendix 4).
of spinners on one side,
questions throughout the
lesson.
and the same amount on
the other in a mixed order
for your partner to match.
Session 3
Coloured dice (see
Students work in groups of
Class discussion
Enabling prompt:
Students will be
appendix 5)
3 and complete “Fair
Students justify their views
Focus group works
Students’ samples of dice
able to challenge
1. The teacher presents
dice?” activity (see
of the game, and justify
together to order the
help teacher to identify
their subjective
coloured dice 1 to the
appendix 6)
their reasons for their ‘fair’
likelihood of events, and
whether they understand
beliefs by using
students, and has them
dice
may not use numerical
fairness and is supported
experimental
choose a colour which they
ways of representation but
by their responses to the
evidence to
predict the dice will land
Summary
refer to language line to
leading questions
determine and
on.
Students become aware of
describe the probability
throughout the dice
compare likelihood
2. Justifications lead whole
fairness within probability,
through language
activity.
of events as well as
class discussion, and
and see that on a di, to
fairness.
another coloured dice is
make it fair for 6 people
Extending Prompt:
presented.
there has to be 6 possible
What else is fair?
3.Step 1 and 2 are repeated
outcomes. This is
- Can you apply what you
4. After discussion of all 3
connected to the outcomes
have learnt about dice
dice, the students order the
on real dice, where no
being fair to other models.
dice along the ‘Language
number is more likely to
How do you know they are
Line’.
occur than another.
fair? Are coins fair? Are
other multi-sided dice fair?
Leading questions:
what did you find out about
the game? Justify why you
believe it is fair/unfair. Did
you believe it was fair
when you were winning?
How might this influence
our view of fairness?
Session 4
Are normal dice fair?
Class discusses the
Class discussion:
Enabling prompt:
Teacher identifies
Students further
Class reflects on what they
similarities and differences
Discussion questions as per
Have small group of
students understanding
understand
found in the previous
of a six sided number di to
appendix 7
students be the ‘recorder’
through analysing their
differences within
lesson while rolling
the coloured di of the
Class data collection
and write down each
record sheets; whether
probability
coloured dice.
previous session
moves towards a larger
persons’ results, then work
they provide an informed
including fairness
What makes a dice fair?
sample space which can
in pairs with students who
prediction, they have
through recording
Why is equal chance
extend students’ view of
have grasped the concept,
linguistically described
and interpreting
important?
results as they see the
but will not extend too far
the probability as well as
Students engage in rotation
data, and
activities of probability
whole class results – due to
and leaving them behind
represented the chance
larger sample space
whilst interpreting results
numerically through
comparing the
Teacher poses question:
games with data collection,
probability of
“When we are playing a
where they first predict the
various outcomes
dice game where we had to
results, and record the
Extending prompt:
both linguistically
throw a 6 to start the game,
results in many ways
Can you simplify the
and numerically.
Johnny said, ‘let’s make it
(see appendix 7)
probabilities? Can you
fractions
that we have to throw a 3
represent the probabilities
instead of 6 because it is
as a percentage? What
easier’. Do you agree with
other ways of recording
him? Why?’
fair results are there? Is a
coin fair?
Secret spinner
Students create their own
Spinner discussion
Enabling prompt:
Students’ tally of results
(refer to appendix 8).
secret spinner, and then
What was in the data that
When predicting the
and correlating secret
Students will
play with a partner (same
encouraged them to alter
colours on their partner’s
spinner predictions are
demonstrate their
steps as appendix 8).
their thinking? Could they
spinner, allow students to
analysed to identify
knowledge of
expect to stay with their
know all the possible
whether they made
likelihood of
answer if the activity went
colours that will definitely
accurate predictions
events, by making
on for 50 spins? What do
appear. They then can
based on the previous
informed
you know about probability focus on the proportion and
predictions based
that helped you to
differing probabilities of
on experimental
determine what the spinner
each colour.
Student self-assessment
evidence, and
looks like?
Extending prompt:
of their process and
Have students create their
learning throughout the
Session 5
representing their
results.
results visually
Students then reflect on
own spinner which has
activity as well as linking
with accurate
their learning by using
segmented sections. Their
to other activities.
interpretations and
these questions as prompts
partner then has to add the
evaluations.
for self-assessment.
fractional parts together to
find the overall proportion
to determine the
probability.
Word Count: 1,391 (with removal of template word count).