EDMA310/360 Mathematics unit planner
Unit title:
Probably Probability
Meg Swinstead S00103322
Unit Overview
Content maths area:
Probability
Grade/year level:
Year 5: Level 5:
Learning Focus (ideas extrapolated from AusVELS):
Mathematical Content Strand: Statistic & Probability
Sub-strand: Chance:


List of outcomes of chance experiments involving equally likely outcomes and represent
probabilities of those outcomes using fraction (ACMSP116)
Recognise that probabilities range from 0 to 1.
Proficiency Strand:


Understanding: using fractions to represent probabilities.
Reasoning: interpreting results of chance.
Rationale:
Probability is an important concept (Bryant and Nunes, 2012), as it is something that we use in
our everyday life and not just specifically for mathematics. Shaughnessy (2006) confirms that
probabilistic thinking is a unique process dissimilar to general mathematical thinking. Frykholm
(2001) states that it is important that students learn the vocabulary used for probability, as it
describes the likelihood of an event to happen.
Assumed prior knowledge of students:
From the ACARA website, in Level 5 students should be able to list outcomes of chance
experiments, represent possibilities as fractions and be able to recognise that probability range
from 0-1. Using Level 4 to assist with assumed prior knowledge students are able to identify
events where the chance of one will not be affected by the previous occurrence. Students have
also just covered fraction, students were able to compare and order common unit fractions and
locate and represent them on a number line. Students were also able to represent fractions as
a percentage.
Grouping strategies to support learning:
Many of the lessons foster whole class discussions and brainstorming, as it facilitate students to
recollect information based on their own memories, digging deep into what they already know
on the lesson topic (Tantillo, 2012; Keene & Zimmermann, 2013). Students are often working in
small groups or pairs, as it is considered an efficient and effective all purpose strategy to
engage students; as well as ensuring students are accountable for thinking and learning
(Tantillo, 2012). Tantillo (2012) also state that working in pairs provides a supportive
environment for less confident students to work collaboratively with other students.
Overview of assessment:
Based on observation of classroom discussion, students will be assessed on the use of
terminology to communicate and understand the required task. Samples from student’s
worksheets and workbook will provide evidential source of the progress and understanding of
students’ probabilistic thinking.
References:
Bryant, P., & Nunes, T. (2012). Children’s understanding of Probability. A Literature Review (Summary
Report). Retrieved from Nuffield Foundation website:
http://http://www.nuffieldfoundation.org/sites/default/files/files/Nuffield_CuP_FULL_REPORTv_
FINAL.pdf
Frykholm, J. (2001). Eenie, Meenie, Minie, Moe … Building on Intuitive Notions of Chance. Teaching
Children Mathematics, 8(2), 112-118. Retrieved from http://www.jstor.org/stable/41197719
Keene, E.O. & Zimmermann, S. (2013). Years Later, Comprehension Strategies Still at Work. The Reading
Teacher, 66(8), 601–606. doi: 10.1002/trtr.1167
Shaughnessy, J. M. (2006). Research on Student's Understanding of Some Big Concepts in Statistics. In G.
Burrill & P. C. Elliott (Eds.), Thinking and reasoning with data and chance: Sixty-eighth yearbook (pp. 7798). Reston, VA: National Council of Teachers of Mathematics
Tantillo, S. (2012). The Literacy Cookbook : A Practical Guide to Effective Reading, Writing, Speaking, and
Listening Instruction. Jossey-Bass. Retrieved 14 October 2014, from
<http://www.myilibrary.com?ID=416400>
MATHEMATICS UNIT PLANNER
Topic: Probability
Key mathematical understandings
(2-4 understandings only; written as statements believed to be
true about the mathematical idea/topic):

Probability is the extant in which something is
likely to happen.

Probability of an event happening can be
shown as a fraction; the number of ways it
can happen over the total number of
outcomes.

Probability can be shown on a line ranging
from ‘impossible, unlikely, even chance, likely
and definitely’.
Year Level: 5
Term: 4
Week: 1-2
Date: October 2014
Key AusVELS Focus / Standard (taken directly from AusVELS documents):
Content strand(s):
Number and Algebra
Measurement and Geometry
Statistics and Probability
Sub-strand(s): Chance
Level descriptions:
Level 5:
 List outcomes of chance experiments involving equally likely outcomes and represent probabilities of those
outcomes using fractions (ACMSP116).
 Recognise that probabilities range from 0-1 (ACMSP117).
Proficiency strand(s):
Understanding
Reasoning
Understanding: Using fractions to represent probabilities
Reasoning: Interpreting results of chance experiments.
Key skills to develop and practise (including
Key equipment / resources:

(4-5 key skills only):

Commenting on the likelihood of winning
simple games of chance by considering the
number of possible outcomes.
Key vocabulary (be specific and include definitions of key words
appropriate to use with students)
strategies, ways of working mathematically, language goals, etc.)

Word Cards


Clothes line rope
Investigating the probabilities of all outcomes
for a simple chance experiment and verifying
that their sum equals 1.

Dice

Coins

Describe probabilities using fractions,
decimals and percentages.

Activity sheets (Appendix 1 & 2)


Student work book

Conduct repeated trials of chance
experiments, identifying the variation between
trails and realising that the results tend to the
prediction with larger numbers of trials.

Witches cones








Outcome; one of the possible results of an
experiment
Probability: measure of the chance of an event
occurring. It measures the certainty of that event.
Event; a possible choice resulting in an outcome.
Probability of an Event; the number of true
outcomes divided by the total number of equally
likely outcomes.
Even chance/ Equally likely; theoretically equal
chances for each of the outcomes.
Impossible event; probability of the event is
equal to 0; the event absolutely cannot happen.
Experiment; an activity where results can be
observed and recorded.
Fair; an object, game, or experiment where all the
outcomes are equally probable.
Odds; one of the possible results of an
experiment.
Sample space; the set of all possible outcomes
of an experiment.
Possible misconceptions
(list of misconceptions
related to the mathematical idea/topic that students might
Key probing questions (focus questions that will be used to develop
Links to other contexts (if applicable, e.g., inquiry unit focus,
understanding to be used during the sequence of lessons; 3 – 5 probing
questions):
current events, literature, etc.):
develop):



Learning
strategies/
skills

All events are equally likely.
When determining probability from statistical
data, simple size is irrelevant.
Results of games of skill are unaffected by
the nature of the participants.
When considering spinners, the number of
the section rather than the size of angles
determines probability.
Analysing
Checking
Classifying
Co-operating
Considering options
Designing
Elaborating
MATHEMATICAL
FOCUS
(what you want the children
to come to understand as a
result of this lesson – short,
succinct statement)
Session 1
 Understand the
terminology of
chance.
 Describe how
likely an event is
to happen.
Estimating
Explaining
Generalising
Hypothesising
Inferring
Interpreting
Justifying
‘TUNING IN’
(WHOLE CLASS FOCUS)




What are the likely chances if I was to roll a 4
using a 6-sided dice?
How many possible outcomes are they when
tossing a coin?
Is this a fair or unfair game?
What is the likelihood of something to happen?
Listening
Locating information
Making choices
Note taking
Observing
Ordering events
Organising
‘INVESTIGATIONS
SESSION’
(a short, sharp task relating to the focus
of the lesson; sets the scene/ context
for what students do in the
independent aspect. e.g., It may be a
problem posed, spider diagram, an
open-ended question, game, or reading
a story)
(INDEPENDENT LEARNING)
(extended opportunity for students to
work in pairs, small groups or
individually. Time for teacher to probe
children’s thinking or work with a small
group for part of the time and to also
conduct roving conferences)
 Introduce to the students
probability.
 Explain events can be
described based on
likelihood of happening.
 Ask for some words that
could be used to describe
the likelihood.
 Show words; very likely,
likely, unlikely, very
unlikely, certain,
impossible & even
chance. Place on board in
no particular order.
 Review unknown vocabulary.
 Select volunteers to
place the words along
the ‘clothes line’ with
one end impossible
and the other end
impossible.
 Probe questions:
What is the chance of
finishing school today?
What is the chance of
growing another nose
tomorrow?
 What number sense
concepts can we
incorporate on the
Performing
Persuading
Planning
Predicting
Presenting
Providing feedback
Questioning

English: the vocabulary used in describing
probability.
Meteorologist/Weathermen: Predicting the
weather.
Fractions
Percentages



Reading
Recognising bias
Reflecting
Reporting
Responding
Restating
Revising
‘REFLECTION & MAKING
CONNECTIONS
SESSION’
(WHOLE CLASS FOCUS)
(focused teacher questions and
summary to draw out the mathematics
and assist children to make links. NB.
This may occur at particular points
during a lesson. Use of spotlight,
strategy, gallery walk, etc.)
 Provide students with
post it notes so they
can write down events
for each of the
likelihoods.
 Read some of the
students’ event
suggestions on the
‘clothes line’
Seeing patterns
Selecting information
Self-assessing
Sharing ideas
Summarising
Synthesising
ADAPTATIONS
- Enabling prompt
(to allow those experiencing difficulty to
engage in active experiences related to
the initial goal task)
- Extending prompt
(questions that extend students’
thinking on the initial task)
Testing
Viewing
Visually representing
Working independently
Working to a timetable
ASSESSMENT
STRATEGIES
(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)
 Enabling prompts:
 Observation from class
- Where would the 0 go
discussions and
on the number line?
students contribution
- Where would 1 go on
to these discussions.
the number line?
 Extending prompts:
 Work sample from the
- Students could survey
post-it-notes of
parents, grandparents,
students understanding
neighbours, friends as
of events and their
to ways probability is
likelihood.
part of their daily lives.
- How can even chance
be represented on the
number line?
Session 2
 Play ‘Heads or Tails’
 Identify and use a  Students stand up;
probability scale
placing hands on head if
line.
they think the coin lands
 Recognising
on head and hands on
probability
bottom if coin lands on
ranges from 0-1.
tails.
 Representing
 If they guess incorrectly
probability as a
students have to sit
down, the winner is the
fraction.
last student standing.
 Draw a probability scale
on the IWB and get the
students to label the
scale with 0, ¼, ½ ¾ and
0
 Teachers proposes a
lottery, the winning
number is one from 1, 2,
3, 4.
 Question: Do these
numbers have equal
chance of being drawn?
How do we know?
 Students do activity
sheet (Appendix 1).
Session 3
 Understanding
Sample space.
 List outcomes of
chance
experiments
involving equally
likely outcomes.
 Introduce ‘Greedy Pig’.

Game. Rolling the die to
accumulate points.
 Emphasise that students
need to stand or sit

between each roll and
record the results so they
count the accumulated
points.

Session 4
 Calculating
possible
 Present class with two
coins, prose question:
what are the possible
Starting with a 6-sided
die, pose question:
What are the odds of
rolling a 4?
Scaffold students’
understanding: What
is the total number of
possibilities for rolling
this die?
Now, introduce a coin,
pose question: What
are the odds of toss a
head?
 In pairs, allow students’
to roll the die 30 times
and toss the coin 30
times recording their
results using a template
(appendix 2)

Allow students in
pairs to play flip the
two coins 100 and
 Students share their
results emphasising on
the language of
fractions.
 What was some of the
similarities between
some of the results?
 Enabling prompts:
 Observation from class
- Use smaller amount
discussions and
of event, for example
students contribution
lottery possibility from
to these discussions.
2 numbers.
 Work samples from
 Extending prompts:
activity sheet (appendix
- User larger amount of
1) on understanding of
event, for example
percentages of possible
lottery possibility r from
events.
10 numbers or more.
 Students using correct
terminology.
 Select students to share
their results.
 Question: Did anyone
get the same results? If
different how?
 Teacher prose question
to probe student
thinking.
 Enabling Prompts:
 Observation from class
-Limit the number of
discussions and
rolls and toss
students contribution
-Use different material,
to these discussions.
coloured spinners.
 Work samples from
activity sheet (appendix
 Extending prompts:
-What would the
2) on understanding of
probability and
percentages of possible
percentage be to roll
events.
odd numbers?
 Students are using
-Would be affected if we
correct terminology.
were to use a 9-sided
die?

 Enabling Prompts:
-Limit the number of
rolls and toss
Referring to the first
activity, share some
results from some

Observation from
class discussions and
students contribution
outcomes from
tossing two
coins.
outcomes when flipping
both these coins?
 Allow students to
write/draw all the
possible outcomes of the
result from flipping 2
coins (HH, HT, TT etc.)
 Prose question:
-Are all outcomes equally
likely?
-What is the probability
of getting 2 heads?
 ‘If we tossed the two
coins simultaneously 100
times, how many of each
of the possible outcomes
would you expect?
record their result.



Choose from the
pairs, P1 and P2.
P1 wins the tossing
round if they get HH
and P2 wins the
tossing round if they
get HT, allow the
pairs have 10 round
game.

students.
Reflecting on the
answers at the start,
what are the possible
outcomes for tossing a
HH, TT and HT out of
100 tosses?
Referring to the
second activity, ‘ Is the
game fair or unfair’ if
so why?
- ‘How can we make it
a fair game?’
-List the possible
outcome of on coin.

-Use different material,
coloured spinners.
 Extending prompts:
-Use different materials,
the possibilities of two

dice.
to these discussions.
Students are using
terminology with
understanding and
communicating with
each other.
Work samples from
students’ books.
Session 5
 Revisit predicting
 Take the students
 What are some
 Enabling Prompts:

 Conduct a chance
possible outcomes with
outside in an open
interesting findings from
-Limit the number of
experiment using
throwing a dice
space. Students begin at
this activity?
tosses
spinners.
the starting line,
 Introduce horseracing
 If you could choose a
 Extending prompts:
(between the starting
 Describing the
game (spring carnival
different horse number
-Use different materials, 
line to the finish line are
probability of the
season) to the students.
would you?
the possibilities of two
20 witches cone).
spinner
nine sided dice.
 Allow students to select a
 What number would
outcomes, using

Roll
two
dice,
add
the
‘horse’ (number 2-12)
you select?
fractions and
score and the total
Students are going to be
Go back outside to play
decimals.
number of the dice is
the horses.

another
round
of
horse
the number of the
 Give them their allocated
racing, allowing students
horse; the horse can
number as a race number
move one cone forward. to change numbers.
to pin on to their shirt,
(students can name their  “Ask the students is this
game a ‘fair’ or ‘unfair’
horse)
game.
 Back in the classroom
ask students to write the
number 2-12 down their
mathematics book,
inform students to write
all possibilities for
Observation from
class discussions and
students contribution
to these discussions.
Students are using
terminology with
understanding and
communicating with
each other.
Work samples from
student’s book.
reaching each number,
(4, can be reached by,
1+3, and 2+2).
 Ask the students to add
all the chances that can
occur and record each
number as a fraction.
 Then ask the students to
find the percentage for
each number.