Ideas for teaching chance, data and interpretation of data
Chance, Data and Interpretation
Unit created by Joanne Villis
Year 3 Australian Achievement Standard:
Students conduct chance experiments and list possible outcomes. They
carry out simple data investigations for categorical variables.
Year 3 Australian Content Descriptors:
Conduct chance experiments, identify and describe possible outcomes
and recognise variation in results (ACMSP067).
Identify questions or issues for categorical variables. Identify data
sources and plan methods of data collection and recording (ACMSP068)
Collect data, organise into categories and create displays using lists,
tables, picture graphs and simple column graphs, with and without the
use of digital technologies (ACMSP069)
Interpret and compare data displays (ACMSP070)
ENGAGE (iDEA 1):
Task: Brainstorm a list of words that could be used to describe the chance
of an event occurring (ie likely, unlikely, impossible etc). Ask students if
they have heard numbers being used to describe chance? Discuss as a class.
Create a class probability line. Ask students to sort words along the line (ie
impossible, rarely, certain, likely, unlikely, uneven chance,) then on
different coloured card numbers to represent chance (e o, ½, 1 and o, 50%
Task: Invite students to think of an
event, write the event on a post it note
and then stick it to the probability line.
Allow students time to read each others
ENGAGE (iDEA 2):
Task: Create scenarios like the ones below for students to consider:
a) I overheard my mum telling our neighbor that on the weekend we would
definitely so something but I could not hear what it was. What might it
b) I heard the teach say, ‘It is… that all of the children in this class will
watch television tonight’ but I didn’t hear one of the word. What might
the missing word be? What is something that is more likely to happen
than what the teacher is talking about?
c) Someone asked the teacher a question and she replied ‘Maybe’. What
might the question be?
d) Sydney went ice skating for the first time, stood up and… What might
have happened next?
e) A family has three children We know that at least one of the children is a
girl. Draw what the other family might look like.
f) A class wrote down some things that they felt were impossible. What
might they have written?
Source: Sullivan, P & Lilburn, P (2008) Open-ended math activities, Second
Edition, Oxford Press, p. 100-101.
ENGAGE (iDEA 3):
Task: Play the fair race game. You can play this game outside with boxes of
dress up clothes or small bean bags.
a) Place students in teams of 4.
b) Ask students to line up in their team so that your class is in 4 lines.
c) Place clothes (or bean bags) in 4 boxes opposite each team. The task is
for team members to take it in turns to run to the box of clothes, put on a
garment, run back and tag the next person in the line (ie like a relay race).
The first team with no clothes left in their box is the winner.
NOTE: For the first race use an even number of items in each box. Then for
the next race change the number of items in each team’s box so that some
have more than others. Race and then ask students if the game was fair?
Discuss why or why not?
EXPLORE (iDEA 1):
Task: This activity is a modified version of an Indigenous Australian Game
known as ‘kal-ka-doon kee-an’ .
Background: “In areas of north Queensland, a game of throwing skill was
played. A large bone, such as an emu shinbone (with twine attached to it)
was thrown over a net (used to catch emus) into a pit or hole. Considering
the distance to the hole, great skill was required to correctly aim the bone
and ensure that it did not touch the net” (Australian Sports Commission,
Language: “The game is called kee’an, which means ‘to play‘ in the Wik-
Mungkan language of north Queensland. The Kalkadoon people from
around the Mount Isa area also played a game similar to the one outlined
and their connection has been recognised as part of the name of this
game” (Australian Sports Commission, 2009, p.64).
Australian Sports Commission (2009), Yulunga Traditional Indigenous
Retrieved from: ausport.gov.au/isp
1.Ask students to list all of the possible outcomes which could occur if they
threw their object. For example: (1) player 1’s object and player 2’s object
will land inside the target (2) player 1’s object will land inside target but
player 2’s will not (3) player 2’s object will land inside the target but player
1’s will not (4) neither of the player’s targets will land inside the target.
2. Model on an IWB or whiteboard how to rule up a table in order to record
3. Model how to record using the tally system. Inform students that they
will need to use the tally system in order to record the results of their game
after each pair has thrown their object.
4. Students play the game and record their results.
5. Demonstrate to students on an IWB or
whiteboard how to draw a column graph.
Students can follow the instructions step by
step in their books as this may be the first
time students have drawn graphs in their
current year level. Remember to encourage
students to name the axis of the graph (ie
possible outcomes and throw results).
6. Repeat step 5 using a bar graph.
7. Use Microsoft Word Charts to create a pie graph.
a) Go to Microsoft Word, Insert, Chart. Select the chart you require.
b) Enter the data into the EXCEL part. This will automatically adjust the
data being displayed in the graph.
EXPLORE (iDEA 2):
Task: Ask students to consider the scenarios below and provide them with
the equipment needed in order to test their thoughts.
a) 2 dice
Scenario 1: Two students were playing a dice game. One student tossed
two dice together and when they landed one was 6 and one was 4. What
other combinations might the students have tossed?
Scenario 2: Zac threw two dice and when they landed he subtracted one
number from the other and wrote down the answer 1. What might the
numbers on each dice have been?
Equipment: 2 dice
b) Bag of coloured paper
Scenario: In a bag there are some coloured pieces of paper. I draw one
piece of paper and it is red. I put it back and draw again. This time the
paper is black. I put it back. After ten draws, I have drawn out three red
and seven black. How many pieces of paper might there be in the bag and
home many might be black?
Equipment: Red and black pieces of paper and a zip lock back.
Source: Sullivan, P & Lilburn, P (2008) Open-ended math activities, Second
Edition, Oxford Press, p. 101-103.
EXPLORE (iDEA 3):
1. Show students a jar with a packet of jelly beans inside. Ask students to
record all of the possible outcomes which could occur if they put their
hand into the jar and selected a jelly bean (ie red, green, blue etc). As
students to record all possible outcomes using a list.
2. Invite students to predict how many red, blue etc jelly beans there are
in the jar and record their predictions in the their book.
3. Tip an additional bag of jelly beans into the jar and ask student to
predict how many of each colour are now in the jar.
4. Ask students to calculate the total of their number of jelly beans for 1
bag and then two bags of jelly beans.
5. Ask students to record their thinking or mathematical reasoning.
6. Let students test their calculations of total jelly bean numbers using a
Note: I used 3 packets and this task took too long. Therefore, I suggest
that 2 packets are used instead.
7. Model/demonstrate how to draw a table in order to record the
outcomes of the investigation.
8.Allow students to pull 2 jelly beans out of the jar at a time a
demonstrate how to record results on an IWB or whiteboard using the
tally system. Invite students to call out their colours in a loud and clear
voice so that peers can hear.
9. Once all jelly beans have been removed from the jar, invite students
to tall their results. If there are inconsistencies amongst students, this
doesn’t matter. The focus if for students to record their own data.
10. Invite students to analyse their data using chance language (ie
greater than, equal, least likely). This process should require about 4
11. Ask student to draw a jar and
inside draw their own jelly beans
which they have collected from
the previous activities.
12. Discuss various ways of
explaining chance (ie words and
percentages). Introduce students
to the idea o representing
probability using fractions. For
example, the bottom number
tells me how in total and the top
number tells me how many I am
talking about. If I had 9 jelly
beans and 4 of them were red,
the probability of me selecting a
red would be 4/9.
I worked on the following activities with a student whilst a student
teacher (Madeleine Hunter) was teaching.
Once the data of the jelly bean numbers had been recording I asked the
1. Consider how she could work out the percentage of each colour of
jelly bean compared to the total.
2. I asked her to record her calculations.
3. She calculated her percentages rounding to the nearing 0.5. This
resulted with a total of 115%.She then decided to calculate the
percentages to the nearest 10 which resulted with an overall total of
98% (we thought this was close enough).
4. The student was then asked to draw a pie graph to represent her
5. Then I gave her a challenge. For example, draw a pie graph
combining the totals red, blue, green , orange and black and white
13. Ask students to create a column graph using a scale of 5 and then an
picture bar graph where 1 jelly bean represents 10 jelly beans.
EXPLORE (iDEA 3):
1. Give each student a Minite.
2. Show students how to rip a Mintie wrapper to create a piece as long as
3. Ask students to measure the length of their Mintie wrapper and round
the length of the wrapper to the nearest 5cm.
4. Students record the length of their Mintie wrapper and the data is
collated as a class using a table.
5. Ask students to draw a picture
graph to represent the various lengths
of Minitie wrappers. Each Mintie on
the picture graph needs to represent
5cm of length.
6. Using EXCEL students enter their Mintie data and then create a column
and bar graph to represent their data.
7. Students interpret the data displayed in their graphs. For example,
what was the greatest length and the shortest length? What is the total
length of the class Mintie wrappers combined? (students may need to use
a calculator). As an extension, students may calculate the average length
of the class Mintie wrappers.
COMPARING DATA (iDEA 1):
Note: These tasks have been selected to link to out Geography unit
which we are teaching at the same time.
1. Download the document ‘Comparing the weather in different parts of
the world’. This resource has been designed to compare rainfall in
Chittagong and London, both yearly and monthly. This is a rich resource
which links Maths, Geography and elements of Humanities.
2. Before students begin to look at the at ask student to think about how
rainfall could be recorded. Visit ABC Splash:
3. Then use Google Earth to locate Chittagong and London on a map.
4. Then explore what a flood is. Download Flood Information Document.
5.Finally, complete the data comparison questions in ‘Comparing the
weather in different parts of the world’.
1. Show students an interactive spinner online and how it can be adjusted.
2. Ask students to think about how we might use the spinner to
investigate chance? What questions could we ask? What could we do?
Brainstorm as a class.
3. As a class choose one question to investigate. Then ask students how
might we conduct our investigation? What could we do? Brainstorm ideas
a class and select one as a class.
4. Conduct the chance investigation as a class.
5. How can we interpret the data? What is it telling us? Ask student to
write 4 sentences to explain the results of the data.
1. Provide students with a collection of objects including dice, flip blocks
2. Inform students that they have been asked to conduct an investigation
about chance using dice, flip blocks or coins. They can choose any of the
objects but they need to complete the following tasks:
a) Write an aim (what are they trying to investigate and what are they
b) Write method (how are they going to conduct their investigation)
c) Write a prediction (what do they think the outcome will be)
d) Determine how they will record their data (this needs to be decided
before they conduct their investigation)
e) Conduct their investigation and record their results
f) Represent their results
g) Interpret their results (what were the outcomes, how did the outcome
compare to your prediction?)
h) Share their investigation with the class
Use of these ideas:
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used by teachers for educational purposes only.