RIC-20265_ACM_Statistics_and_Probability_Year_4–Data_representation_and_interpretation–1

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Australian Curriculum Mathematics 

resource book: Statistics and Probability 

(Years 3 & 4) 

Published by R.I.C. Publications ® 2014 

Copyright © Clare Way 2014 

RIC–20265 

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copyright under the Copyright Act 1968 (Cth) and is owned 

by the Australian Curriculum, Assessment and Reporting 

Authority 2014. 

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elaborations: This is an extract from the Australian 

Curriculum. 

Elaborations: This may be a modified extract from the 

Australian Curriculum and may include the work of other 

authors. 

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• The author’s material aligns with the Australian 

Curriculum content descriptions for the relevant year 

and subject. 

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this material at http://www.australiancurriculum.edu.au/ 

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Australian Curriculum Mathematics 

resource book: 

Statistics and Probability 

(Years 3 & 4) 

Foreword 

Australian Curriculum Mathematics resource book: Statistics and Probability (Years 3 & 4) is one in a series of three teacher resource books that 

support teaching and learning activities in Australian Curriculum Mathematics. The books focus on the Statistics and Probability content strands of 

the Australian mathematics curriculum. The resource books include theoretical background information, resource sheets, hands-on activities and 

assessment activities, along with links to other curriculum areas. 

Titles in this series are: Australian Curriculum Mathematics resource book: Statistics & Probability (Foundation/Years 1 & 2) 

Australian Curriculum Mathematics resource book: Statistics & Probability (Years 3 & 4) 

Australian Curriculum Mathematics resource book: Statistics & Probability (Years 5 & 6) 

Format of this book....................... iv – v 

Year 3 

Chance......................................... 2–11 

• Chance –1 

Conduct chance experiments, identify and 

describe possible outcomes and recognise 

variation in results (ACMSP067) 

–– 

Teacher information............................................ 2 

–– 

Hands-on activities............................................. 3 

–– 

Links to other curriculum areas........................... 4 

–– 

Resource sheets...............................................5–7 

–– 

Assessment...................................................8–10 

–– 

Checklist............................................................ 11 

Data representation and 

interpretation.............................12–40 

• DR&I –1...................................12–21 

Identify questions or issues for categorical 

variables. Identify data sources and plan 

methods of data collection and recording 

(ACMSP068) 

–– 

Teacher information.......................................... 12 

–– 

Hands-on activities........................................... 13 

–– 

Links to other curriculum areas......................... 14 

–– 

Resource sheets...........................................15–18 

–– 

Assessment.................................................19–20 

–– 

Checklist............................................................ 21 

• DR&I –2...................................22–31 

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 


–– 


–– 


–– 


–– 


–– 

Assessment.................................................29–30 

–– 

Checklist........................................................... 31 

Contents 

• DR&I –3...................................32–40 

Interpret and compare data displays 


–– 


–– 

Hands-on activities.....................................33–34 

–– 


–– 


–– 

Assessment.................................................38–39 

–– 

Checklist............................................................ 40 

Answers............................................41 


Chance........................................42–73 

• Chance –1................................42–51 

Describe possible everyday events and order 

their chances of occurring (ACMSP092) 

–– 


–– 


–– 


–– 


–– 

Assessment.................................................49–50 

–– 

Checklist............................................................ 51 

• Chance –2................................52–61 

Identify everyday events where one cannot 

happen if the other happens (ACMSP093) 

–– 


–– 


–– 


–– 

Resource sheets............................................55-58 

–– 

Assessment.................................................59–60 

–– 

Checklist............................................................ 61 

• Chance –3................................62–73 

Identify events where the chance of one will 

not be affected by the occurrence of the other 


–– 


–– 


–– 


–– 


–– 

Assessment.................................................71–72 

–– 

Checklist............................................................ 73 

Data representation and 

interpretation........................... 74–106 

• DR&I –1...................................74–83 

Select and trial methods for data collection, 

including survey questions and recording 

sheets (ACMSP095) 

–– 


–– 


–– 


–– 


–– 

Assessment.................................................81–82 

–– 

Checklist............................................................ 83 

• DR&I –2...................................84–93 

Construct suitable data displays, with and 

without the use of digital technologies, 

from given or collected data. Include tables, 

column graphs and picture graphs where 

one picture can represent many data values 


–– 


–– 


–– 


–– 


–– 

Assessment.................................................91–92 

–– 

Checklist............................................................ 93 

• DR&I –3................................. 94–106 

Evaluate the effectiveness of different 

displays in illustrating data features including 

variability (ACMSP097) 

–– 


–– 


–– 


–– 

Resource sheets.........................................97–102 

–– 

Assessment.............................................103–105 

–– 

Checklist.......................................................... 106 



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Answers..........................................107 

Australian Curriculum Mathematics resource book: Statistics and Probability (Years 3 & 4) R.I.C. Publications ® www.ricpublications.com.au iii

Format of this Book 

This teacher resource book includes supporting materials for teaching and learning in all sections of the Statistics and Probability content strand of 

Australian Curriculum Mathematics. It includes activities relating to sub-strands: Chance and Data representation and interpretation. All content 

descriptions have been included, as well as teaching points based on the Curriculum’s elaborations. Links to the proficiency strands have also been 

included. 

Each section supports a specific content description and follows a consistent format, containing the following information over several pages: 

• teacher information with related terms, student vocabulary, what the content description means, teaching points and problems to watch for 

• hands-on activities 

• links to other curriculum areas 

• resource sheets 

• assessment sheets. 

• a checklist 

Answers relating to the resource and assessment pages are included. 

The length of each content description section varies. 

Related terms includes vocabulary associated 

with the content description. Many of these 

relate to the glossary in the back of the official 

Australian Curriculum Mathematics document; 

additional related terms may also have been 

added. 

Student vocabulary includes words which 

the teacher would use—and expect the 

students to learn, understand and use—during 

mathematics lessons. 

The proficiency strand(s) (Understanding, 

Fluency, Problem Solving solving or Reasoning) relevant 

to each content description are listed. shown in bold. 

Teacher information includes background information relating to the content description, as well as 

related terms, desirable student vocabulary and other useful details which may assist the teacher. 

What this means provides 

a general explanation of the 

content description. 

Teaching points provides 

a list of the main teaching 

points relating to the content 

description. 

What to watch look for for suggests any any 

difficulties and misconceptions 

the students might encounter or 

develop. 



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Hands-on activities includes descriptions or 

instructions for games or activities relating to the 

content descriptions or elaborations. Some of the 

hands-on activities are supported by resource 

sheets. Where applicable, these will be stated for 

easy reference. 

iv Australian Curriculum Mathematics resource book: Statistics and Probability (Years 3 & 4) R.I.C. Publications ® www.ricpublications.com.au

Format of this Book 

Links to other curriculum areas includes activities in other curriculum areas which support 

the content description. These are English, Information and Communication Technology, Health 

and Physical Education, Science, Economics and the Arts). This section may list many links or only 

a few. It may also provide links to relevant interactive websites appropriate for the age group. 

Cross-curricular links reinforce the knowledge that mathematics can be found within, and relate 

to, many other aspects of student learning and everyday life. 

Resource sheets are provided to support 

teaching and learning activities for each 

content description. The resource sheets 

could be cards for games, charts, additional 

worksheets for class use or other materials 

which the teacher might find useful to use or 

display in the classroom. For each resource 

sheet, the content description to which it 

relates is given. 

Assessment pages are included. These 

support activities included in the hands-on 

activities or resource sheets. 



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Each section has a checklist which teachers 

may find useful as a place to keep a record of 

the results of assessment activities, or their 

observations of hands-on activities. 

Answers for resource pages (where 

appropriate) and assessment pages are 

provided. 

Australian Curriculum Mathematics resource book: Statistics and Probability (Years 3 & 4) R.I.C. Publications ® www.ricpublications.com.au v

Year 4—Sub-strand: Data representation and interpretation—DR&I – 1 

Select and trial methods for data collection, including survey questions and recording sheets 


Related Terms 

Teacher Information 

Data 

• A term used to describe a collection 

of numbers or information. 

Survey 

• To collect sample opinions or facts 

from a group. 

Table 

• A means of organising data in rows 

and columns. 

Tally marks 

• Marks made to record items or 

events, usually grouped in fives by a 

diagonal line (e.g. ). 

Venn diagram 

• A diagram that represents sets and 

their relationships. The overlapping 

sections of the circles represent 

more than one choice. 

What this means 

• Students will be presented with a variety of methods they can 

use to survey and collect data. They will be given the opportunity 

to use different methods of recording data and evaluate how 

effective each one is. They will come to realise that when collecting 

data you need to decide what sort of information to collect, where 

and who to collect it from and how they will need to collect it. 

While some methods of collection suit some investigations, other 

surveys or data collection may require a different method. Through 

this learning process students will start to choose the most 

effective way to collect data according to the type of investigation 

they are doing. 

Teaching points 

• Demonstrate the importance of correct questioning when carrying 

out a survey. 

• Present students with a variety of methods for recording and 

collecting data. 

• Encourage students to recognise that the type of data collection 

used depends on the type of survey or investigation. 

• Give students the opportunity to trial various data collection 

methods. 

• Allow students the opportunity to assess and evaluate the 

effectiveness of their data gathering. 

What to look for 

• Students who have difficulty choosing the most effective method 

to collect data for an investigation. 

• Students who have difficulty evaluating the effectiveness of data 

collection methods. 



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Student vocabulary 

questions 

data 

collect 

survey 

tables 

Proficiency strand(s): 

Understanding 

Fluency 

Problem solving 

Reasoning 

74 Australian Curriculum Mathematics resource book: Statistics and Probability (Years 3 & 4) R.I.C. Publications ® www.ricpublications.com.au


Survey topics (pg 77) 

Hands–on Activities 

• Present students with a list of possible topics that could be used in an investigation or survey. 

• Use the topics to initiate a discussion about necessary questions and how investigations can be carried out. 

• Ask pairs of students to choose a topic from the list (or their own topic) and to come up with a question and suggest a 

method for how they would go about finding out this information. 

Methods for collecting data 

• Brainstorm and list all the methods there are for collecting data. For example: a list, a table that uses tally marks, a table 

that uses ticks, a two-way table, a survey of questions, a Venn diagram, a number line. 

• Suggest examples of investigations you could carry out that would use each of the methods the students have 

suggested. For example: draw up a number line and write on one end the word ‘never’, the other end, ‘always’ and the 

word ‘sometimes’ in the middle. Ask students a question such as ‘Do you go to the beach on the weekend?’ Ask those 

students who never do to raise their hand then use ticks, dots or any mark to show these students above the word 

never. Then repeat the same method for ‘sometimes’ and ‘always’. 

Tables for data collection (pg 78) 

• Give each student a copy of the sample tables that can be used to collect data. What type of investigation could these 

tables be used for? 

• Ask students to write a question to find out what electronic equipment their classmates like to use the most. Which 

table would be best to use in this investigation? Ask students to choose one to use when surveying their classmates. 

• Once completed, ask students to compare methods of data collection. Which do they think was the best or easiest to 

use and read? 

Two-way tables (pg 79) 

• Two-way tables are a good method to show different opinions in a survey. For example, you could ask the question, ‘Do 

you like fruit, vegetables or both?’ and present this information in a two-way table. Look at the example of likes/dislikes 

fruit and likes/dislikes vegetables. Ask students questions about the table. Is the information clear? 

• Use the blank two-way table to survey 10 of your classmates if they like Xbox , PlayStation or both. Look at the results. 

Is this an effective way to present the information? Is there another way? 

Venn diagram (pg 80) 

• A Venn diagram can represent sets of information and relationships between 

these sets. The overlapping sections of the circles represent more than one 

choice. They are useful for showing information where those surveyed can 

choose more than one category. 

• Ask the class to raise their hand if they like Xbox , PlayStation , Wii , two of 

these or all three. Show their responses with a ✗ on a large Venn diagram. 

• Give the students a Venn diagram and ask them to survey 10 of their 

classmates to see if they like action movies, comedy movies or scary movies. 

Make a plan 

• Model to students how to make a plan for collecting data. For example, if you 

wanted to find out if you classmates prefer a party at home or at a venue, you 

would follow these steps: 

–– 

Write a survey question. 

–– 

Draw up a Venn diagram and survey your classmates as to their favourite type of party. 

–– 

Ask each student in your class the survey question and record their response with a ✗ on the Venn diagram. 

–– 

Total up the responses on the diagram. 

–– 

Write one or two statements about the results. 



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• Ask students to choose a topic and write a plan on how they are going to investigate it. 

Xbox 

Wii 

PlayStation 

Australian Curriculum Mathematics resource book: Statistics and Probability (Years 3 & 4) R.I.C. Publications ® www.ricpublications.com.au 75


Links to Other Curriculum Areas 

English 

• Writing: In small groups brainstorm and make a list of students likes and dislikes. Discuss how these words are 

considered opposites e.g. if you were to say you like quiet music you may dislike loud music. 

• Writing: Create your own book of questions. They could be questions about life, questions you could use in a survey, 

questions you might use in an interview etc. 

• Spelling: Make a list of words that are opposite. For example: night—day, light—dark, heavy—light, tall—short. 

Information and Communication Technology 

• Demonstrate to students how to draw up a table in a word document. Tables are useful tools for collecting and 

recording information. Before you create a table you need to work out how many rows and columns you need 

according to the number of categories you have in your survey. 

• Go to the website , click ‘Data’ then find ‘How to do a survey‘ and ‘Survey questions’. Read 

through both of these and compare their methods to what you know and have learnt. 

Science 

• Tables and diagrams are often used by scientists to show investigated information. For example: Investigate mini-beasts 

on the internet or use a resource book and then use a table such as the one below to show how many legs a variety of 

mini-beasts have. 

lizard 

beetle 

ant 

spider 

slater 

centipede 

f ly 

2 legs 4 legs 6 legs 8 legs 

• Use a Venn diagram to make a list of items in the classroom that are recyclable or non-recyclable. 

10 or 

more legs 



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Resource Sheet 

Survey topics 

Copy and distribute. 

Birthday months 

Favourite takeaway food 

CONTENT DESCRIPTION: Select and trial methods for data collection, including survey questions and recording sheets (ACMSP095) 

Favourite sport 

Favourite subject 

Favourite pastime activity 

Favourite electronic device 

Number of people in 

the family 

Class pets 

Holiday destinations 

Favourite outings 

Party venues 

Favourite colour 

Hair colour 

Eye colour 

Favourite fruit 

Favourite vegetable 

Favourite drink 

Travelling to school 

methods 

Bedtimes 

Dinnertimes 

Favourite reading material 



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Favourite movies 

Favourite TV shows 

First name initial 

Favourite footwear 

Favourite musical artist 




Tables for data collection 




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Two-way tables 


Likes fruit Dislikes fruit Likes vegetables 

Dislikes 

vegetables 


Harry Caleb Harry Georgia 

Georgia Scout Caleb Lexia 

Lexia Sophie Matt 

Sophie Alex Scout 

Matt 

Alex 

Leila 

Yong 

Leila 

Yong 

Likes Xbox Dislikes Xbox Likes PlayStation Dislikes 

PlayStation 



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Venn diagram 


Action 

movie 

Scary 

movie 

Comedy 

movie 



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Year 4—Sub-strand: Data representation and interpretation—DR&I – 1 Assessment 1 

Name: 

date: 

1. If you wanted to survey your class to find out which day their birthday fell on 

this year, what question would you need to ask? 

? 

2. Ask at least 10 of your classmates your question and record their responses on 

the table below you think works best for this survey. 


Sunday 

Names S M Tu W Th F Sa 

Monday 

Tuesday 

Wednesday 

Thursday 

Friday 

Saturday 

3. Look at your information and answer the following questions: 

(a) 

(b) 



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Which day did the most birthdays fall on? 

Which day did the least birthdays fall on? 

(c) Do you think the table you chose was the best method? Yes No 

Why/why not? 

4. Could you use a Venn diagram for this survey? Yes No 

Why/why not? 


Assessment 2 Year 4—Sub-strand: Data representation and interpretation—DR&I – 1 

Name: 

date: 

1. 10 students were surveyed on whether they liked reading and writing. Transfer 

their responses onto the two-way table below. 

Ashley – I like reading and writing. Ben – I like reading but don’t like writing. 

Jay – I don’t like reading or writing. Mia – I like reading and writing 

Samuel – I like both 

Sky – I only like writing 

Eden – I like reading but not writing. Josh – I like both 

Faith – I only like reading 

Manuel – I like reading and writing 

Likes reading Dislikes reading Likes writing Dislikes writing 

2. Now represent this information on the Venn diagram using crosses (✗). 

Likes 

reading 

3. Does the Venn diagram give us all the information? 

4. Which method shows the survey information the best? 

Why? 

Likes 

writing 



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Checklist 

Select and trial methods for data collection, including survey questions and recording sheets 


Student Name 

Selects topics and writes 

appropriate questions for 

data collection 

Chooses the most 

effective method to 

collect data 

Compares the 

effectiveness of different 

methods of collecting 

data 



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DR&I – 1 

Year 4 Answers 

Page 81 Assessment 1 

1. What day does your birthday fall on this year? 

4. No—too many categories 

Page 82 Assessment 2 

1. 

2. 

Likes reading 

Ashley 

Samuel 

Eden 

Faith 

Ben 

Mia 

Josh 

Manuel 

Likes writing 

Ashley 

Samuel 

Mia 

Sky 

Josh 

Manuel 

Dislikes reading 

Jay 

Sky 

Dislikes writing 

Jay 

Eden 

Faith 

Ben 

3. No, as it doesn’t tell us who dislikes reading and writing. 

4. Two-way table 



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RIC-20265_ACM_Statistics_and_Probability_Year_4–Data_representation_and_interpretation–1

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