Australian Curriculum Mathematics: Statistics and Probability - Book 2 (Middle Primary)

RIC-6113 5.6/790

Australian Curriculum Mathematics resource book: Statistics and Probability (Years 3 & 4) Published by R.I.C. Publications® 2014 Copyright© Clare Way 2014 ISBN 978-1-921750-35-2 RIC– 6113

Titles in this series: Australian Curriculum Mathematics resource book: Statistics and Probability (Foundation/Years 1 & 2) Australian Curriculum Mathematics resource book: Statistics and Probability (Years 3 & 4) Australian Curriculum Mathematics resource book: Statistics and Probability (Years 5 & 6) All material identified by is material subject to copyright under the Copyright Act 1968 (Cth) and is owned by the Australian Curriculum, Assessment and Reporting Authority 2014.

For all Australian Curriculum material except 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.

Disclaimer: ACARA neither endorses nor verifies the accuracy of the information provided and accepts no responsibility for incomplete or inaccurate information.

In particular, ACARA does not endorse or verify that: • The content descriptions are solely for a particular year and subject; • All the content descriptions for that year and subject have been used; and • The author’s material aligns with the Australian Curriculum content descriptions for the relevant year and subject.

You can find the unaltered and most up to date version of this material at http://www.australiancurriculum.edu.au/ This material is reproduced with the permission of ACARA.

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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)

Contents 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 (ACMSP069) – – – – – –

Teacher information ......................................... 22 Hands-on activities .......................................... 23 Links to other curriculum areas ........................ 24 Resource sheets ..........................................25–28 Assessment ................................................29–30 Checklist .......................................................... 31

• DR&I –3 ..................................32–40 Interpret and compare data displays (ACMSP070) – – – – – –

Teacher information ......................................... 32 Hands-on activities ....................................33–34 Links to other curriculum areas ........................ 34 Resource sheets ..........................................35–37 Assessment ................................................38–39 Checklist ........................................................... 40

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

Year 4 Chance .......................................42–73 • Chance –1 ...............................42–51 Describe possible everyday events and order their chances of occurring (ACMSP092) – – – – – –

Teacher information ......................................... 42 Hands-on activities .......................................... 43 Links to other curriculum areas ........................ 44 Resource sheets ..........................................45–48 Assessment ................................................49–50 Checklist ........................................................... 51

• Chance –2 ...............................52–61 Identify everyday events where one cannot happen if the other happens (ACMSP093) – – – – – –

Teacher information ......................................... 52 Hands-on activities .......................................... 53 Links to other curriculum areas ........................ 54 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 (ACMSP094) – Teacher information ......................................... 62 – Hands-on activities .......................................... 63 – Links to other curriculum areas ........................ 64

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

– Resource sheets ..........................................65–70 – 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) – – – – – –

Teacher information ......................................... 74 Hands-on activities .......................................... 75 Links to other curriculum areas ........................ 76 Resource sheets ..........................................77–80 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 (ACMSP096) – – – – – –

Teacher information ......................................... 84 Hands-on activities ....................................85–86 Links to other curriculum areas ........................ 86 Resource sheets ..........................................87–90 Assessment ................................................91–92 Checklist ........................................................... 93

• DR&I –3 ................................94–106 Evaluate the effectiveness of different displays in illustrating data features including variability (ACMSP097) – – – – – –

Teacher information ......................................... 94 Hands-on activities ....................................95–96 Links to other curriculum areas ........................ 96 Resource sheets ........................................97–102 Assessment ............................................103–105 Checklist ......................................................... 106

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

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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.

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.

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 shown listed. in bold.

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 look watchforforsuggests suggestsany any difficulties and misconceptions the students might encounter or develop.

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)

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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.

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)

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v

Year 3—Sub-strand: Chance – 1

Conduct chance experiments, identify and describe possible outcomes and recognise variation in results (ACMSP067)

TEACHER INFORMATION

RELATED TERMS Chance

What this means

• The likelihood of an event occurring.

• Students will have the opportunity to recognise that some events and experiments produce different results each time they are carried out. They will have the opportunity to prove this by conducting simple experiments of chance such as tossing a coin or drawing out objects from a bag. They will come to understand that there will be variations in their results if they were to repeat the same experiment.

Outcome

• The result of an event or experiment.

Variations

Teaching points

• A change from the normal or standard.

• Set up a variety of chance experiments for students to engage in.

• Help students recognise that some chance experiments, when repeated, will have a number of possible outcomes.

• Encourage students to recognise variations in the results of chance experiments.

• Allow students the opportunity to describe the possible outcomes of a chance experiment.

What to look for • Students who have difficulty identifying the variations within a chance experiment.

• Students who have difficulty describing the results of a chance experiment.

Student vocabulary chance outcome experiments variations

Proficiency strand(s): Understanding Fluency Problem solving Reasoning

identifying

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Year 3—Sub-strand: Chance – 1

HANDS–ON ACTIVITIES Which colour?

• Place the following coloured balls, beads or blocks in a paper or cloth bag: 8 yellow, 4 blue and 2 red. Predict what colour you are most likely to draw out the first time.

• Draw out 5 of the items, predicting what colour they might be before you draw them out. Write down your predictions, then write down the colours.

• Repeat the same experiment 3 times, drawing out 5 colours each time. Were the results the same or different each time?

• What would happen if there were equal numbers of the coloured items in the bag; for example, 4 yellow, 4 blue and 4 red? With an equal chance, would the results be the same or different? Carry out this experiment 3 times and discuss the results.

Heads or tails? (pg 5) • Discuss how when you flip a coin it will always turn out either heads or tails.

• Play a game using a coin where all the students start standing. Students choose a coin side by placing their hands on their heads for the ‘heads’ side and their hands on their backsides for the ‘tails’ side. Flip the coin and those who picked the correct action to match the coin side stay standing; those who didn’t sit down. Continue the game until there is only one person standing.

• Ask students to toss a coin 10 times and record the results on the table provided. Would the results be the same or different if you were to repeat the experiment? Repeat the experiment. What did you discover?

Ruler flip • Using the same method as tossing a coin, ask students to flip a ruler and see if it lands number-side up or blank-side up.

• Draw up a simple table like the ones below and repeat the experiment 10 times, recording the results in the table.

1

2

3

4

5

6

7

8

Number-side up

Total:

Blank-side up

Total:

9

10

• Discuss the results with students. Would they be the same if you were to repeat the experiment?

Roll the dice (pg 6) • Ask students to roll a dice until they get a six (6); discuss and compare how many rolls of the dice it took.

• Discuss using the words likely and unlikely the chances of rolling a 6 on the first roll. The chance of rolling a 6 within 3 rolls? Within 6 rolls?

• Ask students to devise their own chance experiment using a dice. They may use the table provided or draw up their own table to record their results.

• Model to students how they can transfer their information onto a simple graph.

Dice games of chance (pg 7) • Use the cube net outline to make a dice. Number each side with dots or numbers, cut out the cube net and glue it together. Use the dice to play the following games.

• Students work with a partner and take turns to roll a dice, recording and adding their numbers as they go. The first person to reach 50 or over is the winner.

• To make the game more challenging you may wish to add two dice and play first to 100.

• Alternatively, start at 50 or 100 and work backwards, subtracting numbers until they reach 0.

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

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3

Year 3—Sub-strand: Chance – 1

HANDS–ON ACTIVITIES (CONTINUED) Deck of cards • Game: Place a symbol of each suit of cards in a corner of the classroom (hearts, diamonds, spades and clubs). Ask students to choose a suit/corner of the room to stand in. The teacher then selects a card from a playing deck and holds it up. The students standing in the corner of the room that matches the card selected are out and have to sit down.

Continue the game until there is only one or a small group of students left standing.

• Ask students to create their own game or chance experiment using a deck of cards. Present these to the class.

LINKS TO OTHER CURRICULUM AREAS English • Writing: Model how to set out a science experiment (procedure writing). For example, if you were to write up a chance experiment using a dice, you would need to include the following steps: aim, equipment, procedure, results and conclusion.

Information and Communication Technology • Using a computer locate <www.kidsmathgamesonline.com> and play the ‘Probability game for kids’.

Health and Physical Education • The teacher places four different coloured cones or markers in each corner of a playing field or open space. Students must select a colour and run to that cone or marker. The teacher then draws out a matching colour from a bag and those students standing at that colour must then sit out of the game. The game continues until only one student is left standing.

• Many games in sport are games of chance; select a game such as tunnel ball, T-ball or kick ball and discuss the chances of a team winning. What helps a team have a greater chance of winning? Play a team game as a class.

Science • Choose a chance experiment to write up as a science report. For example, drawing coloured balls from a bag, drawing suits from a deck of cards, tossing a coin, rolling a dice and so on. Use procedure writing to work through and record the experiment (see English).

Economics • Discuss how there are many games of chance within our community. Some involve money and gambling; for example, horse racing, lotto, raffles, casinos, card games and poker machines. These are all games of chance and not guaranteed to win money. It is poor economics to rely on games of chance for monetary gain or income.

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Year 3—Sub-strand: Chance – 1

RESOURCE SHEET Heads or tails?

Copy and distribute.

1

2

3

4

5

6

7

8

9

10

Total

1

2

3

4

5

6

7

8

9

10

Total

1

2

3

4

5

6

7

8

9

10

Total

1

2

3

4

5

6

7

8

9

10

Total

Heads

CONTENT DESCRIPTION: Conduct chance experiments, identify and describe possible outcomes and recognise variation in results (ACMSP067)

Tails

Heads Tails

Heads Tails

Heads Tails

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

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5

Year 3—Sub-strand: Chance – 1

RESOURCE SHEET Roll the dice Copy and distribute.

1

2

3

4

5

6

2

3

4

5

6

Dice graph:

1 6

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

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CONTENT DESCRIPTION: Conduct chance experiments, identify and describe possible outcomes and recognise variation in results (ACMSP067)

Dice table:

Year 3—Sub-strand: Chance – 1

RESOURCE SHEET Dice games of chance

CONTENT DESCRIPTION: Conduct chance experiments, identify and describe possible outcomes and recognise variation in results (ACMSP067)

Copy and distribute.

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

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Assessment 1

Year 3—Sub-strand: Chance – 1

NAME:

DATE:

1. Place 10 coloured balls, counters or beads in a bag you can’t see through—6 green, 3 blue and 1 yellow.

(a) It is

that a yellow ball will be drawn out first.

(b) It is

that a green ball will be drawn out first.

(c) It is

that a blue ball will be drawn out first.

3. Draw out five balls and record the results in the table below.

1st

2nd

3rd

4th

4. Were your predictions from question 2 correct?

5th

Yes

No

5. If you were to repeat the experiment again (draw out 5 balls) do you think the results would be the same or different?

Why?

6. Place the 10 balls in the bag again and record how many times it takes until you draw out each colour. (a) Green:

times

(b) Blue:

times

(c) Yellow:

times

7. If you wanted to give the colours an even chance of being drawn out, what would you need to do?

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CONTENT DESCRIPTION: Conduct chance experiments, identify and describe possible outcomes and recognise variation in results (ACMSP067)

2. Predict what might happen by completing these sentences using words such as very likely, likely or unlikely.

Assessment 2

Year 3—Sub-strand: Chance – 1

NAME:

DATE:

1. If you were to toss a coin do you think it will come up heads or tails?

2. Toss a coin. Was your prediction correct?

Yes

No

CONTENT DESCRIPTION: Conduct chance experiments, identify and describe possible outcomes and recognise variation in results (ACMSP067)

3. Toss a coin 10 times and record the results in the table below using ticks.

Heads

Total:

Tails

Total:

4. Were the results what you expected?

Yes

No

5. If you were to repeat the experiment, do you think the results would be Why?

the same or different?

6. Repeat the experiment recording the results on the column graph below.

Each bar should represent one coin toss. Answer the questions: (a) Was this experiment the same or different to the last? (b) Which side came up the most? (c) Which side came up the least? (d) Compare your results with a friend’s. Were they the same or different?

Heads

Tails

(e) Would it be likely or unlikely to toss 10 of the same side in a row?

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

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Assessment 3

Year 3—Sub-strand: Chance – 1

NAME:

DATE:

1. Roll a dice and record the number of times it takes until you roll a 1. times 2. Complete the dice experiment below.

Aim: To discover how many 1s appear when a dice is rolled 10 times.

Equipment:

Steps: 1. Roll the dice 10 times.

2. Record the results in the table.

Roll

1st 2nd 3rd 4th 5th 6th 7th 8th 9th 10th

Results

Results: 1s appeared within 10 rolls of a dice.

Conclusion: I found that

3. If you were to repeat the experiment above, would the results be the same Why?

or different?

4. How many rolls does it take to roll a 6? Try this experiment three times.

1st trial: 10

times

2nd trial:

times

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

3rd trial:

times

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CONTENT DESCRIPTION: Conduct chance experiments, identify and describe possible outcomes and recognise variation in results (ACMSP067)

• a dice and pencil

Checklist

Year 3—Sub-strand: Chance – 1

Conduct chance experiments, identify and describe possible outcomes and recognise variation in results

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

Students can compare and discuss results

Students can carry out a chance experiment

STUDENT NAME

Students can predict possible outcomes from a chance experiment

(ACMSP067)

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Year 3—Sub-strand: Data representation and interpretation—DR&I – 1

Identify questions or issues for categorical variables. Identify data sources and plan methods of data collection and recording (ACMSP068)

TEACHER INFORMATION

RELATED TERMS Data

What this means

• A term used to describe a collection of numbers or information.

Table

• Students will be able to look at and refine questions that are suitable for gathering data. For example, instead of looking at students’ favourite books to read they can refine the research to just the students in their class. They will be given the opportunity to investigate questions and suggest their own areas for investigation. They will learn to gather data from information and people around them and plan ways to collect and display this data. Students will be asked to evaluate their initial question and recognise the effectiveness of their data gathering.

• A means of organising data in rows and columns.

Teaching points

Tally marks

• Present students with a variety of topics and questions to be used to investigate and gather data.

• Marks made to record items or events, usually grouped in fives by a diagonal line (e.g. ).

• Encourage students to suggest their own questions and areas for investigation.

Variable

• A quantity or something that can change its values.

Picture graph

• A graph that represents data in picture form. One picture may represent one or more item.

• Help students recognise that sometimes questions need to be refined in order to gain the right information for a task.

• Encourage students to collect data and gather information from those around them and situations they are familiar with.

• Allow students the opportunity to assess and evaluate the effectiveness of their data gathering.

What to look for • Students who have difficulty formulating a question suitable to use for an investigation.

• Students who have difficulty making a plan for an investigation.

Student vocabulary questions investigation variables data collect

Proficiency strand(s): Understanding Fluency Problem solving Reasoning

record

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Year 3—Sub-strand: Data representation and interpretation—DR&I – 1

HANDS–ON ACTIVITIES Topics for investigation (pg 15) • Brainstorm and make a list of topics students could use for investigation.

• Use the topic list to formulate questions for investigation.

• Give each student a topic and ask them to come up with a question. Read the question to the class and think about what each question is asking. What would you hope to find out from the question? Is it worded properly?

Refining questions (pg 16) • Model how to refine a question so that it only involves an investigation with one variable. For example: What is your favourite food to eat for breakfast? This can become ‘what is your favourite breakfast cereal?’ (The one variable is cereal, whereas in the first question there can be a variety of answers.)

• Distribute questions to students and ask them to refine them so they are more specific.

Make a plan • Model to students how to make a plan for collecting data. For example, if you wanted to find out how your class members travelled to school you might use the following plan: – Write a survey question.

– Make a list of all the ways students could travel to school.

– Draw up a table to use in a survey and include the list of ways to travel to school.

– Ask each student in your class the survey question and record their response with a tick in the table.

– Total up the responses in the table.

– Write one or two statements/comments about the results.

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

Summarising data (pg 17) • Once data has been collected it is often easier to read if it is summarised and organised into categories or groups.

• Look at the symbols representing the ball sports a group of Year 3 students play and summarise the information into a table and then into a picture graph.

• Discuss the findings.

Favourite reading material (pg 18) • If you wanted to find out what type of reading material the students in your class like to read, what question would you need to ask? For example: What do you like to read?

• If you wanted to refine your research you could list the types of books students read; for example, fiction, nonfiction, comic, picture story, joke book, magazine and newspaper.

• Use the table provided or draw up your own and survey your class members to find out their favourite reading material.

Favourite breakfast/cereal • Ask the students to suggest a question they could use to find out their classmates favourite breakfast.

• How could they refine this question? For example, they could just ask about their favourite cereal e.g. What is your favourite cereal? (The one variable is cereal.)

• Ask students to create their own survey question and table to use to survey their classmates about their favourite cereal. Summarise the results on a table and present this to the class or compare with a partner.

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Year 3—Sub-strand: Data representation and interpretation—DR&I – 1

LINKS TO OTHER CURRICULUM AREAS English • Questions: Look at the format of a question sentence. Always starts with a capital letter and finish with a question mark (?). Look at how you can turn a sentence into a question; for example: My favourite fruit is an apple—What is your favourite fruit?

• Turn the list of sentences below into question sentences.

– My favourite colour is blue.

– My middle name is William.

– On the summer holidays I like to go to the beach.

– I like to read comic books in my spare time.

– On the weekends I like to go for bike rides.

– My favourite subject at school is maths.

• Ask students to make a list of questions they could use to interview a friend.

Information and Communication Technology • Use a word processing document to type up your list of questions for your friend interview (see English). Print out your survey and give it to a friend to complete.

• Demonstrate to students how to draw up a table in a word processing 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. (Instructions may vary slightly according to the type of program.)

1. Go to ‘Insert’.

2. Click on ‘Table’.

3. Scroll down and click on ‘Insert table’.

4. Decide on the number of columns and rows your table requires and input the information.

5. Click OK. Show students how you can move your table and change the width and length of the rows and columns using the cursor.

6. Print out your table and use it for a survey.

Drama • Pretend you are a TV reporter and you have to interview your friend. Working with your friend, use the questions you created to interview a friend (see English) and pretend you are reporting this interview to the nation on live television.

• Create a list of questions you could use to interview your favourite actor/actress or singer. Working in pairs, dramatise a television interview—one person is the TV reporter asking the questions and the other person is the actor/actress/ singer.

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Year 3—Sub-strand: Data representation and interpretation—DR&I – 1

RESOURCE SHEET Topics for investigation

CONTENT DESCRIPTION: Identify questions or issues for categorical variables. Identify data sources and plan methods of data collection and recording (ACMSP068)

Copy, laminate and cut.

Favourite subject

Sports

TV shows

Favourite sport

Ice-cream flavours

Weather

Sandwich fillings

Pets

Travelling to school

Family members

Holiday destinations

Breakfast cereal

After-school activities

Favourite fruit

Favourite colour

Favourite snack

Favourite dinner

Hobbies

Milkshake flavours

Electronic games

Hair colour

Eye colour

Bed time

Car colours

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Year 3—Sub-strand: Data representation and interpretation—DR&I – 1

RESOURCE SHEET Refining questions Copy and laminate.

What is your favourite activity?

Do you have a pet?

What is your favourite food?

What do you like to do at school?

What is your favourite lunch?

Do you like to read?

Do you like to play sport?

Where do you go in the holidays?

What car/s does your family have?

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

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CONTENT DESCRIPTION: Identify questions or issues for categorical variables. Identify data sources and plan methods of data collection and recording (ACMSP068)

What is your favourite breakfast?

Year 3—Sub-strand: Data representation and interpretation—DR&I – 1

RESOURCE SHEET Summarising data Copy and distribute.

CONTENT DESCRIPTION: Identify questions or issues for categorical variables. Identify data sources and plan methods of data collection and recording (ACMSP068)

Transfer this data into the picture graph below.

Year 3 ball sports – Picture graph

netball

basketball

tennis

football

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

soccer

baseball

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Year 3—Sub-strand: Data representation and interpretation—DR&I – 1

RESOURCE SHEET Favourite reading material Copy and distribute.

CONTENT DESCRIPTION: Identify questions or issues for categorical variables. Identify data sources and plan methods of data collection and recording (ACMSP068)

Fiction books

Nonfiction books

Picture books

Comic books

Joke books

Magazines

Newspapers

Other 18

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

R.I.C. Publications® www.ricpublications.com.au

Assessment 1

Year 3—Sub-strand: Data representation and interpretation—DR&I – 1

NAME:

DATE:

1. List three suggestions of topics you could survey your class about. (a) (b) (c)

CONTENT DESCRIPTION: Identify questions or issues for categorical variables. Identify data sources and plan methods of data collection and recording (ACMSP068)

2. Turn the ideas above into questions you could use in a survey. (a) ? (b) ? (c) ?

3. If you wanted to find out what your classmates’ favourite farm animal is, which would be the best question to ask? Tick the best one.

What is your favourite animal?

What is your favourite animal at the zoo?

What is your favourite animal at the farm?

4. If you wanted to find out your classmates favourite snack food, what question would you ask them?

?

5. Choose five snack foods you could include in your survey.

1.

2.

3.

4.

5.

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

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19

Assessment 2

Year 3—Sub-strand: Data representation and interpretation—DR&I – 1

NAME:

DATE:

1. If you wanted to know what your classmates’ favourite ice-cream flavour is, what question would you need to ask?

?

Vanilla

3. Transfer your information into the picture graph below.

4. Look at your table and graph and answer these questions: (a) Which is easier to read?

table

graph

(b) Which flavour was the most popular? (c) Which flavour was the least popular? (d) Was any flavour not selected? If so, which one? (e) Would the results be the same or different if you were to survey another class?

same

different

Why?

20

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

R.I.C. Publications® www.ricpublications.com.au

CONTENT DESCRIPTION: Identify questions or issues for categorical variables. Identify data sources and plan methods of data collection and recording (ACMSP068)

2. Use the table below to fill in the ice-cream flavours and survey your class.

Use ticks or tally marks to represent each choice.

Checklist

Year 3—Sub-strand: Data representation and interpretation—DR&I – 1

Identify questions or issues for categorical variables. Identify data sources and plan methods of data

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

Makes a plan for collecting data

Collects and records data

STUDENT NAME

Identifies, suggests and refines questions for data collection

collection and recording (ACMSP068)

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21

Year 3—Sub-strand: Data representation and interpretation—DR&I – 2

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)

TEACHER INFORMATION

RELATED TERMS Data

What this means

• A term used to describe a collection of numbers or information.

• Students will be given the opportunity to collect and sort information into categories. The categories make the data easier to see, count and interpret. They will also see the benefits of presenting gathered data in lists and displays. They will learn that using tables they have either drawn up themselves or created using a computer will help them gather and record data. Students will learn to present their information into simple picture graphs and column graphs and discover that these are efficient ways of presenting their information clearly so that the data can be easily read and interpreted by themselves and others.

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. ).

Picture graph

• A graph that represents data in picture form. One picture may represent more than one unit/item.

Column graph

• A vertical arrangement of objects, or an up and down layout.

Teaching points • Present and help students sort groups of items into categories.

• Encourage students to use lists when sorting information into categories and gathering data.

• Help students recognise that tables are a useful tool to use when gathering data.

• Model and allow students to present given and gathered information into picture graphs.

• Model and allow students to present given and gathered information into column graphs.

• Allow students the opportunity to assess and evaluate the effectiveness of their data gathering and presenting techniques.

What to look for • Students who have difficulty deciding which items to place in which category.

• Students who have difficulty drawing up tables using a computer.

• Students who have difficulty correctly transferring their data into a graph.

Student vocabulary collect data categories lists

Proficiency strand(s): Understanding Fluency Problem solving Reasoning

tables picture graphs column graphs

22

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

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Year 3—Sub-strand: Data representation and interpretation—DR&I – 2

HANDS–ON ACTIVITIES Categories (pg 25) • Categories are a useful way of sorting gathered information. Ask students to make a list of all the things they like to do in their spare time. Decide on appropriate headings and sort this list into categories; for example, sport, art/craft, social and relaxation.

• Supermarket trolley: Sort the items in the supermarket trolley into the four categories listed.

Morning tea snacks • Make a list of all the different foods your classmates have bought into school today for their morning tea snack.

• Look at the list and decide on at least three category headings you could use.

• Sort the snacks under your headings.

• Looking at the sorted information, which was the most popular category/snack? Which was the least popular? Was it easier to tell this information from looking at your list or looking at the categories?

Lists • Lists are a good place to start when collecting data. For example, if you had a survey question asking ‘What is your favourite animal at the zoo?’, you may start with a list of possible animals for people to choose from.

• Make a list of all the possible animals there can be at a zoo. Then ask 10 of your classmates to choose their favourite animal from the list. Circle or place a tick next to the animal to show their response.

Two-way tables • Tables are a useful way to sort and present information. A two-way table normally is used to show two responses to a survey. For example, you could ask your classmates if they liked or disliked carrots and record their response on a twoway table like the one below.

Likes carrots

Dislikes carrots

• Ask 10 of your classmates if they like or dislike carrots and record their names in a two-way table like the one shown.

Drawing up tables using a word processing document • Tables for recording data can be drawn up by hand or by using a computer word processing document. Follow these steps to draw up a table that has 4 columns and 6 rows. (Instructions may vary slightly according to the type of program.)

Step 1: Go into a word processing program on your computer.

Step 2: Click on the ‘Insert tab’.

Step 3: Click on the table heading and icon.

Step 4: Scroll down and click on the ‘Insert table’ heading.

Step 5: Fill in the number of columns and rows you wish your table to have, then click on OK. Step 6: You can adjust the width and length of your rows and columns by moving your cursor onto the line you wish to move.

Picture graph – Weekend shoes (pgs 26–27) • Make a list of the possible shoes your classmates like to wear on the weekend.

• Ask you classmates to choose from your list their favourite shoe to wear on the weekend.

• Transfer your gathered information into a picture graph, using the table provided and the shoe pictures to help you.

• Which were the most popular and least popular shoe choices?

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

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23

Year 3—Sub-strand: Data representation and interpretation—DR&I – 2

HANDS–ON ACTIVITIES (CONTINUED) Column graph (pg 28) • Show students what a column graph can look like (Number of students at North Bend Primary School). Discuss what it is showing and ask them questions such as: Which year has the most and least students? How many junior, middle and upper students are there? How many students go to North Bend PS altogether? Is this graph a clear way to show and compare the year levels?

• Ask students to list all the subjects they learn at school.

• Transfer this list onto a table drawn up by hand or using the computer.

• Ask your classmates to choose their favourite subject and record their response with a tick or tally mark.

• Transfer the information provided into a column graph; students may draw up their own or use the one provided.

• Discuss and compare results. Is the column graph easier to read than the table?

LINKS TO OTHER CURRICULUM AREAS English • Grammar – Lists: Draw up a table like the one below and brainstorm and list words to go under each heading.

Nouns (words that name)

Verbs (action words)

Adjectives (words that describe)

• Lists can also be used to create spelling lists of words with common blends; for example, ‘th’, ‘wh’, ‘ie’ or ‘ough’ words.

Look at some common spelling blends and brainstorm words for a list.

Information & Communication Technology • Demonstrate how the computer is a good tool to record information, make lists, create tables and even design graphs.

(See Hands-on activities: drawing up tables using a word processing document.)

The Arts • Suggest what topics are best displayed in a picture graph. For example: favourite ice-cream flavours.

• Working with a partner, survey your classmates on their favourite ice-cream flavour and present the information in a picture graph. Use brown card to represent the cone and scrunched coloured tissue paper to represent the ice-cream flavours.

• Media: Look through newspapers and magazines to locate different graphs. What types of graphs are used in the media? Cut out some examples and create a class poster.

24

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

R.I.C. Publications® www.ricpublications.com.au

Year 3—Sub-strand: Data representation and interpretation—DR&I – 2

Categories Copy and distribute.

ST

EA

K

Sort the items from the shopping trolley under the headings below.

SAUSAGES Milk

CONTENT DESCRIPTION: 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)

RESOURCE SHEET

Fruit bowl

Pantry

Fridge

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

Freezer

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25

Year 3—Sub-strand: Data representation and interpretation—DR&I – 2

Picture graph – Weekend shoes (part 1) Copy and distribute.

26

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

R.I.C. Publications® www.ricpublications.com.au

CONTENT DESCRIPTION: 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)

RESOURCE SHEET

Year 3—Sub-strand: Data representation and interpretation—DR&I – 2

CONTENT DESCRIPTION: 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)

RESOURCE SHEET Picture graph – Weekend shoes (part 2) Copy and distribute.

Sports shoes or runners

Thongs

Sandals

Crocs

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

Going out formal shoes

Canvas shoes

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27

Year 3—Sub-strand: Data representation and interpretation—DR&I – 2

Column graph Copy, enlarge and laminate or copy and distribute.

Number of students at North Bend Primary School 28 27 26 25 24 23 22 21 20 19

Number of students

18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Preprimary

Year 1

Year 2

Year 3

Year 4

Year 5

Year 6

Year level 28

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

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CONTENT DESCRIPTION: 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)

RESOURCE SHEET

Assessment 1

Year 3—Sub-strand: Data representation and interpretation—DR&I – 2

CONTENT DESCRIPTION: 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)

NAME:

DATE:

Henry asked his classmates what they like to do in their spare time and he listed their responses below.

Ben – watch TV Sarah – watch TV Riley – ride my bike Lucy – watch TV Yang – play Xbox™ Sienna – play netball Eden – play on iPad™

George – ride my bike Lexia – play on iPad™ Cam – play soccer Joe – play football Sophie – read Yvonne – read Dylan – ride my bike

Mia – draw Jack – play Xbox™ James – read Ethan – computer games Mike – ride my bike Jacob – play basketball

1. Sort the list above into the categories in the table using ticks or tally marks.

Electronic games Ride a bike Play a sport Watch TV Read Draw 2. On a separate sheet of paper or on the back of this page, present the information from your table into a picture graph.

3. Looking at your table and graph, answer the following questions: (a) How many students like to ride a bike in their spare time? (b) Which category was the most popular? (c) Which was the least popular? (d) Do you think it was easier to read the information from the list, the table or the graph?

Why?

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NAME:

Year 3—Sub-strand: Data representation and interpretation—DR&I – 2

DATE:

The following items were sold to Year 3 at the school canteen on Friday.

1. Sort the information above into the table. Use ticks to represent each food item and include a total.

Hot food

Total:

Sandwiches/rolls

Total:

Snacks

Total:

Drinks

Total:

2. Now present the information in a picture graph.

3. Which is the easiest to read?

table

picture graph

4. Which category was the most popular?

30

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

R.I.C. Publications® www.ricpublications.com.au

CONTENT DESCRIPTION: 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)

Assessment 2

Checklist

Year 3—Sub-strand: Data representation and interpretation—DR&I – 2

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

Uses picture graphs and column graphs to display data

Uses lists and tables to display data

STUDENT NAME

Organises information into categories

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)

R.I.C. Publications® www.ricpublications.com.au

31

Year 3—Sub-strand: Data representation and interpretation—DR&I – 3

Interpret and compare data displays (ACMSP070)

TEACHER INFORMATION

RELATED TERMS Interpret

What this means

• To show, clarify or explain the meaning of something.

• Students will be shown a variety of data taken from various sources and have the opportunity to explain what they are showing. They will be shown tables and graphs that have been created by hand and by computer and asked to comment on what they represent. Students will be asked to transfer data from lists and tables into simple graphs and then compare and comment on the ways that it has been presented. Students will also be encouraged to work with other classmates researching, presenting and comparing their results. They will look at how they have presented their data and compare it to other classmate’s displays.

This outcome will allow students to compare the similarities and differences in how data is displayed and comment on its effectiveness.

Data

• A term used to describe a collection of numbers or information.

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. ).

Picture graph

• A graph that represents data in picture form. One picture may represent one or more unit/item.

Column graph

• A vertical arrangement of objects or an up and down layout.

Teaching points • Show students various tables and graphs and ask them a variety of questions to assist them in interpreting the data.

• Encourage students to comment on why some tables and graphs are easier to read than others. What makes a display easy to read?

• Help students to create displays that are easy to read, compare and interpret.

• Allow students to present given and gathered data into picture and column graphs.

• Give students the opportunity to compare their data presentations with others, looking for and describing similarities and differences.

What to look for • Students who have difficulty creating tables and graphs.

• Students who have difficulty interpreting data presented in tables and graphs.

Student vocabulary interpret/explain data compare tables

Proficiency strand(s): Understanding Fluency Problem solving Reasoning

picture graphs column graphs

32

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

R.I.C. Publications® www.ricpublications.com.au

Year 3—Sub-strand: Data representation and interpretation—DR&I – 3

HANDS–ON ACTIVITIES Graphs in the media • Use a search engine to show students picture graph examples. A great example can be found at <www.youtube.com/ watch?v=O7VZaoJeY6U> • Search for images of picture graphs and column graphs for kids. What are the graphs showing us? Is this a good way of presenting information?

• Give students newspapers and magazines and ask them to cut out and paste at least one example of a graph into their book. Present the graph to the class and describe what type of graph it is. What it is showing? Is the graph easy or hard to read?

Interpreting a picture graph (pg 35–36) • Show students the two picture graphs of animals at a farm. What differences can you see between the two graphs?

Which graph is easier to read? What makes one of the graphs better than the other?

• Ask students questions about the information shown on the better graph; for example: – How many pigs are at the farm?

– How many more sheep are there than cows?

– Which animal is there the most of?

– Which animal is there the least of?

Interpreting column graphs (pg 37) • Show students the two representations of a column graph that show the number of students that used the class computer over a week. One of the graphs is labelled and the other is not.

• Ask the students to interpret each graph. Which of the two graphs is easiest to read? Why? • Survey the class as to how many students had used the class computer over the last week at school. Model to the students how to present this information clearly in a column graph.

Favourite fruit • Ask all the students in the class what is their favourite fruit? List the suggestions and create a list or table showing all the students responses.

• Discuss which type of graph would be best to display the information. (A picture graph would be effective.)

• Ask all the students to display the gathered information in a picture graph on provided paper.

• Have students sit in small groups of two or three and compare and discuss their graphs.

Column graph – Going to bed times • Ask students what time they go to bed on school nights. Use a simple table to record their answers; for example:

7.30 pm

8 pm

8.30 pm

9 pm

• Ask students to transfer this information into a column graph. Remember to use headings.

• Ask students to sit in small groups and compare their bedtime graphs. Which graphs are the easiest to read and why?

Some students may wish to present their column graph to the whole class.

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

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Year 3—Sub-strand: Data representation and interpretation—DR&I – 3

HANDS–ON ACTIVITIES (CONTINUED) Favourite season • Ask students to carry out their own investigation to find out their classmates favourite season of the year. They will need to follow these steps: – Draw up a table that includes the four seasons.

– Ask each classmate to select one season as their favourite and record their response in their table using ticks or tally marks.

– Transfer the information to either a picture graph or column graph.

• Allow students the opportunity to compare their graphs within small groups.

• Some students may wish to present their completed graph to the class. Discuss and compare which graphs are easiest to read and interpret.

LINKS TO OTHER CURRICULUM AREAS English • Facts and opinions: Make a list of facts and opinions about the season of summer. For example: In summer there are many hot days (fact). I like summer (opinion).

• Opinions are often needed when interpreting a graph. Looking at different graphs students have created or seen on the computer or in newspapers, complete the following sentence: I think this is a good graph because …

Information and Communication Technology • Use the computer to search for picture graphs and column graphs. What are they showing?

• If you have access to studyladder <www.studyladder.com.au> log on and go to the Mathematics section. Select Data and statistics then select ‘Reading picture graphs’ and ‘Reading a column graph’.

• Play a game that involves creating and interpreting graphs; see <www.kidsmathsgamesonline.com/numbers/ mathdata.html> • Allow students the opportunity to explore and experiment creating simple graphs using the computer ‘Insert’ tab or the ‘Chart’ feature in the Insert tab, located within word processing programs.

The Arts and Science • Column graphs and picture graphs can be creative. A variety of shades and colours make a column graph easier to read rather than using one colour for all columns. Picture graphs can be creative, using pictures to represent data.

• Scientists use graphs to present their data. Using the computer, locate a graph that represents your city’s weather.

• Use a picture graph or column graph to represent the weather in your local area over the last 5 days.

34

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

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Year 3—Sub-strand: Data representation and interpretation—DR&I – 3

RESOURCE SHEET Interpreting a picture graph Copy and distribute.

CONTENT DESCRIPTION: Interpret and compare data displays (ACMSP070)

Number of animals

Sunny Meadow farm animals

pigs

cows

horses

chickens

sheep

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

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35

Year 3—Sub-strand: Data representation and interpretation—DR&I – 3

RESOURCE SHEET Interpreting a picture graph

CONTENT DESCRIPTION: Interpret and compare data displays (ACMSP070)

Copy and distribute.

36

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

R.I.C. Publications® www.ricpublications.com.au

Year 3—Sub-strand: Data representation and interpretation—DR&I – 3

RESOURCE SHEET Interpreting column graphs Copy and distribute.

Graph 1

Number of students

Number of students using the class computer in Year 3 10 9 8 7 6 5 4 3 2 1 Monday

Tuesday

Wednesday

Thursday

Friday

Thursday

Friday

Days of the week

CONTENT DESCRIPTION: Interpret and compare data displays (ACMSP070)

Graph 2

10 9 8 7 6 5 4 3 2 1 Monday

Tuesday

Wednesday

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

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37

Assessment 1

Year 3—Sub-strand: Data representation and interpretation—DR&I – 3

NAME:

DATE: Year 3B’s favourite takeaway foods

Fish & chips Sushi BBQ chicken Key: one graphic = one student

Hamburger Pizza

1. Look at the picture graph above and answer the following questions: (a) What type of graph is this? (b) What is the title of the graph? (c) Which is the most popular takeaway food? (d) How many students chose sushi? (e) Is this graph easy to read?

Yes

No

2. Use the table below and the same food choices to survey your classmates on their favourite takeaway food. Use ticks or tally marks.

Fish & chips Sushi BBQ chicken Hamburger Pizza

3. Transfer the information above onto a picture graph on the back of this page. What were the most popular and least popular choices?

38

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

R.I.C. Publications® www.ricpublications.com.au

CONTENT DESCRIPTION: Interpret and compare data displays (ACMSP070)

Why?

Assessment 2

Year 3—Sub-strand: Data representation and interpretation—DR&I – 3

NAME:

DATE:

Number of students

Year 3R’s class birthdays 6 5 4 3 2 1 Jan.

Feb.

Mar.

Apr.

May

June

July

Aug.

Sept.

Oct.

Nov.

Dec.

Months of the year

1. Look at the graph above and answer the following questions: (a) What type of graph is it? (b) What is the graph showing? (c) Which month had the most birthdays? (d) Which months had no birthdays?

CONTENT DESCRIPTION: Interpret and compare data displays (ACMSP070)

(e) Which two months had 3 birthdays? (f) Which month had only 1 birthday? (g) How many students are in Year 3R? 2. Describe what the graph below is showing:

Students in Year 3R Girls Boys 1

2

3

4

5

6

7

3. Is this graph easy to read? Yes No

8

9

10

11

12

13

14

15

Why/why not?

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

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39

Checklist

Year 3—Sub-strand: Data representation and interpretation—DR&I – 3

40

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

Interprets picture and column graphs

Creates picture graphs and column graphs

STUDENT NAME

Compares and describes graphs

Interpret and compare data displays (ACMSP070)

R.I.C. Publications® www.ricpublications.com.au

Year 3 Answers

Year 3

DR&I – 1 Page 19

Assessment 1

3. What is your favourite animal at the farm?

DR&I – 2 Page 25

Resource sheet

Fruit bowl

oranges grapes bananas apples plums

Page 29

Pantry

taco shells spaghetti fruit salad tin sugar cereal muesli bars rice flour tin of tomatoes tin of tuna chips biscuits

Fridge

butter eggs fish cheese yoghurt milk sausages steak

Freezer

ice-cream icy pole frozen pies frozen peas

Assessment 1

Electronic games Ride a bike Play a sport Watch TV Read Draw

Page 30 1.

Assessment 2

Hot food

✓✓✓✓✓✓✓✓✓

Total:

9

Sandwiches/rolls

✓✓✓✓✓✓✓

Total:

7

Snacks

✓✓✓✓✓✓✓✓✓✓✓✓✓✓✓

Total:

15

Drinks

✓✓✓✓✓✓✓✓✓✓

Total:

10

4. snacks

DR&I – 3 Page 38

Assessment 1

1. (a) picture graph (c) pizza Page 39

(b) Year 3B’s favourite takeaway foods (d) 5

Assessment 2

1. (a) column graph (b) Year 3R’s class birthdays (c) September (d) February, August and November (e) July and October (f ) June (g) 28 2. How many girls and boys there are in Year 3R.

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

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41

Year 4—Sub-strand: Chance– 1

Describe possible everyday events and order their chances of occurring (ACMSP092)

TEACHER INFORMATION

RELATED TERMS Chance

What this means

• The likelihood of an event occurring.

• Students will be given the opportunity to look at the everyday things and events that occur in their lives. They will realise that some things are likely to occur every day while other things are least likely to occur. Students will be asked to rate everyday events in order from least likely to happen to most likely to happen. They will compare these lists to others as they may find they could vary slightly. Events at school will probably be similar for all students but they may discover that events at home may differ.

Teaching points • Make a list of everyday events that happen at school. Students may work in small groups to discuss and arrange these in order from most likely to occur to least likely to occur.

• Help students recognise that some events are not likely to occur due to a number of circumstances beyond their control.

• Encourage students to recognise events at home that are likely to occur. Compare these to events that are less likely to occur.

• Allow students the opportunity to use number lines to order events from most likely to occur to least likely to occur.

What to look for • Students who have difficulty understanding the concept of chance, and that some things are likely and others are unlikely.

Student vocabulary events chance least likely most likely

42

Proficiency strand(s): Understanding Fluency Problem solving Reasoning

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

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Year 4—Sub-strand: Chance– 1

HANDS–ON ACTIVITIES School events (pg 45) • Look at the list of things that can typically happen in a school day (see Teaching points). Discuss which of these are most likely to occur each day and which are least likely to occur.

• Ask students to cut out the events and arrange them in order from most likely to least likely. Allow students the opportunity to compare their list with others and present it to the class.

• Ask students to make their own list of school events which they could then give to a friend to order from most likely to least likely to happen.

Home events (pg 46) • Ask students to cut out and rate the events on the list of common home activities from most likely to least likely to occur.

• Allow students the opportunity to compare their list with a classmate, discussing similarities and differences.

• Ask students to make their own list of events that may or may not happen at home and rate these from most likely to least likely to occur.

Number line (pg 47) • Ask students to rate five events from least likely to most likely to occur using a number line like the example provided.

Weekend events • Brainstorm and list all the events that could occur on the weekend; for example, students may be playing a sport, visiting a friend or relative, going to a party, going away, relaxing etc.

• Ask students to choose five events from the list that they may possibly do on the weekend and rate them from most likely to least likely to happen. Present these to the class.

Holidays • Make a list of at least five things you may do in the next school holiday. Use numbers 1 (most likely to occur) to 5 (least likely to occur) to to rate them.

• Share your holiday chance lists with a classmate.

Spare time dice (pg 48) • Make a dice that can help you decide what you might like to do in your spare time. List six activities you like to do in your spare time and write each one on a side of the cube net provided. Rate them from 1 to 6 (most to least favourite).

• Cut out the cube net and join the sides together with glue or sticky tape to make your dice.

• Roll your dice to decide what you might do in your spare time. How many rolls does it take to get your favourite activity?

• Use your dice to play a game of chance with a classmate. Which activities come up the most or the least?

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

R.I.C. Publications® www.ricpublications.com.au

43

Year 4—Sub-strand: Chance– 1

LINKS TO OTHER CURRICULUM AREAS English • Writing (Maths): Create lists and timetables showing everyday events that occur at school and at home.

• Creative writing: Ask students to use their imagination to create a writing piece about a wonderful weekend or use the following statements to start their creative writing: – What I would really like to do this weekend is …

– My most boring weekend was when …

– The best school day would be …

Information and Communication Technology • Use a word processing program to create a timetable of events that happen at school or at home. You could create a table first to write these in.

• Use the internet to investigate your city’s weather over the next week. Make a list of all the types of weather conditions you could have and rate them as most likely to least likely to occur over a week. For example, if it is summer in your city, it is most unlikely for it to snow during the week.

The Arts • Create your favourite holiday scene. You may like to use crayon, pencils, markers or a collage of materials to show all its special features.

• Drama: – Ask students to choose an activity they do at home before or after school and dramatise it to the class. The student who guesses correctly is then next to have a turn.

– Dramatise activities students like to do on the weekend. Students may choose from the given list below or use their own idea.

• Weekend activities: play basketball, netball, football, soccer, tennis; go dancing; go swimming, bike riding, roller skating, shopping; reading; drawing; watching TV; visiting friends, relatives; go to the movies; go to a park; go to the city; play computer/TV games; go to the beach; go to a party; tidy my bedroom; help at home.

44

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

R.I.C. Publications® www.ricpublications.com.au

Year 4—Sub-strand: Chance– 1

RESOURCE SHEET School events Copy and distribute.

Have a recess break Have a maths lesson Do some writing CONTENT DESCRIPTION: Describe possible everyday events and order their chances of occurring (ACMSP092)

Have a sports lesson Have a lunch break Visit the library Read or hear a story Learn a language Do a science experiment Use the class computer Australian Curriculum Mathematics resource book: Statistics and Probability (Years 3 & 4)

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45

Year 4—Sub-strand: Chance– 1

RESOURCE SHEET Home events Copy and distribute.

Eat dinner Go to bed Eat breakfast Get ready for school Go to sport practice Have a shower or bath Play outside Do homework Watch TV 46

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

R.I.C. Publications® www.ricpublications.com.au

CONTENT DESCRIPTION: Describe possible everyday events and order their chances of occurring (ACMSP092)

Read a book

Year 4—Sub-strand: Chance– 1

RESOURCE SHEET Number line

Least likely

CONTENT DESCRIPTION: Describe possible everyday events and order their chances of occurring (ACMSP092)

Most likely

Copy and distribute.

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

R.I.C. Publications® www.ricpublications.com.au

47

Year 4—Sub-strand: Chance– 1

RESOURCE SHEET Spare time dice

CONTENT DESCRIPTION: Describe possible everyday events and order their chances of occurring (ACMSP092)

Copy and distribute.

48

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

R.I.C. Publications® www.ricpublications.com.au

Assessment 1

Year 4—Sub-strand: Chance– 1

NAME:

DATE:

1. List five things that you are likely to do at school today.

2. Rate them from 1 to 5 as most likely (1) to least likely (5) to do.

CONTENT DESCRIPTION: Describe possible everyday events and order their chances of occurring (ACMSP092)

3. Looking at the list of school activities below, rate them in order from most likely (1) to least likely (10) to happen.

Use the class computer

Have a maths lesson

Play a ball game at lunchtime

Tidy my desk

Complete a reading task

Have a spelling test

Visit the principal’s office

Go on an excursion

Play with my friends at recess

Do a science experiment

4. Use the number line to place these events where you believe they should go. (Write the matching letter on the number line.)

• Have a music lesson (A)

• Start a story (B)

• Play a sport (C)

• Help a classmate (D)

• Do my neatest writing (E)

• Start a new book (F)

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

Most likely R.I.C. Publications® www.ricpublications.com.au

49

Assessment 2

Year 4—Sub-strand: Chance– 1

NAME:

DATE:

1. Look at the images below and write if they are likely or unlikely to happen to you today.

2. Write three things you are most likely and least likely to do after school today.

Least likely

1.

1.

2.

2.

3.

3.

3. Use the number line to rate these after-school activities in order from most likely to least likely to happen. (Write the matching letter on the number line.)

• Go ice skating (A) • Ride a zebra (B) • Go to the shop (C) • Have a snack (D) • Visit a relative (E) Least likely

Most likely

4. Rate these events from most likely (1) to least likely (8) to happen to you this weekend.

50

Go to a friend’s house

Play a sport

Go to a party

Go to the beach

Go shopping

Go on a holiday

Visit the zoo

Go to the movies

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

R.I.C. Publications® www.ricpublications.com.au

CONTENT DESCRIPTION: Describe possible everyday events and order their chances of occurring (ACMSP092)

Most likely

Checklist

Year 4—Sub-strand: Chance– 1

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

Rates events from least likely to most likely

Understands likely and unlikely events

STUDENT NAME

Suggests everyday events

Describe possible everyday events and order their chances of occurring (ACMSP092)

R.I.C. Publications® www.ricpublications.com.au

51

Year 4—Sub-strand: Chance– 2

Identify everyday events where one cannot happen if the other happens (ACMSP093)

TEACHER INFORMATION

RELATED TERMS Identify

What this means

• To establish something as being a particular person or thing.

• Students will come to realise that some events can only happen as a result of another event. For example, normally for a child to go to bed at night they first need to get ready for bed. The weather is another example of one event happening to allow another to occur. It cannot rain unless there are grey clouds around or it will not be hot if it is not a sunny day. Students will be given the opportunity to discuss and suggest these type of events and even place them in order.

Chance

• The likelihood of an event occurring.

Teaching points • Give students examples of events that happen as a result of other events.

• Allow students to suggest these types of events.

• Decide which events can or can’t happen without another event.

• Assist students to place related events in order.

What to look for • Students who have difficulty understanding the concept that some events can only happen as a result of another event happening.

• Students who do not participate in class discussions.

Student vocabulary

Proficiency strand(s):

events

Understanding

chance

Fluency

occur before/after

Problem solving Reasoning

can/can not

52

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

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Year 4—Sub-strand: Chance– 2

HANDS–ON ACTIVITIES Matching events (pg 55) • Give an example of an event that can only happen if something else happens; for example, you can’t be at school unless you travel there first.

• Look at the list of events provided. Cut out and match up the events, identifying those that can only happen when another one happens.

• Share event matches with a partner, comparing and discussing results.

Weather (pg 56) • Which weather events normally follow each other? For example: if there are grey clouds it normally means it is going to rain.

• Make a list of weather predictions that normally occur in each season of the year in your city. Draw up a table like the one below to help you.

Summer e.g. sun = hot

Autumn

Winter

Spring

• Use the weather symbols provided to create a picture graph showing what the weather has been like over the past week in your local area. Cut out the symbol/s and place them above each day of the week in your book or on paper to create your graph.

Sporting or social event • In order for you to play a sport or go to a social event what things have to happen in the order for you to get there ready and prepared? Choose one example and make a list of all the things you would need to do to be ready.

• Present your list to the class.

Ordering events – Getting ready for school (pg 57) • What events have to happen in order for you to get ready for school each morning? List them in the order that they occur in your house. Compare your list with a classmate. Are they the same or different? Maybe the events are the same but the order is different?

• What things do you have to do to get ready for bed each night? Make a list and order the events from first to last, using numbers. Compare lists with a classmate—are they the same or different?

• Cut and place the ‘getting ready for school‘ events in order that they normally occur in your house. Compare your list with a classmates’ list; how are they the same or different?

• What steps would you need to take in order to go on a holiday? Make a list. Share your list and discuss which events/ steps need to happen before you can move onto the next event/step. For example: you normally need to book accommodation or travel arrangements before you pack or can go on a holiday.

Before and after (pg 58) • Look at the illustrations and decide which events may have to happen before and after the event in the picture. Work in small groups discussing and/or writing about each event. For example: Before you can win a prize in a raffle you have to buy a ticket.

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

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53

Year 4—Sub-strand: Chance– 2

LINKS TO OTHER CURRICULUM AREAS English • Spelling: Look at words that are opposites. Brainstorm and make a list of words or write a list of one of the words and ask students to write the opposite of those words. For example: can—cannot, will—won’t, pack—unpack, likely— unlikely, possible—impossible. Discuss how sometimes opposite words use a prefix at the start of a word to change the meaning or make it opposite; for example, possible—impossible (the prefix is im).

• Writing: Choose between can or cannot then complete these sentences about events that are effected by other events: – I can get ready for school on time if I …

– I cannot get ready for school on time if I …

– I can win the game if …

– I cannot win the game if …

– I can buy – I cannot buy

if … if …

Information and Communication Technology • Use the internet to investigate what causes extreme weather or catastrophes such as storms, cyclones, hurricanes, erupting volcanoes, earthquakes and tsunamis. Choose one of these and look at what events have to happen to cause these events to occur. Present your findings to the class.

Science • Discuss how in science experiments a number of steps must happen in order to reach a conclusion.

• What do plants need to grow and survive? Make a list; for example: water, sunlight, food from the soil, shelter etc. Focus on water; in order for most plants to grow they must be able to draw up water from the soil. How does this happen?

Conduct a simple experiment where students place a stick of celery in a glass or water that is coloured with food dye.

After an hour observe what has happened. What steps were needed to make this happen?

54

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

R.I.C. Publications® www.ricpublications.com.au

Year 4—Sub-strand: Chance– 2

RESOURCE SHEET Matching events

CONTENT DESCRIPTION: Identify everyday events where one cannot happen if the other happens (ACMSP093)

Copy and distribute.

Travel to school

Travel on a plane

Buy a raffle ticket

Go to bed

Learn to kick a football

No rain

Wet ground

Go on a holiday

Stormy weather

Arrive at school

Pack for a holiday

Get answers correct in a times table test

Book a plane ticket

Rain, thunder and lightning

Dry ground

Go to football training

Get ready for bed

It has rained

Learn times tables

Win a raffle prize

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

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55

Year 4—Sub-strand: Chance– 2

RESOURCE SHEET Weather

CONTENT DESCRIPTION: Identify everyday events where one cannot happen if the other happens (ACMSP093)

Copy and distribute.

56

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

R.I.C. Publications® www.ricpublications.com.au

Year 4—Sub-strand: Chance– 2

RESOURCE SHEET Ordering events – Getting ready for school Copy and distribute.

Clean my teeth Have a shower or bath Travel to school CONTENT DESCRIPTION: Identify everyday events where one cannot happen if the other happens (ACMSP093)

Pack my school bag Get dressed Brush my hair Make my bed Get out of bed Eat breakfast Wake up Australian Curriculum Mathematics resource book: Statistics and Probability (Years 3 & 4)

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57

Year 4—Sub-strand: Chance– 2

RESOURCE SHEET Before and after Enlarge, copy and laminate.

CONTENT DESCRIPTION: Identify everyday events where one cannot happen if the other happens (ACMSP093)

TM

58

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

R.I.C. Publications® www.ricpublications.com.au

Assessment 1

Year 4—Sub-strand: Chance– 2

NAME:

DATE:

1. What things do you need to do in order for you to get to school on time each morning? List five of the most important things.

1.

2.

3.

4.

5.

2. To get ready for bed at night what do you need to do? Place these events in the order you get ready from 1 to 5.

Get into bed Brush my teeth

CONTENT DESCRIPTION: Identify everyday events where one cannot happen if the other happens (ACMSP093)

Say goodnight to my family Have a bath or shower Put my pajamas on 3. Complete these sentences about events: (a) If I want to win a game of basketball/football/netball/soccer I have to

(b) If I want to win a prize in a raffle I have to

(c) If I want to have a birthday party this year I have to

(d) If I want to do well at my school work I have to

(e) If I want to get ready for school on time I have to

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

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59

Assessment 2

Year 4—Sub-strand: Chance– 2

NAME:

DATE:

Before:

Before:

After:

After:

Before:

Before:

After:

After:

2. In order to do well in a times tables test, what would you need to do?

3. If there was to be a storm in your city describe what the weather may be like.

60

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

R.I.C. Publications® www.ricpublications.com.au

CONTENT DESCRIPTION: Identify everyday events where one cannot happen if the other happens (ACMSP093)

1. Look at the illustrations and suggest what might have happened before and after each event.

Checklist

Year 4—Sub-strand: Chance– 2

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

Order everyday events

Match possible everyday events

STUDENT NAME

Suggest what would follow an event

Identify everyday events where one cannot happen if the other happens (ACMSP093)

R.I.C. Publications® www.ricpublications.com.au

61

Year 4—Sub-strand: Chance– 3

Identify events where the chance of one will not be affected by the occurrence of the other (ACMSP094)

TEACHER INFORMATION

RELATED TERMS Identify

What this means

• To establish something as being a particular person or thing.

• Students will come to realise that some events that happen by chance are not as a result of other events. For example, if you fall over and graze your knee today it doesn’t mean you will do the same thing tomorrow. The probability of a new baby being a boy or a girl does not depend on the gender of the previous baby born to the same family. Students will be given the opportunity to justify that some events just happen with no other event causing it to occur; in other words, they are a random act.

Chance

• The likelihood of an event occurring.

Teaching points • Give students examples of random events that occur in isolation.

• Allow students to predict which events are random and which events are not.

• Assist students to recognise from a list events which are random and which are not.

• Encourage students to justify which events are not affected by other events.

• Ask students to rate events between certain and impossible on a number line.

What to look for • Students who have difficulty recognising the difference between the events that occur in isolation and the events that happen as a result of something else happening.

• Students who have difficulty justifying their answers or suggestions.

Student vocabulary events chance affected occur

Proficiency strand(s): Understanding Fluency Problem solving Reasoning

can/can’t happen

62

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

R.I.C. Publications® www.ricpublications.com.au

Year 4—Sub-strand: Chance– 3

HANDS–ON ACTIVITIES Random acts (pg 65) • Look at the illustrations and discuss what makes each of these events random. Discuss how these events are not affected by another event.

• Have small groups of students discuss a random event and report it back to the whole class.

• Brainstorm and make a list of other events that are random and not affected by others.

School events • Brainstorm and list things that can happen at school that are one-off random events. For example: a school fete, a visit from the local member of parliament, a bird gets trapped in a classroom, a fire causes the school to close, the teacher gives you free time.

• Choose one of these random events and write about it.

Siblings (pg 66) • Using the table provided, survey 10 classmates to see how many siblings they have and if they are brothers or sisters.

• See if there are any patterns.

• Discuss the probability of the gender of a new baby to a family. For example: if a family has already a boy it doesn’t necessarily mean the next baby will be a boy.

Certain to impossible (pg 67) • Look at the given list of events and decide what may be certain, likely or impossible. Place the events in order or on a number line to show this.

• Ask students to make a list of five home events that they could place on a similar number line, rating them from certain to impossible.

Coin toss (pg 68) • Tossing a coin is a random chance event that can produce two outcomes—heads or tails. It is not affected by any other events.

• Toss a coin 10 times and record the outcome on the table provided.

• If you were to repeat the experiment, would the results be the same or different? Repeat the experiment 3 more times and compare and discuss the results.

• What other games of chance are random and not affected by other events?

Odd or even (pgs 69–70) • Rolling a dice is another example of a random game of chance that is not affected by anything else.

• Ask students to make a dice using the cube net provided. Roll the dice and record out of 20 rolls how many odd numbers and how many even numbers there were.

• Compare results with fellow classmates and discuss the similarities and differences.

Carnival activities • What activities can you find at a carnival or fete that are chance games or events that are not affected by any other event? For example: putting balls in the clown’s mouth. Discuss and make a list.

• Design your own fete or carnival plan on a poster. What rides or chance games would you include?

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

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63

Year 4—Sub-strand: Chance– 3

LINKS TO OTHER CURRICULUM AREAS English • Writing: If I was principal for a day …

• Imagine you had to be principal for a day; what things would you do, what random events would you have?

• Language: What does ‘Luck of the draw’ mean? Discuss in terms of random, one-off acts or events.

• What other sayings do we have? Make a list of sayings you have heard before and discuss their meaning. For example: ‘Two heads are better than one’, ‘Once bitten, twice shy’ etc.

Information and Communication Technology • Use the internet to investigate random one-off events that can occur in our world—natural occurrences may be interesting; for example, the white tiger.

• Search for random weather patterns and look at interesting patterns of weather that can occur randomly.

• Using a computer, locate the website <www.kidsmathgamesonline.com> and play the ‘Probability game for kids’.

Health and Physical Education • Group students into three teams and play a game of tunnel ball. The teams should be even in number so they have an even chance of winning. If the lines are uneven, ask a student to have two turns to even it up. Tunnel ball is a game where the only skills needed are to roll the ball between the team’s legs accurately. Once the ball reaches the end of the tunnel the last person in the line picks up the ball and runs to the front. Then it is their turn to roll the ball down the tunnel. The game continues until every person in the line has had a turn at the front. Discuss how if all teams follow the game rules, they all have the same chance of winning. The results are only affected if a team member does not run when they should, incorrectly rolls the ball or stands with their legs together, which will block the ball.

• Try over-under ball or side-to-side ball using the same teams or mix the teams up before changing the game.

The Arts • Use charades to dramatise events that can randomly happen at home or at school. For example: falling down while playing at school, being chosen to read at a school assembly, random phone call at home saying you have been selected for a holiday to Disneyland, deciding to go on a family picnic etc.

64

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

R.I.C. Publications® www.ricpublications.com.au

Year 4—Sub-strand: Chance– 3

RESOURCE SHEET Random acts

CONTENT DESCRIPTION: Identify events where the chance of one will not be affected by the occurrence of the other (ACMSP094)

Copy, enlarge and laminate.

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

R.I.C. Publications® www.ricpublications.com.au

65

Year 4—Sub-strand: Chance– 3

RESOURCE SHEET Siblings Copy and distribute.

Siblings:

Boy = B

Girl = G

CONTENT DESCRIPTION: Identify events where the chance of one will not be affected by the occurrence of the other (ACMSP094)

Name

66

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

R.I.C. Publications® www.ricpublications.com.au

Year 4—Sub-strand: Chance– 3

RESOURCE SHEET Certain to impossible Copy and distribute.

Certain

Event

CONTENT DESCRIPTION: Identify events where the chance of one will not be affected by the occurrence of the other (ACMSP094)

Possibly or 50% chance

Impossible

Write these events next to where you believe they should go on the scale above.

The school sports carnival will be on a Thursday.

Twins are born to a family at school.

I will have dinner at home tonight.

I will visit the moon this year.

I will have lunch at school today.

I will go to bed tonight.

I will complete all my work at school today.

Our class will complete a maths task today.

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

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67

Year 4—Sub-strand: Chance– 3

RESOURCE SHEET Coin toss Copy and distribute.

Heads = H or Tails = T 1st

2nd

3rd

4th

5th

6th

7th

8th

9th

10th

8th

9th

10th

8th

9th

10th

8th

9th

10th

1st

2nd

3rd

4th

5th

6th

7th

Heads = H or Tails = T 1st

2nd

3rd

4th

5th

6th

7th

Heads = H or Tails = T 1st

68

2nd

3rd

4th

5th

6th

7th

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

R.I.C. Publications® www.ricpublications.com.au

CONTENT DESCRIPTION: Identify events where the chance of one will not be affected by the occurrence of the other (ACMSP094)

Heads = H or Tails = T

Year 4—Sub-strand: Chance– 3

RESOURCE SHEET Odd or even (part 1)

CONTENT DESCRIPTION: Identify events where the chance of one will not be affected by the occurrence of the other (ACMSP094)

Copy and distribute.

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

R.I.C. Publications® www.ricpublications.com.au

69

Year 4—Sub-strand: Chance– 3

RESOURCE SHEET Odd or even (part 2) Copy and distribute.

1

6

11

16

2

7

12

17

3

8

13

18

4

9

14

19

5

10

15

20

Roll the dice 20 times and record if the number is odd (O) or even (E).

1

6

11

16

2

7

12

17

3

8

13

18

4

9

14

19

5

10

15

20

Roll the dice 20 times and record if the number is odd (O) or even (E).

70

1

6

11

16

2

7

12

17

3

8

13

18

4

9

14

19

5

10

15

20

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

R.I.C. Publications® www.ricpublications.com.au

CONTENT DESCRIPTION: Identify events where the chance of one will not be affected by the occurrence of the other (ACMSP094)

Roll the dice 20 times and record if the number is odd (O) or even (E).

Assessment 1

Year 4—Sub-strand: Chance– 3

NAME:

DATE:

CONTENT DESCRIPTION: Identify events where the chance of one will not be affected by the occurrence of the other (ACMSP094)

1. Look at the illustrations below and explain why these are random events.

2. Is rolling a dice or tossing a coin a random event?

Yes

No

Why?

3. Roll a dice 20 times and see how many odd and even numbers you get. Record them on the table below. odd = O 1

2

3

4

5

6

7

8

even = E

9 10 11 12 13 14 15 16 17 18 19 20

4. Look at your table and answer the following questions: (a) How many odds numbers were rolled? (b) How many even numbers were rolled? (c) If you were to repeat the experiment, do you think the results would be the same, similar or different?

Explain your answer:

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

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71

Assessment 2

NAME:

Year 4—Sub-strand: Chance– 3

DATE:

1. Write these events next to the scale where you believe they should go.

• Go home after school today

• A tossed coin lands on tails

• Go to bed before 10 pm tonight

• Have a roll or sandwich today

• Visit the Prime Minister of Australia

• Twins are born today in my city

• Go to the movies on the weekend

• Fly to China on the weekend Event

Possibly or 50% chance

Impossible 2. Suggest an event that could happen to you that is random and out of your control.

3. Circle the events that you do not have any control over. Underline the events that you do have control over.

72

• what I eat for breakfast

• what I read

• what I eat for lunch

• what I watch on TV

• what I eat for dinner

• what sport/activity I do

• what time I go to bed

• what friends I play with

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

R.I.C. Publications® www.ricpublications.com.au

CONTENT DESCRIPTION: Identify events where the chance of one will not be affected by the occurrence of the other (ACMSP094)

Certain

Checklist

Year 4—Sub-strand: Chance– 3

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

Understands and plays games of chance

Place events on a scale from certain to impossible

STUDENT NAME

Identify random events

Identify events where the chance of one will not be affected by the occurrence of the other (ACMSP094)

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

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

TEACHER INFORMATION

RELATED TERMS Data

What this means

• A term used to describe a collection of numbers or information.

• A means of organising data in rows and columns.

• 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.

Tally marks

Teaching points

• Marks made to record items or events, usually grouped in fives by a diagonal line (e.g. ).

• Demonstrate the importance of correct questioning when carrying out a survey.

Survey

• To collect sample opinions or facts from a group.

Table

Venn diagram

• A diagram that represents sets and their relationships. The overlapping sections of the circles represent more than one choice.

• 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.

Student vocabulary questions data collect survey

Proficiency strand(s): Understanding Fluency Problem solving Reasoning

tables

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

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

HANDS–ON ACTIVITIES Survey topics (pg 77) • 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.

Xbox™

PlayStation™

• 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.

Wii™

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.

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

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

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

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 <www.mathsisfun.com>, 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.

2 legs

4 legs

6 legs

8 legs

10 or more legs

lizard beetle ant spider slater centipede f ly • Use a Venn diagram to make a list of items in the classroom that are recyclable or non-recyclable.

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

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

RESOURCE SHEET Survey topics

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

Copy and distribute.

Birthday months

Favourite takeaway food

Favourite sport

Favourite fruit

Favourite subject

Favourite vegetable

Favourite pastime activity

Favourite drink

Favourite electronic device

Travelling to school methods

Number of people in the family

Bedtimes

Class pets

Dinnertimes

Holiday destinations

Favourite reading material

Favourite outings

Favourite movies

Party venues

Favourite TV shows

Favourite colour

First name initial

Hair colour

Favourite footwear

Eye colour

Favourite musical artist

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

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77

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

RESOURCE SHEET Tables for data collection

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

Copy and distribute.

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

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

RESOURCE SHEET Two-way tables Copy and distribute.

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

Likes fruit

Dislikes fruit

Likes vegetables

Dislikes vegetables

Harry

Caleb

Harry

Georgia

Georgia

Scout

Caleb

Lexia

Lexia

Sophie

Matt

Sophie

Alex

Scout

Matt

Leila

Alex

Yong

Leila Yong

Likes Xbox™

Dislikes Xbox™

Likes PlayStation™

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

Dislikes PlayStation™

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

RESOURCE SHEET Venn diagram Copy and distribute.

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

Action movie

Scary movie

80

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

R.I.C. Publications® www.ricpublications.com.au

Assessment 1

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

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

Tuesday

Wednesday

Thursday

Friday

Saturday

3. Look at your information and answer the following questions: (a) Which day did the most birthdays fall on? (b) Which day did the least birthdays fall on? (c) Do you think the table you chose was the best method?

Yes

No

Yes

No

Why/why not?

4. Could you use a Venn diagram for this survey?

Why/why not?

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

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81

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 Dislikes reading

Likes writing

Dislikes writing

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

Likes reading

Likes writing

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

4. Which method shows the survey information the best?

Why?

82

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

R.I.C. Publications® www.ricpublications.com.au

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

Likes reading

Checklist

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

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

Compares the effectiveness of different methods of collecting data

Chooses the most effective method to collect data

STUDENT NAME

Selects topics and writes appropriate questions for data collection

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

R.I.C. Publications® www.ricpublications.com.au

83

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

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 (ACMSP096)

TEACHER INFORMATION

RELATED TERMS Data

What this means

• A term used to describe a collection of numbers or information.

• Students will be presented with data and asked to transfer this information onto a table, column graph or picture graph in order to make data easier to read and interpret. They will be shown how to draw up a table or graph by hand as well as using digital technology such as a computer. Students will also be given the opportunity to investigate a topic and collect their own data and present it either on a table, column graph or picture graph. They will realise that picture graphs can represent larger numbers of items/units by using a key that shows a symbol may represent more than one item.

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. ).

Column graph

• A vertical arrangement of objects, or an up and down layout.

Picture graph

• A graph that represents data in picture form. One picture may represent more than one unit/item.

Teaching points • Present students with data and suggest the most effective way to present it so that it can be read and interpreted easily, such as a table, column graph or picture graph.

• Model how to draw up a column graph and picture graph by hand using a ruler. Include a heading and labels for the graphs and a key for the picture graph showing that one item may represent more than one.

• Demonstrate to students how to construct a table or column graph using a computer.

• Give students the opportunity to collect and display their own data.

What to look for • Students who have difficulty transferring data onto a table or graph.

• Students who need assistance using the computer to construct a table or graph.

Student vocabulary data collect survey tables

Proficiency strand(s): Understanding Fluency Problem solving Reasoning

column graphs picture graphs

84

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

R.I.C. Publications® www.ricpublications.com.au

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

HANDS–ON ACTIVITIES Canteen sales (pg 87) • Look at the canteen sales taken at River’s Edge Primary School over one day. Discuss how this can be presented in a clearer, easy-to-read table. Ask students questions about the information.

• Model to students how to draw up a table using a pencil and ruler. First show students how to work out how many columns and rows are needed. Transfer the canteen sales onto the table using tally marks.

• Model how students can use the computer to draw up a table. Word processing programs usually have a ‘Table’ function. (Instructions may vary slightly according to the type of program.)

1. Go to ‘Insert’.

2. Click on ‘Table’.

3. Scroll down and click on ‘Insert table’.

4. Decide on the number of columns and rows your table requires and input that information.

5. Click OK. Show students how you can move your table and change the width and length of the rows and columns using the cursor.

6. Print out your table and use it for a survey.

Picture graph – canteen sales (pgs 88–89) • Using the canteen sales, show students how to present this information in a picture graph. Demonstrate how to use a key where one picture may represent a number of items in order to reduce the size of the picture graph. In this case the key is 1 picture = 2 items. Use the graph template and the canteen item pictures to create the picture graph.

Picture graph – Pencil case contents • Ask students to empty out and count the contents of their pencil case. Use a simple table to tally up the equipment; for example:

Coloured pencils

Erasers

Markers

Scissors

Lead pencils

Glue sticks

Pens

Other

• Transfer this information onto your own picture graph where 1 picture = 2 or 3 items. Include the key and headings.

• Ask students to compare their picture graph with another classmate. Answer questions such as who has the most pencils, erasers etc. Who has the least? Is this type of graph easy to read? Is it an effective way to present the information?

Column graph – Student heights (pg 90) • Ask five students in the class to volunteer to have their height measured. Record these measurements.

• Draw up a simple column graph using a ruler and pencil on poster paper and show these heights on the graph by shading each column (or use the resource page template).

• Demonstrate to students how to draw up a column graph using a computer. (Instructions may vary slightly according to the type of program.)

1. Click on ‘Insert’ and look for the charts menu item.

2. Choose the column graph by clicking on that menu item.

3. Choose the first graph and follow the instructions, inputting the student’s heights in each column.

4. Save or print the graph.

• Working in groups of five, students take turns to measure each other’s height. Record the 5 heights then present the information in a column graph that is drawn by hand or computer.

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

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

HANDS–ON ACTIVITIES (CONTINUED) Class survey • Ask students to choose one of three topics to investigate: class birthdays, class pets or class sports.

• To conduct their investigation students need to devise a question, survey the class and record their information on a table, column graph or picture graph.

• Ask students to present their investigation to the class.

LINKS TO OTHER CURRICULUM AREAS English • Spelling: Look at words with the sound blend ‘ph’ at the start or end of words. For example: graph, and telegraph or phone and phrase.

Information and Communication Technology • Look at and experiment with creating graphs and charts using a computer. Within a word processing document locate the Charts menu item under the Insert tab. Try creating a column graph showing the number of boys and girls in the class or hair colour of the students in the class.

• Go to <www.mathsisfun.com>, go to the heading ‘Data’, click on ‘Graphs index’ then select ‘Make a bar graph’. Create a bar graph of your choice using information you have previously gathered in an investigation. Print out your graph.

Economics • Look at the canteen sales information (see Resource sheet page 87). Discuss and decide what the prices of the items listed may be. Then look at the sales information and total up the amounts of each item sold. Which item took the most and least amount of money? Based on this information, which items do you think the canteen would keep selling? Are there any items the canteen may no longer wish to sell?

Science • Using the internet, investigate the average heights of 10-year-old boys and girls and compare them. Look at graphs that may be presented with this information. How does the information compare to the heights of students in the class?

Look at the column graphs completed in Hands-on activities and use this information to compare with the information discovered using the internet.

The Arts • Use a variety of colours, shadings, dots and lines to create column graphs that stand out.

• Create an interesting picture graph about class eye colour. Use coloured card to create the eyes to use on the picture graph and use the key 1 eye = 2 eyes.

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

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

RESOURCE SHEET River’s Edge Primary School canteen sales Copy, enlarge and laminate.

Quiche

Wrap

CONTENT DESCRIPTION: 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 (ACMSP096)

Sandwich

Roll

Sushi

Muffin

Popcorn

Fruit

Water

Juice

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

R.I.C. Publications® www.ricpublications.com.au

87

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

RESOURCE SHEET River’s Edge Primary School canteen sales picture graph (part 1) Copy and distribute.

88

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

R.I.C. Publications® www.ricpublications.com.au

CONTENT DESCRIPTION: 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 (ACMSP096)

Quiche Sandwich

Roll

Wrap

Sushi

Muffin

Popcorn

Fruit

Water

Juice

Key: 1 picture = 2 items

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

RESOURCE SHEET River’s Edge Primary School canteen sales picture graph (part 2)

CONTENT DESCRIPTION: 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 (ACMSP096)

Copy and distribute.

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

R.I.C. Publications® www.ricpublications.com.au

89

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

RESOURCE SHEET Column graph – Student heights Copy and distribute.

Title: 160 158 156 154 152 150 148 146 CONTENT DESCRIPTION: 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 (ACMSP096)

144

Height in centimetres

142 140 138 136 134 132 130 128 126 124 122 120 118 116 114 112 110

Student names 90

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

R.I.C. Publications® www.ricpublications.com.au

Assessment 1

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

NAME:

DATE:

A group of Year 4 students were asked what their favourite drink was and these were their responses: Greta – water

Liam – water

Jay – soft drink

Ida – milk

Matt – sports drink

Sophia – water

Lisa – juice

Kyle – soft drink

Luke – milk

Yong – juice

Ben – milk

Lily – water

James – water

Ruby – water

Faith – juice

Tom – milk

Siena – sports drink

Lucca – juice

George – water

Dom – soft drink

Rose - water

CONTENT DESCRIPTION: 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 (ACMSP096)

1. Transfer this information onto the table below using tally marks.

2. Represent the same information in a picture graph on a separate sheet of paper. Use symbols to represent the drinks. Remember to include a heading and a key that shows 1 picture = 2 items.

3. Look at the table and/or graph and answer these questions: (a) Which drink was the most popular? (b) Which was the least popular? (c) Which drink did three students choose? (d) Which drink would you choose?

4. Which is easier to read and interpret— the list, the table or the picture graph?

Why?

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

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Assessment 2

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

NAME:

DATE:

1. If you wanted to investigate which day of the week your classmates attend a sports training session (one or more), what question would you ask? ?

2. Ask 10 classmates your question and record the results on the table below.

Monday

Tuesday

Wednesday

Thursday

Friday

Saturday

Sunday

3. Transfer this information onto the column graph below.

10

8 7 6 5 4 3 2 1 Monday

Tuesday

Wednesday Thursday

Friday

Saturday

Sunday

4. Look at your gathered data and answer the following questions: (a) Which day was the most popular for sports training? (b) Were there any days students did not train? (c) Which day did only a few students train?

5. Explain how you could present a column graph like this one using a computer.

92

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

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CONTENT DESCRIPTION: 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 (ACMSP096)

9

Checklist

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

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

Can use a computer to create a table or column graph

Can collect and display data in a table, picture or column graph

STUDENT NAME

Can transfer and display given data in a table, picture or column graph

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 (ACMSP096)

R.I.C. Publications® www.ricpublications.com.au

93

Year 4—Sub-strand: Data representation and interpretation—DR&I – 3

Evaluate the effectiveness of different displays in illustrating data features including variability (ACMSP097)

TEACHER INFORMATION

RELATED TERMS

What this means

Data • A term used to describe a collection of numbers or information.

Variability • A quantity that can change its value. For example, one symbol can represent more than one data value.

Symbols

• A letter, mark or picture that represents something.

• Students will be given the opportunity to look at a variety of data representations in the media including in newspapers, magazines and on the internet. They will be asked to classify, interpret and evaluate these displays in order to ascertain how effective they are in displaying their data. Students will look at graphs and displays that have symbols that represent more than one item or data value—for example, one symbol may represent five data values— so they can interpret correct amounts within the display. Students will also be given different data displays and graphs to look at and work out what information they are providing. They will be expected to use these data displays to suggest questions that could be asked and answered from the information.

Teaching points • Provide students with a range of newspapers and magazines to go through to locate and cut out data displays. Classify these data displays under headings of table, picture graph, column graph or line graph.

• Allow students to search the internet for data displays about a topic such as your city’s weather or population.

• Ask students to interpret different types of displays and evaluate their effectiveness.

• Allow students to interpret graphs that have symbols that represent more than one data value.

• Give students the opportunity to ask and answer questions related to the displays/graphs.

What to look for • Students who have difficulty reading, understanding and interpreting graphs in the media.

• Students who need assistance asking and answering questions about data displays.

• Students who have difficulty calculating the values of symbols that equal more than one.

Student vocabulary data displays evaluate data value/symbols table

Proficiency strand(s): Understanding Fluency Problem solving Reasoning

picture graph (or pictograph) column graph (or bar graph)

94

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Year 4—Sub-strand: Data representation and interpretation—DR&I – 3

HANDS–ON ACTIVITIES Tables and graphs in the media • Provide students with a variety of newspapers, magazines and brochures and ask them to locate any tables or graphs they can find and cut them out.

• Select one of these data displays and work out what information it is giving us. Report this information to a small group or to the whole class.

• Classify and paste the data displays collected under the following headings:

Table

Picture graph Column graph

Line graph

Pie graph

Data displays on the internet • Use a computer to search the internet for tables or graphs showing your local city’s weather. Ask students to print them out and paste them onto paper. What type of display is it? Is it effective? Write a statement or two about what they are showing.

• Search the internet for the population growth in your local city. What type of display or graph did you find? What is it showing?

Interpreting graphs (pg 97) • Look at the different displays provided and suggest what type of display/graph each one is.

• Suggest what heading each display should have.

• Write at least two questions that could be asked about the information in each of the displays.

• Answer these questions: – Are these displays effective?

– Are they easy to read and interpret?

– Why/why not?

Childrens farm visitors table (pg 98) • Look at the table provided. What is it showing?

• If one symbol = 10 people, ask students to calculate the number of visitors to the childrens farm each day.

• Ask students questions about the information shown in the table: – Which day had the most number of visitors?

– Which day had the least number of visitors?

– How many visitors to the farm were there over the week?

– Is this an effective way to record farm visitors? Explain why.

Picture graph – Clothing sales (pg 99) • Look at the graph provided. What type of graph is it? What information is it giving us?

• What value does each symbol represent?

• Calculate how many of each item was sold.

• Write at least 3 questions that could be asked using this graph, then give your questions to a classmate to answer.

• Is this graph an effective way to represent clothing sales? Why/why not?

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

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Year 4—Sub-strand: Data representation and interpretation—DR&I – 3

HANDS–ON ACTIVITIES (CONTINUED) Column graph – Swimming events (pg 100) • Look at the graph provided. What type of graph is it? What information is it giving us?

• Why are two different colours used?

• Write at least 3 questions that could be asked using this graph, and then give your questions to a classmate to answer.

• Is this graph an effective way to represent clothing sales? Why/why not?

LINKS TO OTHER CURRICULUM AREAS English • Questions: Question sentences require a capital letter at the start and a question mark at the end. What sorts of questions are commonly used to interpret graphs? Brainstorm and create a list.

• Graphs and data displays provide a great opportunity for students to develop their skill of asking and answering questions. Using a graph/display given to them or one they have located themselves in a newspaper or magazine, ask students to come up with 3 to 5 questions that a graph or display could provide the answers to. Swap these questions and graph/display with a classmate and allow students the opportunity to answer them. Do they understand what the graph/data display is telling them?

• Reading: In which types of books could you possibly find displays and graphs? Allow the students the opportunity to visit the library to locate a graph/data display in a book. Hint: Nonfiction books would more commonly contain graphs/ data displays

Information and Communication Technology • Explore the internet for different types of graphs and data display. Google picture graphs and column graphs and see what comes up.

• Go to <www.mathsisfun.com>, click ‘Data’, then scroll down to ‘How to show data’. Select the following three areas to look at and read through: bar graphs (column graphs), pictographs (picture graphs) and showing the results of a survey.

Science • Data displays and graphs are commonly used in the area of science to display results. For example: weather, population, animal population, habitat and food source, height and weight of people/animals, how long people of different cultures live, plant growth etc.

• Using the internet investigate the average lifespan of an animal that interests you. Is any of the information presented in a display or graph? If so, what type of graph have they used? What information is it giving you?

The Arts • Art – Person outline (pg 101): Decorate an outline of a person to represent you. Use materials such as different types of paper and cardboard, wool, fabric etc.

• Use the created class members to make a picture graph displaying class member’s birthdays. Label each month and have students attach their person above their birthday month.

• Is this an effective way to present class birthdays? Is it easy to read/interpret?

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

R.I.C. Publications® www.ricpublications.com.au

Year 4—Sub-strand: Data representation and interpretation—DR&I – 3

RESOURCE SHEET Interpreting graphs Copy and distribute.

Key:

Heading:

= 2 people

Walk Bike/scooter Car

Train

Heading:

Key:

Chocolate

Vanilla

Strawberry

Choc chip

Rainbow

Mint

= 4 ice-creams

Bubble gum

Heading: 12 11 10

Number of students

CONTENT DESCRIPTION: Evaluate the effectiveness of different displays in illustrating data features including variability (ACMSP097)

Bus

9 8 7 6 5 4 3 2 1 Soccer

Netball

Basketball

Football

Rugby

Volleyball

Tennis

Baseball

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

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Year 4—Sub-strand: Data representation and interpretation—DR&I – 3

RESOURCE SHEET Childrens farm visitors table Copy and distribute.

Greenslope childrens farm – Visitors record: April 15–22

Key:

= 10 people

CONTENT DESCRIPTION: Evaluate the effectiveness of different displays in illustrating data features including variability (ACMSP097)

Monday

Tuesday

Wednesday

Thursday

Friday

Saturday

Sunday

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

R.I.C. Publications® www.ricpublications.com.au

Year 4—Sub-strand: Data representation and interpretation—DR&I – 3

RESOURCE SHEET Clothing sales Copy and distribute.

Sales 1–7 July

CONTENT DESCRIPTION: Evaluate the effectiveness of different displays in illustrating data features including variability (ACMSP097)

Key: 1 item = 20

Jeans

Short-sleeved T-shirts

Long-sleeved T-shirts

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

Hooded jumpers

Jackets

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Year 4—Sub-strand: Data representation and interpretation—DR&I – 3

RESOURCE SHEET Swimming events Copy and distribute.

District swimming final: 10-year-olds 20

boys

18

girls

Number of students

14 12 10 8 6 4 2 0 freestyle

backstroke

breaststroke

butterfly

Swimming strokes

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

R.I.C. Publications® www.ricpublications.com.au

CONTENT DESCRIPTION: Evaluate the effectiveness of different displays in illustrating data features including variability (ACMSP097)

16

Year 4—Sub-strand: Data representation and interpretation—DR&I – 3

RESOURCE SHEET Art – Person outline

CONTENT DESCRIPTION: Evaluate the effectiveness of different displays in illustrating data features including variability (ACMSP097)

Copy and distribute.

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

R.I.C. Publications® www.ricpublications.com.au

101

Assessment 1 – part 1

Year 4—Sub-strand: Data representation and interpretation—DR&I – 3

NAME:

DATE: Staff car park

Key:

= 4 cars

White

Beige

Silver

Blue

Black

Yellow 1. Look at the display above and answer the following questions: (a) What type of graph is this? (b) What is the graph showing? (c) What does one car symbol represent? (d) Which car colour is there the most of? (e) How many red cars are there? (f)

How many black cars are there?

(g) Which car colour is there the least of? (h) Is this graph an effective way to display this information?

Yes

No

Why?

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

R.I.C. Publications® www.ricpublications.com.au

CONTENT DESCRIPTION: Evaluate the effectiveness of different displays in illustrating data features including variability (ACMSP097)

Red

Assessment 1 – part 2

Year 4—Sub-strand: Data representation and interpretation—DR&I – 3

NAME:

DATE: Class sizes 14 boys 12 girls

Number of students

10 8 6 4

CONTENT DESCRIPTION: Evaluate the effectiveness of different displays in illustrating data features including variability (ACMSP097)

2 0 Foundation

Year 1

Year 2

Year 3

Year 4

Year 5

Year 6

Year levels

2. Look at the class sizes data and answer these questions: (a) What type of graph is it? (b) Which class has the most boys? (c) Which class has the most girls? (d) Which class has equal number of boys and girls? (e) How many students are in Year 1 altogether? (f)

Is this an effective way of showing class sizes?

Why?

Extension question 3. How many students attend this school altogether?

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

R.I.C. Publications® www.ricpublications.com.au

103

Assessment 2 – part 1

Year 4—Sub-strand: Data representation and interpretation—DR&I – 3

NAME:

DATE: Key:

= 2 days

Days below

Days above 30 0C

1. Look at the data above and answer the following questions: (a) What type of display is this? (b) What possible title could this display have? (c) What does one sun represent? (d) What possible months could this be? (e) What possible season could this be?

2. Suggest two possible questions you could ask about the display above. (a) ? (b) ?

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

R.I.C. Publications® www.ricpublications.com.au

CONTENT DESCRIPTION: Evaluate the effectiveness of different displays in illustrating data features including variability (ACMSP097)

30 0C

Assessment 2 – part 2

Year 4—Sub-strand: Data representation and interpretation—DR&I – 3

NAME:

DATE:

40 38 36 34 32 30 28 26 24 22

CONTENT DESCRIPTION: Evaluate the effectiveness of different displays in illustrating data features including variability (ACMSP097)

20 18 16 14 12 10 Monday

Tuesday

Wednesday

Thursday

Friday

3. Look at the display above and answer the following questions: (a) What type of graph is it? (b) Suggest a title for the graph. (c) What are the numbers on the side showing? (d) What months might it be?

4. Make two statements about what the graph is showing.

(a) (b) 5. Locate a table or graph from a newspaper, magazine or the internet. Cut it out and paste it on the back of this sheet. Write two statements about what information it is showing.

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

R.I.C. Publications® www.ricpublications.com.au

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Checklist

Year 4—Sub-strand: Data representation and interpretation—DR&I – 3

106

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

Can suggest questions and statements about data displays

Can interpret graphs with symbols that represent more than one data value

STUDENT NAME

Can name and interpret data displays in the media

Evaluate the effectiveness of different displays in illustrating data features including variability (ACMSP097)

R.I.C. Publications® www.ricpublications.com.au

Year 4 Answers

Year 4

Page 92

CHANCE – 3 Page 71

Assessment 2

1. On which day/s do you attend a sports training session?

Assessment 1

2. Yes, because it is a game/act of chance.

DR&I – 3

DR&I – 1 Pages 102–103 Page 81

Assessment 1

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

4. No—too many categories Page 82 1.

Assessment 2

Likes reading

Dislikes reading

Ashley Samuel Eden Faith Ben Mia Josh Manuel Likes writing

Jay Sky

Dislikes writing

Ashley Samuel Mia Sky Josh Manuel

Jay Eden Faith Ben

2.

1. (a) (b) (c) (d) (e) (f ) (g) (h) 2. (a) (b) (c) (d) (e) (f )

Assessment 1

picture graph numbers of coloured cars in the staff car park 4 cars silver 8 14 yellow Yes, it is clear and easy to read and interpret, and it has a key.

Column graph Year 3 Year 5 Year 4 21 Yes, because it is clean and easy to read and interpret.

3. 144 Pages 104–105 1. (a) (b) (c) (d) (e) 3. (a) (b) (c) (d)

Assessment 2

picture graph Days below and above 30 °C 2 days December, January or February summer column graph Weekly temperature temperature in degrees Celsius December, January or February

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

4. Two-way table

DR&I – 2 Page 91 1.

Assessment 1

Water Milk Juice Sports drink Soft drink

3. (a) water (b) sports drink (c) soft drink

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

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