Australian Curriculum Mathematics: Statistics and Probability - Book 3 (Upper Primary)

RIC-6114 5.2/791

Australian Curriculum Mathematics resource book: Statistics and Probability (Years 5 & 6) Published by R.I.C. Publications® 2014 Copyright© Clare Way 2014 ISBN 978-1-921750-36-9 RIC– 6114

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)

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For all Australian Curriculum material except elaborations: This is an extract from the Australian Curriculum.

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AUSTRALIAN CURRICULUM MATHEMATICS RESOURCE BOOK: STATISTICS AND PROBABILITY (YEARS 5 & 6) Foreword Australian Curriculum Mathematics resource book: Statistics and Probability (Years 5 & 6) 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 5 Chance .........................................2–21 • Chance – 1 List outcomes of chance experiments involving equally likely outcomes and represent probabilities of those outcomes using fractions (ACMSP116) – – – – – –

Teacher information ........................................... 2 Hands-on activities ........................................3–4 Links to other curriculum areas .......................... 4 Resource sheets ..............................................5–8 Assessment ..................................................9–10 Checklist ........................................................... 11

• Chance – 2 Recognise that probabilities range from 0 to 1 (ACMSP117) – – – – – –

Teacher information ......................................... 12 Hands-on activities ....................................13–14 Links to other curriculum areas ........................ 14 Resource sheets ..........................................15–18 Assessment ................................................19–20 Checklist ........................................................... 21

Data representation and interpretation ............................22–51 • DR&I –1 Pose questions and collect categorical or numerical data by observation or survey (ACMSP118) – – – – – –

Teacher information ......................................... 22 Hands-on activities ....................................23–24 Links to other curriculum areas ........................ 24 Resource sheets ..........................................25–27 Assessment ................................................28–30 Checklist ........................................................... 31

• DR&I –2

• Chance – 3

Construct displays, including column graphs, dot plots and tables, appropriate for data type, with and without the use of digital technologies (ACMSP119) – – – – – –

Compare observed frequencies across experiments with expected frequencies (ACMSP146)

Teacher information ......................................... 32 Hands-on activities ....................................33–34 Links to other curriculum areas ........................ 34 Resource sheets ..........................................35–38 Assessment ................................................39–40 Checklist ........................................................... 41

Describe and interpret different data sets in context (ACMSP120) Teacher information ......................................... 42 Hands-on activities .......................................... 43 Links to other curriculum areas ........................ 44 Resource sheets ..........................................45–48 Assessment ................................................49–50 Checklist ........................................................... 51

Year 6 Chance .......................................52–79 • Chance – 1 Describe probabilities using fractions, decimals and percentages (ACMSP144) – – – – – –

Interpret and compare a range of data displays, including side-by-side column graphs for two categorical variables (ACMSP147) – – – – – –

Teacher information ......................................... 80 Hands-on activities ....................................81–82 Links to other curriculum areas ........................ 82 Resource sheets ..........................................83–86 Assessment ................................................87–88 Checklist ........................................................... 89

• DR&I –2 Interpret secondary data presented in digital media and elsewhere (ACMSP148)

Teacher information ......................................... 52 Hands-on activities ....................................53–54 Links to other curriculum areas ........................ 54 Resource sheets ..........................................55–56 Assessment ................................................57–58 Checklist ........................................................... 59

• Chance – 2

– – – – – –

Teacher information ......................................... 90 Hands-on activities .......................................... 91 Links to other curriculum areas ........................ 92 Resource sheets ..........................................93–95 Assessment ................................................96–97 Checklist ........................................................... 98

Answers ...................................99–100

Conduct chance experiments with both small and large numbers of trials using appropriate digital technologies (ACMSP145) – – – – – –

Teacher information ......................................... 70 Hands-on activities ....................................71–72 Links to other curriculum areas ........................ 72 Resource sheets ..........................................73–76 Assessment ................................................77–78 Checklist ........................................................... 79

Data representation and interpretation ............................80–98 • DR&I –1

• DR&I –3 – – – – – –

– – – – – –

Teacher information ......................................... 60 Hands-on activities .......................................... 61 Links to other curriculum areas ........................ 62 Resource sheets ..........................................63–66 Assessment ................................................67–68 Checklist ........................................................... 69

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

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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 on the final page of the book.

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 5 & 6)

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

FORMAT OF THIS BOOK Links to other curriculum areas includes activities in other curriculum areas which support the content description. These are English, Information and Communication Technology, Health and Physical Education, Science, Economics, the Arts and Languages). 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 on the final page of the book.

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

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v

Year 5—Sub-strand: Chance – 1

List outcomes of chance experiments involving equally likely outcomes and represent probabilities of those outcomes using fractions (ACMSP116)

TEACHER INFORMATION

RELATED TERMS Chance (Probability)

What this means

• The likelihood of an event occurring.

• Students will participate in simple chance experiments and comment on the likelihood of winning these games of chance by considering the possible outcomes. They will use a variety of chance words as well as fractions to describe possible outcomes of chance experiments. Students will be exposed to probability through a variety of simple chance games such as coin toss, dice games, spinners, guessing games and the game of rock-paperscissors.

Outcome

• The result of an event or experiment.

Fractions

• A fraction is part of a whole. A fraction is obtained by dividing a whole or given amount into a certain number of equal parts and taking a certain number of them, for example 2⁄3 refers to 2 of 3 equal parts. In a fraction the top number is referred to as numerator (or number of parts you have) and the bottom number is the denominator (or the number of parts the whole is divided equally into).

Teaching points • Students will discuss and use chance words to describe possible outcomes of simple chance experiments.

• Introduce fractions as another means to represent the likelihood of an outcome.

• Allow students to be involved in a variety of simple chance experiments and games.

• Ask students to predict and comment on outcomes before and after an experiment.

What to look for • Students who have difficulty predicting possible outcomes prior to an experiment.

• Students who have difficulty using fractions to describe probability.

Student vocabulary outcomes chance/ probability likelihood experiments

Proficiency strand(s): Understanding Fluency Problem solving Reasoning

fractions

2

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

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Year 5—Sub-strand: Chance – 1

HANDS–ON ACTIVITIES Black or red?

• Using a deck of cards ask students to predict which colour might be drawn out first from the deck – black or red?

• Discuss what percentage or fraction chance you have of getting a red card first. Is there the same chance of getting a black card first?

• Game: Black or Red? The object of this game is to simply guess which colour the card will be each time a card is flipped. Students show their choice by standing to choose black or kneeling to choose red. The teacher shuffles the deck then turns over the first card to reveal the colour – the students whose colour was not revealed sit down. Students may change their choice throughout the game. The game continues until there is only one student left which means they are the winner.

• Discuss student’s chances of winning this game – do they have equal chance of winning? If 10 red cards were drawn out in a row, what is the likelihood of the next card being black?

Dice roll (pg 5) • If you were to roll a dice, what fraction of a chance do you have of rolling a six first roll? Answer 1⁄6.

• Ask students to roll the dice 6 times and work out the fraction that each number was rolled. For example, if they rolled 2 sixes out of 6 rolls the fraction would be 2⁄6, if they rolled 1 three the fraction would be 1⁄6 and if they rolled no fours the fraction would be 0⁄6.

• Complete the experiment three times and record the results using ticks and fractions on the table provided. Were the results the same or different each time? Is this what students expected? Discuss.

Spinners (pages 6–7) • Look at each spinner provided and discuss what the chances would be of the spinner landing on each colour? Use chance words such as more likely, less likely or even chance to describe the probability. Then use fractions to describe and predict which colour the spinner will land on.

• Copy the spinner provided onto card and distribute to students. Students divide their spinner into 4 equal parts and colour each part a different colour. Using scissors and a spilt pin, cut out the circle and the spinner hand and attach the two together using the spilt pin.

• Predict what colours the spinner may land on over 10 spins and 20 spins. Carry out the experiment recording the results on a table such as the one below using ticks or tally marks.

Blue Green Yellow Red

Guess the number • The teacher thinks of a number between 1 and 20 and asks students to guess the number. Discuss: does every student have an equal chance of guessing the number? What happens as there are more guesses? (There is a greater chance of winning.)

• Ask students to play guess the number game in pairs.

Drawing straws • If you were to cut 4 straws in different lengths (one full length, one ¾ length, one at half-length and one at quarterlength) what fraction of a chance would you have of choosing the full length straw if the lengths were hidden from view? Give students four straws between two and working with a partner ask them to carry out their chance experiment with the straws (they need to cut them first). Why is this a game of chance?

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

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3

Year 5—Sub-strand: Chance – 1

HANDS–ON ACTIVITIES (CONTINUED)

Rock-paper-scissors (jan-ken-pon) • Rock-paper-scissors or jan-ken-pon (Japanese name) is a hand game usually played by two players. The game is often used as a choosing method in a similar way as guess the number, coin toss, drawing straws or dice roll.

However, it is not as random as these games as it involves players choosing which action may help them win.

Paper beats rock Scissors beats paper

• Ask students to suggest other games similar to rock-paper-scissors and use them to choose who takes a turn or who may be ‘it’ in a game.

Rock beats scissors

LINKS TO OTHER CURRICULUM AREAS English • Procedure writing: Ask students to write their own set of rules for an existing game of chance they know or make-up their own game of chance. Include an aim, equipment, procedure, results and conclusion.

• Reading: Read about the Japanese culture and games they like to play in a nonfiction book from the library or on the Internet.

Information and Communication Technology • Using a computer locate the following website <www.ixl.com> and click on the math’s area. Click on Year 5 and under the title ‘Probability and statistics’ select the task ‘Calculate probability’.

Languages • Use the internet to investigate the game rock-paper-scissors and what it is called in other languages such as Japanese ‘Jan-ken-pon’ or Ro-sham-bo (American)

The Arts • Cube net (pg 8): Give students a copy of a cube net and ask them to decorate each side. They may even like to label each side with a spare time activity so they can use this dice to help them decide which activity they may like to do.

• Spinner: Ask students to create their own spinner. Divide the spinner into 3 or 4 equal sections and decorate each section using lines and patterns. They could use their spinner to help them decide who the leader in a game is.

4

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

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Year 5—Sub-strand: Chance – 1

RESOURCE SHEET Dice roll

CONTENT DESCRIPTION: List outcomes of chance experiments involving equally likely outcomes and represent probabilities of those outcomes using fractions (ACMSP116)

Copy and distribute.

Dice number

1

2

3

4

5

6

Number of times rolled

Fraction

Dice number

/6

1

/6

2

/6

3

/6

4

/6

5

/6

6

Number of times rolled

Fraction

Dice number

/6

1

/6

2

/6

3

/6

4

/6

5

/6

6

Number of times rolled

Fraction

/6

/6

/6

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

/6

/6

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/6

5

Year 5—Sub-strand: Chance – 1

RESOURCE SHEET Spinners (part 1)

CONTENT DESCRIPTION: List outcomes of chance experiments involving equally likely outcomes and represent probabilities of those outcomes using fractions (ACMSP116)

Copy and distribute.

blue green yellow red

6

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

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

Year 5—Sub-strand: Chance – 1

RESOURCE SHEET Spinners (part 2) Making a spinner Copy onto card and distribute.

CONTENT DESCRIPTION: List outcomes of chance experiments involving equally likely outcomes and represent probabilities of those outcomes using fractions (ACMSP116)

Equipment needed: scissors and a split pin.

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

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7

Year 5—Sub-strand: Chance – 1

RESOURCE SHEET Cube net

CONTENT DESCRIPTION: List outcomes of chance experiments involving equally likely outcomes and represent probabilities of those outcomes using fractions (ACMSP116)

Copy and distribute.

8

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

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

Assessment 1

Year 5—Sub-strand: Chance – 1

CONTENT DESCRIPTION: List outcomes of chance experiments involving equally likely outcomes and represent probabilities of those outcomes using fractions (ACMSP116)

NAME:

DATE:

1. Looking at the 10 straws, if you couldn’t see their length, predict what fraction out of 10 you would have of choosing the following: (a) a long straw: (b) a medium straw: (c)

a short straw:

2. Are you more likely or less likely to choose a long straw the first time?

1

2

3

3. Look at the three spinners above and answer the questions: (a) Which spinner would you have the best chance of landing on stripes? (b) Which spinner would you have the best chance of landing on spots? (c) Which spinner would you have the best chance of landing on solid colour? (d) Which spinner would you have half (1⁄2) a chance of landing on spots? (e) Which spinner would you have 2⁄3 chance of landing on stripes? (f)

What fraction of a chance does spinner 3 give you of landing on each section?

4. If you were to create a spinner which gave 3 ⁄4 of a chance of landing on a solid section, what would it look like?

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

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9

Assessment 2

Year 5—Sub-strand: Chance – 1

NAME:

DATE:

2. Shuffle a deck of cards. (a) Predict what colour card may be drawn off the top of the deck first? (b) Was your prediction correct?

Yes

No

3. If you were to draw 20 cards out of a deck, what fraction do you think would be: (a) red?

(b) black?

4. Carry out this chance experiment.

Use tally marks or ticks to fill in the results on the table below.

Fraction

Black

/20 Fraction

Red

/20

Were your predictions correct?

Yes

No

If you were to repeat this experiment the results would be the same.

True

False

5. Use your deck of cards to predict and carry out an experiment to see which suit is drawn out the most out of 10 picks. Then use the table below to record your results.

Prediction: circle which you think will be drawn out the most:

Spade

Club

Heart

Diamond

6. (a) Write a statement about your results.

(b) Why is this a game of chance?

10

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

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CONTENT DESCRIPTION: List outcomes of chance experiments involving equally likely outcomes and represent probabilities of those outcomes using fractions (ACMSP116)

1. Describe what can happen in a game of Rock-paper-scissors. How can you win?

Checklist

Year 5—Sub-strand: Chance – 1

List outcomes of chance experiments involving equally likely outcomes and represent probabilities of

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

Students can carry out simple chance games and experiments

Students can use fractions to describe chance experiment outcomes

STUDENT NAME

Students can predict possible outcomes from a chance experiment

those outcomes using fractions (ACMSP116)

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11

Year 5—Sub-strand: Chance – 2

Recognise that probabilities range from 0 to 1 (ACMSP117)

TEACHER INFORMATION

RELATED TERMS Chance (Probability)

What this means

• The likelihood of an event occurring.

• Students will be given the opportunity to look at and discuss chance events and experiments using a scale system from 0 to 1. They will come to recognise that 0 on the scale would relate to something having no chance of winning or be impossible to achieve, while 1 on the scale would represent a certainty. Students have already been exposed to rating chance events and games using words such as likely and unlikely and using fractions and numbers 1 to 10. This outcome shows students another way of rating their chances using a scale of 0 to 1.

Scale

• Chance can be recorded on a scale from 0 to 1. 0 would represent an event be impossible, 0.5 would describe an event as a 50% or equal chance of happening and 1 would describe an event as being certain to happen.

Teaching points • Introduce students to the scale of 0 to 1 on a number line and help them rate everyday events using this system.

• Allow students to predict probability within simple chance games and experiments using this scale.

• Give students the opportunity to carry out these chance experiments to see if their predictions are correct.

• Look at what things can affect outcomes from chance games and experiments and how this could alter the scale.

What to look for • Students who have difficulty predicting possible outcomes prior to an experiment.

• Students who have difficulty using a scale with decimal numbers to recognise probability.

Proficiency strand(s): Student vocabulary outcomes chance/probability likelihood

Understanding Fluency Problem solving Reasoning

scale

12

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

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Year 5—Sub-strand: Chance – 2

HANDS–ON ACTIVITIES Chance events (pg 15) • Brainstorm and list some chance events and model to students how these could be placed onto a chance scale of 0 to 1 like the one shown below. For example, I will do some writing at school today may rate highly (0.8) whereas a clown will visit school today may rate as low as 0.

0 0.1 0.2 0.3 Impossible Unlikely

0.4 0.5 0.6 Even chance

0.7

0.8 Likely

0.9

1.0 Certain

• Give students a list of ten events, labelled A to J, and ask them to place them on the chance scale of 0 to 1. Students may find it easier to place the letter on the scale rather than the event.

Coin toss • If you were to toss a coin what would the probability be that it would land on heads first? Where would this sit on the chance scale?

• Rate the following statements about tossing a coin 10 times on a chance scale of 0 to 1.

– It will land on heads 6 out of 10 times – It will land on tails 5 out of 10 times – It will land on heads only once out of 10 – It will land on tails 3 times out of 10 – It will land on heads 10 out of 10 times – It will land on tails 2 out of 10 times • After student predictions, carry out the experiment of tossing a coin and record the results on a simple table. Were your predictions correct? Where do your results sit on the chance scale?

1

2

3

4

5

6

7

8

9

10

Total

Heads Tails Spinning wheel (pg 16) • Look at the spinning wheel a teacher uses in to reward her class and ask students to draw up a chance scale in their books. Match each section on the spinning wheel to where you think they belong on the scale: e.g. maths game, no homework, prize, free time etc.

0 0.1 0.2 0.3 Impossible Unlikely

0.4 0.5 0.6 Even chance

0.7

0.8 Likely

0.9

1.0 Certain

Coloured straws • Place the following coloured straws into a paper bag: 4 pink, 3 green, 2 yellow and 1 orange.

• Predict using the scale 0 to 1 what the probability of drawing out each colour would be you: for example, green 0.6 chance.

• Carry out the experiment and see if your predictions were correct.

Handball competition (pg 17) • Discuss how in some games chance can be affected by skills. In sporting competitions those who play sport would have more chance of winning than those who do not play sport.

• Look at the handball target and the students who are involved in the handball competition. Rate each student’s chance of winning using the scale of 0 to 1. For example: Luke may have a 0.8 chance of winning because he plays football.

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

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13

Year 5—Sub-strand: Chance – 2

HANDS–ON ACTIVITIES (CONTINUED) Jelly bean jar • Imagine out of 100 jelly beans placed in a jar 60 are red, 30 are white and 10 are black. What are the chances of the following happening (use your knowledge of scale to predict probability): – A black jelly bean is drawn out of the jar.

– A red jelly bean is drawn out of the jar.

– A white jelly bean is drawn out of the jar.

• Partner students and allow them to set up a chance experiment similar to this one. Ask students to first predict what might happen using the chance scale before carrying out the experiment. Ask students to present their results to the class or teacher—were their predictions correct?

LINKS TO OTHER CURRICULUM AREAS English • Imaginative writing: Brainstorm and make a list of things students would love to see happen at school or at home but would be almost impossible. Turn these suggestions into ideas for an imaginative writing piece. For example: – The day the alien spaceship landed at school …

– The day I ended up inside my Xbox™ game …

– The day I dug up one million dollars in my backyard …

– The day Stephen Spielberg asked me to star in his latest movie …

Information and Communication Technology • Locate the website <www.mathsisfun.com> and click on the heading ‘Data’. Scroll down and locate the heading ‘The probability line’ and click on it. Read through the information then complete some of the questions at the end.

The Arts • Spinning wheel (pg 18): Ask students to create their own spinning wheel that can be used to help students decide what they may like to do at school in their lunch break. The spinning wheel is divided into 10 sections so those activities students like to do the most should be on the most section; for example, if a student loves playing basketball at lunch time, draw basketballs on 5 or more of the sections. Decorate each section and use a split pin to connect the spinning hand to the spinner.

Health and Physical Education • Set up a handball competition or a basketball shooting competition. Ask students before their turn to rate themselves on a scale of 0 to 1 what chance they have of scoring through the basket or hole first time around.

• Beanbags in the bin: Give each student 10 turns at throwing a beanbag into a bin from a distance. Before they start, ask them to predict how many beanbags they think they can throw into the bin. Ask students to translate this as a probability score; for example, if they predict 8 out of 10, then their probability will be 0.8. After throwing the beanbags ask the students to assess their predictions.

14

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Year 5—Sub-strand: Chance – 2

RESOURCE SHEET Chance events Copy and distribute.

(A) I will go home after school today.

(B) I will have vegetables with dinner tonight.

(C) A tossed coin will land on tails first toss.

(D) It will rain today.

(E) I will do some reading today.

(F) I will travel by helicopter to school tomorrow.

(G) I will do my homework tonight.

(H) The principal will visit the classroom in the next half hour.

(I)

I will go to the movies after school today.

CONTENT DESCRIPTION: Recognise that probabilities range from 0 to 1 (ACMSP117)

(J) I will watch TV sometime in the next 6 hours.

0 0.1 0.2 0.3 Impossible Unlikely

0.4

0.5 0.6 Even chance

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

0.7

0.8 Likely

0.9

1.0 Certain

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Year 5—Sub-strand: Chance – 2

RESOURCE SHEET Spinning wheel

16

TIM EE

E M A G

NO HOMEWORK

FR

EE

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

TIM

E CONTENT DESCRIPTION: Recognise that probabilities range from 0 to 1 (ACMSP117)

FR

EE

TIM

E

GAME MATHS

FR

E

S H T A M

ME A S G H T MA

TIM

RK

EE

MEWO

O NO H

FR

E

Copy and distribute.

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Year 5—Sub-strand: Chance – 2

RESOURCE SHEET Handball competition Copy and distribute.

50 20

CONTENT DESCRIPTION: Recognise that probabilities range from 0 to 1 (ACMSP117)

10

Read their background information and then rate these students’ chances of winning the handball competition using the probability scale; 0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9 and 1.0. (a) Luke has played football with a club for 4 years. (b) Jessica plays netball and has 3 brothers that play football. (c) Lucca plays soccer. (d) Amelia takes dancing and gymnastic classes. (e) Joseph is a swimmer. (f) Libby plays basketball, soccer and tennis. (g) Nic plays basketball but likes to play football at school with friends. (h) Mary likes to play football at school. (i) Jim has joined a football club this year. (j) Ollie doesn’t like sport but enjoys music.

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

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17

Year 5—Sub-strand: Chance – 2

RESOURCE SHEET Spinning wheel

CONTENT DESCRIPTION: Recognise that probabilities range from 0 to 1 (ACMSP117)

Enlarge onto card and distribute.

18

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

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

Assessment 1

Year 5—Sub-strand: Chance – 2

NAME:

DATE:

1. Rate the likelihood of these events happening using the scale 0 to 1.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

(a) I will have a sandwich for lunch today. (b) A tossed coin will land on heads. (c) The dice will land on 6 on the first roll. (d) I will have dinner with my family tonight. (e) It will snow at school today. (f)

I will go to the beach this weekend.

(g) I will be invited to a birthday party this month. (h) I will win a school raffle this year.

2. Suggest three examples of events that may happen in your family this weekend and rate their probability (between 0 and 1).

CONTENT DESCRIPTION: Recognise that probabilities range from 0 to 1 (ACMSP117)

3. 10 coloured balls were placed into a paper bag.

Rate your chances (from 0 to 1) of drawing out the following colours first time around.

green

yellow white

(a) Yellow: (b) White: (c)

Green:

4. Suggest and/or draw below what you would have to do to the coloured balls to make the probability 0.5.

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

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19

Assessment 2

Year 5—Sub-strand: Chance – 2

NAME:

DATE:

1. What chance is there of the following events occuring? Rate the events between 0 and 1 on the scale below. Place the letters on the scale.

(A) I will win a swimming race.

(B) I will win a running race.

(C) I can shoot a basketball or netball through the ring on the first attempt.

(D) I will be given $20 today.

(E) I always win board games.

(F) I will go to high school next year.

(G) I will star in a movie this year.

(H) I will win a raffle or competition this year.

0 0.1 0.2 0.3 Impossible Unlikely

0.4

0.5 0.6 Even chance

0.7

0.8 Likely

0.9

1.0 Certain

2. Look at the spinning wheel and rate your chances from 0 to 1 of landing on the following sections with the first spin.

(b) 2nd prize: (c) 3rd prize: (d) 4th prize: 3. Does having more spins of the wheel increase your chances of landing on the first prize?

Yes

No

Explain why:

4. Suggest at least one other game of chance or experiment where you have an even chance of winning.

20

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

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

CONTENT DESCRIPTION: Recognise that probabilities range from 0 to 1 (ACMSP117)

(a) 1st prize:

Checklist

Year 5—Sub-strand: Chance – 2

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

Students can carry out chance experiments to test their predictions

Students can predict the probability of chance games using the scale 0 to 1

STUDENT NAME

Students can rate everyday events on a scale of 0 to 1

Recognise that probabilities range from 0 to 1 (ACMSP117)

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

21

Year 5—Sub-strand: Data representation and interpretation—DR&I – 1

Pose questions and collect categorical or numerical data by observation or survey (ACMSP118)

TEACHER INFORMATION

RELATED TERMS Categorical data

• Data that can be arranged into categories.

Numerical data

• Data that can be counted or measured (also known as quantitative data).

Observation

• Data that can be gathered by observing or watching.

What this means • Students will discuss and look at the differences between categorical data (data that can be arranged into categories) and numerical data (data that can be counted or measured). They will be given the opportunity to explore appropriate questions in order to gather these two different types of data. Students will also learn that the question they ask will then lead to the type of information they wish to gather; for example, an open question such as ‘What is your favourite subject?’ will gain different information to a closed question such as ‘Do you like sport or art?’. They will discover that posing questions is the first important step to gathering data.

Teaching points • Identify the difference between numerical and categorical data.

Survey

• To collect sample opinions or facts from a group.

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

• Explore appropriate questions required to collect the two different types of data.

• Give students the opportunity to trial various methods of data collection and recording using observation and surveys with people 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 choosing the most effective method to collect their data for an investigation.

• Students who have difficulty wording survey questions to reflect the type of data required.

Student vocabulary questions categorical data numerical data observe

Proficiency strand(s): Understanding Fluency Problem solving Reasoning

survey

22

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

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

Year 5—Sub-strand: Data representation and interpretation—DR&I – 1

HANDS–ON ACTIVITIES Categorical and numerical data (pg 25) • Define and discuss the differences between categorical data (data that can be arranged into categories) and numerical data (data that can be counted or measured).

• Give students the provided examples of topics and ask them to suggest which heading they would fall under. Hint: some may come under both headings.

• Examples: number of pets, types of pets, number of cars in the car park, types of cars, family members, hair colour, eye colour, favourite subject, favourite colour, student height, favourite sport, insect types, insect numbers, canteen sales, favourite holiday destinations, favourite sandwich filling, how students travel to school.

• Ask students to suggest other examples of categorical or numerical data, or topics that could fall under both headings.

Open and closed questions (pg 26) • An open question can provide a variety of answers; for example, ‘What is your favourite TV show?’ A closed question will just give you one answer or a yes/no response; for example, ‘Do you like watching Masterchef®?’

• Categorise the questions provided as open or closed by cutting and pasting them under the appropriate heading or writing open or closed next to each question.

Weekend activities • Brainstorm all the activities students do on the weekend. Decide on what categories these activities could be grouped under; e.g. sport, family, friends, outing, relaxing etc.

• Ask students to group these activities under the chosen headings.

• What open survey question could you ask your classmates if you wanted to know what they like to do on the weekend?

• Ask 10 of your classmates a closed question about their weekend activities; for example, ‘Do you like going out or staying home on the weekend?’

Number of class pets (pg 27) • If you wanted to find out how many pets your classmates had, what question would you need to ask?

• Use your question and the table provided to survey your classmates.

• Is this data numerical or categorical?

• What would be the best way to present this gathered data?

• If you wanted to find out what types of pets your classmates have would this information be categorical or numerical?

Why?

Favourite school subjects • Make a list of the subjects you study at school. Now write an open survey question you could ask your classmates about their favourite subject.

• Survey your classmates using your question and record their answers on a table listing all possible subject choices (you can draw it up by hand or create one on the computer).

• Discuss students’ findings and decide if it is numerical or categorical data.

• Choose two of the most-favourite subjects and ask the students a closed question about these; for example, ‘Do you prefer maths or language?’

Vehicle count • Working in pairs, investigate the question: What types of vehicles pass your school over 15 minutes? Draw up a table similar to the pets resource sheet and list all the possible vehicles that could pass your school; e.g.

Car

Van

Motorbike

Bicycle

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

Truck

Emergency vehicle

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23

Year 5—Sub-strand: Data representation and interpretation—DR&I – 1

HANDS–ON ACTIVITIES (CONTINUED) • Allow students to observe passing traffic for 15 minutes, recording the numbers of vehicles that pass on the table provided using ticks or tally marks.

• Could this data be categorical, numerical or both?

• If the question had been ‘How many cars pass your school?’ What type of information would students need to gather?

Discuss how the question is very important and dictates what needs to gathered. For example, if the question only mentioned cars then only cars would be counted, but if it mentions vehicles then all modes of transport using the road would be counted.

• What kind of information can we learn from this type of survey?

Insects at school • If we wanted to investigate what types of insects were at school, one method could be to observe insects in the playground.

• Ask students to create and paste a one metre square piece of white paper onto one area of the playground floor. Leave it there for half an hour and observe what types and how many insects walk onto the paper. Create a table to record insect types.

• Compare results and discuss how this can be numerical and categorical data, as the insects can be counted and categorised.

LINKS TO OTHER CURRICULUM AREAS English • Writing: Open and closed questions. Provide students with a list of questions about school and ask them to decide whether they are open or closed.

– Do you like school?

– What is your teacher’s name?

– What is your favourite subject?

– What grade are you in?

– What do you like to do at lunchtime?

– How do you get your work finished?

– Do you like reading or drawing in your spare time?

– When did you start at your school?

• Ask students to make a list of open and closed questions to use in an interview for a friend.

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. This method is suitable when working with a word processing 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 the table and use it for a survey.

Science • Tables and diagrams are often used by scientists to show investigated information. Use a table to identify the different insect species you discovered at school during your investigation (see Insects at school). Categorise and describe their features.

Flying insects e.g. Blow fly: 2 body parts, 6 legs, 2 wings

24

Crawling insects e.g. Worm: segmented body, no legs

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

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

Year 5—Sub-strand: Data representation and interpretation—DR&I – 1

RESOURCE SHEET Categorical and numerical data Copy and distribute.

Number of pets, types of pets, number of cars in the car park, types of cars in the car park, family members, student hair colour, student eye colour, favourite subject, favourite colour, student height, favourite sport, types of insects at school, number of insects at school, canteen sales, favourite holiday destinations, favourite sandwich filling, how students travel to school, number of students in each class, student birthdays, students favourite video game, students favourite TV show.

Numerical data

CONTENT DESCRIPTION: Pose questions and collect categorical or numerical data by observation or survey (ACMSP118)

Categorical data

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

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25

Year 5—Sub-strand: Data representation and interpretation—DR&I – 1

RESOURCE SHEET Open and closed questions Copy and distribute.

What is your favourite thing to do on the weekend?

Do you like reading or writing better?

What is your favourite animal?

Which sports do you like to watch on TV? Do you like watching cooking shows on TV?

Do you like carrots?

What is your favourite vegetable?

Which fruit do you like to eat?

Do you like apples or pears?

Do you like to swim at the beach or a swimming pool?

How many times have you visited a zoo?

What is your favourite movie?

Who is your favourite actor/actress?

Do you like PlayStation™ or Xbox™?

How many people are in your family?

What is your favourite pet?

26

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

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

CONTENT DESCRIPTION: Pose questions and collect categorical or numerical data by observation or survey (ACMSP118)

What would you like to do for your next birthday?

Year 5—Sub-strand: Data representation and interpretation—DR&I – 1

RESOURCE SHEET Number of class pets

0 pets

1 pet

2 pets

3 pets

4 pets

CONTENT DESCRIPTION: Pose questions and collect categorical or numerical data by observation or survey (ACMSP118)

5 pets

6 pets

7 pets

8 or more pets

Copy and distribute.

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

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

27

Assessment 1

Year 5—Sub-strand: Data representation and interpretation—DR&I – 1

NAME:

DATE:

1. Match the correct word to the definitions: Categorical or Numerical (a) Data that can be counted or measured: (b) Data that can be arranged into groups: 2. Place a C (categorical), N (numerical) or both next to these investigations. (a) Number of girls and boys at the school (b) Museum visitors during the month of April (c) Types of class pets (d) Number of cars in the staff car park (e) Snacks students eat at recess (f)

Favourite farm animals

(g) Sandwich sales at the canteen

3. If you wanted to find what snacks students in your class had at recess, what question would you need to ask? ?

4. Ask 10 of your classmates your question and record their responses on the table. (Note: you may not need all the columns.)

Fruit

Savoury biscuits

Sweet biscuits

Cake/ muffin

5. Is this investigation gathering categorical or numerical data?

6. Make a statement about your findings.

28

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

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

CONTENT DESCRIPTION: Pose questions and collect categorical or numerical data by observation or survey (ACMSP118)

(h) How students travel to school

Assessment 2

Year 5—Sub-strand: Data representation and interpretation—DR&I – 1

NAME:

DATE:

A group of students were asked what their favourite pastime activity was and the responses are listed below.

Ben – playing football Nic – playing Xbox™ Jake – playing football Yang – dancing Faith – going to the movies Lachlan – watching TV Indy – playing with my iPod™

Sasha – walking my dog Gina – watching TV Mike – playing basketball George – swimming Kyle – playing on my iPad™ Sienna – ballet Kate – shopping with friends

Alex – playing soccer Lily – shopping Helena – visiting friends Riley – playing PlayStation™ Jess – playing netball Marc – playing hockey

1. Group these students in the categories below.

CONTENT DESCRIPTION: Pose questions and collect categorical or numerical data by observation or survey (ACMSP118)

Sport/Active

Social

Media

2. Looking at the categories, answer the following questions: (a) Which category was the most popular?

Least popular? (b) Could these categories be given a different heading?

If so, what do you suggest?

(c) Was this survey question categorical or numerical? (d) Would you call this survey question open or closed?

3. Survey 10 of your classmates as to their favourite pastime activity. Write your question below and their responses in a table with your own category headings. ?

4. Make a statement about your results.

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

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29

Assessment 3

Year 5—Sub-strand: Data representation and interpretation—DR&I – 1

NAME:

DATE:

1. Describe and give an example of an open and closed question.

Open question: ?

Closed question: ?

2. Place a O (open) or a C (closed) next to these example questions: (a) What is your favourite song? (b) Do you like cooking or music TV shows? (c) Do you like doing sport or art? (d) What is your favourite food?

(f)

Which ice-cream flavour do you like best?

(g) Do you like dogs or cats? (h) If you had to choose between walking or riding by car to school which one would you pick?

3. Select one of the questions above and carry out an investigation gathering data in order to answer the question. Draw up a table on the back of this page or construct a table using a computer and print it out.

Question: ?

4. What results did you discover?

5. Is this data categorical or numerical?

Why?

30

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

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

CONTENT DESCRIPTION: Pose questions and collect categorical or numerical data by observation or survey (ACMSP118)

(e) Where was the best holiday you have had?

Checklist

Year 5—Sub-strand: Data representation and interpretation—DR&I – 1

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

Can pose a question to carry out an observation or survey

Understands the difference between open and closed questions

STUDENT NAME

Understands the difference between categorical and numerical data

Pose questions and collect categorical or numerical data by observation or survey (ACMSP118)

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

31

Year 5—Sub-strand: Data representation and interpretation—DR&I – 2

Construct displays, including column graphs, dot plots and tables, appropriate for data type, with and without the use of digital technologies (ACMSP119)

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 explore and present a variety of data using a number of different display methods including tables, column graphs, dot plots, line graphs and pie charts. They will be asked to assess each method to determine which type of display is most suitable for the type of data they are investigating. For example, line graphs are only suitable to use when something is measured over a period of time, dot plots are only suitable when comparing small amounts of data, and column graphs and pie charts help group and display data in categories.

Students will carry out investigations and interpret the best way to display their gathered data and at the completion be able to justify their choice of representation.

Table

• A means of organising data in rows and columns.

Column graph

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

Dot plot

• A set of data represented by using dots over a number line.

Line graph

• A graph formed by line segments and connecting points to represent certain data.

Pie chart

• A chart in which the sectors of a circle are used to show a whole in terms of its parts, with each sector often representing a category.

Teaching points • Introduce students to the different types of data displays: tables, dot plots, column graphs, line graphs and pie charts.

• Identify the best methods for displaying given and gathered data, then use the appropriate display.

• Allow students the opportunity to construct each type of data display.

• Encourage and demonstrate to students how to use the computer to construct data displays.

• Allow students to interpret their displays and justify their choice of representation.

What to look for • Students who have difficulty choosing the most effective method to display their data.

• Students who have difficulty using the computer to construct a graph. A set of instructions by the class computer may be useful.

Student vocabulary displays tables column graphs dot plots

Proficiency strand(s): Understanding Fluency Problem solving Reasoning

line graphs pie charts

32

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

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Year 5—Sub-strand: Data representation and interpretation—DR&I – 2

HANDS–ON ACTIVITIES Data displays (pg 35) • Discuss and brainstorm all the methods of displaying data that students are aware of.

• Look at the examples of different types of graphs (provided) and name them. Identify what information each one is giving us. Look at each graph and ask students to suggest reasons why each graph type has been chosen for that particular type of data.

• Ask students to find an example of each of the following data displays in a newspaper or magazine: a table, a column or bar graph, a dot plot, a line graph and a pie chart. Paste them into their book and write at least one statement about what each one is representing.

Using tables – lunch orders (pg 36) • Look at the example of a school canteen lunch order list. Why do you think this information has been displayed in a table? Is it easy to read this way? Is there any other way it could have been displayed?

• Draw up your own table on a computer using a word processing or graph program and include items your school canteen may have on its lunch order list. If your school doesn’t have a canteen make up some of your own items you think a canteen should serve for lunch.

• Survey your classmates by asking them to select an item/s they may choose for a lunch order. Use ticks or tally marks on your table to display their choice.

• Was this an effective method to record this data? Could you have used any other method?

Column graphs • A column graph can also be referred to as a bar graph. It is a graph that displays categories of information in columns or bars vertically or horizontally. Brainstorm with the students what information might be good to display on column graphs.

• Ask the students what their favourite season is and display this information in a column graph in their books, using a ruler to draw the vertical axis, (labelled with numbers), and a horizontal axis labelled with the seasons.

• Then ask students to redo their column graph on a computer. Print it out and paste it into their books. Allow students to compare their column graphs and comment on which is more effective.

Dot plots (pg 37) • Look at the dot plot showing the number of household TV’s a class of students have. Ask students questions about the information such as which number is the most common and least common? Is this information presented clearly? Is there another way we could present this data?

• Ask students to survey their classmates on the number of TV’s they have in their home and record the information using a dot plot. Allow students to compare and comment on their displays.

Line graphs: Harry’s height • Ask students to give examples of when line graphs are used. For example, students should have a ‘Child health record’ that recorded their weight and length growth when they were younger. Line graphs are commonly used to plot points to reflect growth or change.

• Ask students to draw up a line graph in their books or on graph paper and plot Harry’s height from 1 to 11 years, represented below in the table. Allow students to compare and comment on their displays. Looking at the graph do you think Harry is tall or short? Is there another way this information could have been accurately represented or is this the best method?

Harry’s height

1 yr 75 cm

2 yrs 90 cm

3 yrs 4 yrs 5 yrs 6 yrs 7 yrs 8 yrs 9 yrs 10 yrs 11 yrs 100 cm 105 cm 118 cm 125 cm 130 cm 136 cm 145 cm 150 cm 158 cm

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

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33

Year 5—Sub-strand: Data representation and interpretation—DR&I – 2

HANDS–ON ACTIVITIES (CONTINUED) Pie charts (pg 38) • Pie or sector charts can be useful for displaying data that has been grouped into categories, amounts or sectors. Ask students to give some examples of data they have seen displayed in a pie chart.

• Look at the example of the pie chart showing how a student spends her day. Using the blank pie chart, ask students to represent how they spend an entire school day. Out of a day (24 hours) they will need to work out approximately how many hours they spend at school, sleeping, eating, playing, relaxing etc. Ask students to compare their display with a classmate and comment on similarities and differences.

• Was this information best suited to a pie chart or could it have been displayed in another form?

• Relate pie charts to fractions. If half of a group of visitors to a museum were families, a quarter were single adults and a quarter were seniors, how would this look on a pie chart?

LINKS TO OTHER CURRICULUM AREAS Information and Communication Technology • Look at and experiment with creating graphs and charts using a computer. Try creating a column graph showing the number of boys and girls in your class or hair colour of the students in your class.

• Go to <www.mathsisfun.com> website and go to the heading Data, click ‘Graphs index’, then select ‘Make a bar graph, line graph or pie chart’ and create a suitable graph of your choice using information you have previously gathered in an investigation. Print out your graph.

Science • Using the class computer and the internet investigate the past week’s weather in a city of your choice. How is this presented? Which graph or display would be best to show temperatures? (Line graph.) Create a line graph showing the temperatures in your capital city for the week to come.

The Arts • How creative can you be in presenting various graphs such as a column graph or pie chart. Experiment with a computer and create a display, or alternatively use fabric and various types of paper to create an interesting pie chart.

Health and Physical Education • Look at height and weight relationships. If you were to look at a Child’s health record book they show a healthy height and weight range. Investigate this using a child health record book or use the internet to look up healthy height to weight ratio.

34

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

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

Year 5—Sub-strand: Data representation and interpretation—DR&I – 2

RESOURCE SHEET Data displays Copy and distribute.

TV programs Weekly viewing

9

20

8

18

7

16

Number of people (thousands)

6 TV programs

5 4 3 2 1

14 12 10 8 6 4 2 ay Fr id

da y rs Th u

ne

sd

ay W ed

M

sd

da y on

on

s

t or Sp

Ca rto

le

w s Si tc om

Ne

ty Lif es

24-hour day

ay

0

0

Tu e

Number of people (thousands)

CONTENT DESCRIPTION: Construct displays, including column graphs, dot plots and tables, appropriate for data type, with and without the use of digital technologies (ACMSP119)

10

Travelling to school bike/scooter

walk

car

bus

train

school

sleep

leisure time

eating

Number of people in a family

1

2

3

4

5

6

7

8

Number of people Australian Curriculum Mathematics resource book: Statistics and Probability (Years 5 & 6)

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

35

36

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

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

1

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18

CONTENT DESCRIPTION: Construct displays, including column graphs, dot plots and tables, appropriate for data type, with and without the use of digital technologies (ACMSP119)

1

1

Cheese sandwich

Water

1

Vegemite™ sandwich

1

1

Steamed dim sim

Blackcurrant juice

1

Fish burger

1

1

Chicken burger

Orange juice

1

Sushi roll

1

1

Salad wrap

Apple juice

1

Salad roll

1

1

Pizza

Salad bowl

1

Hot dog

1

1

Quiche

Toasted sandwich

1

Pastie

1

1

Sausage roll

Ham sandwich

1

Pie

Item

19

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Year 5—Sub-strand: Data representation and interpretation—DR&I – 2

RESOURCE SHEET

Using tables – lunch orders Copy and distribute.

Year 5—Sub-strand: Data representation and interpretation—DR&I – 2

RESOURCE SHEET Dot plots

CONTENT DESCRIPTION: Construct displays, including column graphs, dot plots and tables, appropriate for data type, with and without the use of digital technologies (ACMSP119)

Copy and distribute.

0

1

2

3

4

5

Televisions per household

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

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

37

Year 5—Sub-strand: Data representation and interpretation—DR&I – 2

RESOURCE SHEET Pie charts Copy and distribute.

24-hour day

sleep

leisure time

eating

38

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

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

CONTENT DESCRIPTION: Construct displays, including column graphs, dot plots and tables, appropriate for data type, with and without the use of digital technologies (ACMSP119)

school

Assessment 1

Year 5—Sub-strand: Data representation and interpretation—DR&I – 2

NAME:

DATE: 16

Number of students

CONTENT DESCRIPTION: Construct displays, including column graphs, dot plots and tables, appropriate for data type, with and without the use of digital technologies (ACMSP119)

14 12 10 Boys Girls

8 6 4 2 0

Foundation

Year 1/2

Year 3/4

Year 5/6

1. Looking at the graph above answer the following questions: (a) What type of graph is this? (b) What do you think this graph is showing?

(c) Suggest a title for this graph: (d) Which year level has an equal number of boys and girls? (e) Which year level has the most boys? (f)

Which year level has the most girls?

2. Do you think this graph is a good way to present this information?

Yes

No

Why?

3. Looking at the Household pets display, answer these questions: (a) What type of graph is this?

Household pets in Year 5B = 1 student

(b) Which number of pets is the most common? (c) Which number of pets is the least common?

0

1

2

3

4

5

6+

(d) What does 6+ mean?

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

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

39

Assessment 2

Year 5—Sub-strand: Data representation and interpretation—DR&I – 2

NAME:

DATE:

1. Use the table below to survey your classmates on what their favourite t-shirt colour is. Write the question you would ask them first. ?

Blue

Green Yellow

Pink

Purple

Black

Grey

White

Orange

2. Present the data in a graph of your choice. You can use the space on the back of this sheet or create your display on a computer, print it out and attach it to this page.

3. Answer the following questions: (a) Which graph type did you use?

Why? (b) Which colour was the most popular? (c) Which colour/colours were not chosen? (d) What other method could you use to display this information?

4. Look at the survey topics and suggest a good method to present the data.

Choose from the following, you may choose more than one. table

dot plot

picture graph

column graph

line graph

pie chart

(a) Types of class pets (b) How students travel to school (c) Favourite ice-cream flavours (d) Weekly temperature (e) Students birthdays (f)

A baby’s weight development

(g) Favourite subjects at school (h) Activities over a 24-hour day

40

(i)

Canteen food orders

(j)

Favourite TV shows

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

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

CONTENT DESCRIPTION: Construct displays, including column graphs, dot plots and tables, appropriate for data type, with and without the use of digital technologies (ACMSP119)

Red

Checklist

Year 5—Sub-strand: Data representation and interpretation—DR&I – 2

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

Can construct data displays using a computer

Can carry out investigations and construct various displays by hand

STUDENT NAME

Names and interprets different data displays

Construct displays, including column graphs, dot plots and tables, appropriate for data type, with and without the use of digital technologies (ACMSP119)

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

41

Year 5—Sub-strand: Data representation and interpretation—DR&I – 3

Describe and interpret different data sets in context (ACMSP120)

TEACHER INFORMATION

RELATED TERMS Data

What this means

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

• Students will be asked to interpret a variety of data displays including tables, column graphs, picture graphs, line graphs, dot plots and diagrams. Students will be shown what to look for when reading and interpreting a graph, including things such as the title and headings on each axis. In some cases they will be given the opportunity to compare similar types of data sets in order to determine which may be the best deal; for example, the best mobile phone deal or which bill costs less. Students will be asked to collect data and decide the best method to present their information. They will also be given a set of data presented in a few different ways and be asked to comment on which they believe is the easiest to read and interpret.

Teaching points • Expose students to a variety of data displays: tables, dot plots, column graphs, line graphs and pie charts, and demonstrate how to interpret them.

• Allow students the opportunity to compare data sets when choosing the best deal.

• Give students the opportunity to gather and present data using the most appropriate method.

• Encourage students to interpret displays and justify the choice of representation.

What to look for • Students who have difficulty interpreting graphs; they may need assistance to look for clues such as titles and axis headings.

• Students who have difficulty choosing the most effective method to display their data.

• Students who have difficulty comparing data and cannot see the difference between two sets of data.

Student vocabulary data displays data sets

42

Proficiency strand(s): Understanding Fluency

comparing

Problem solving

interpreting

Reasoning

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

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

Year 5—Sub-strand: Data representation and interpretation—DR&I – 3

HANDS–ON ACTIVITIES Interpreting displays (pg 45) • Ask students to suggest what things you need to look for when interpreting data displays and graphs. What things make a display easy to read? For example, things such as the main title and smaller vertical and horizontal axis labels give us clues. A key in a picture graph is a vital clue as to the number or amount of people or items that were included in the display.

• Look at the different data displays and ask students to interpret each one. Predict what the vertical and horizontal axis may be showing or representing.

• Ask students to locate at least 3 different data displays/graphs in newspapers or magazines. Cut them out, paste them into their books and describe the information each one is displaying.

Comparing displays (pg 46) • Sometimes we need to compare two displays to see which may be a better deal; for example, two mobile phone bills or which electricity company gives the best deal.

• Look at the two mobile phone bills and ask students to interpret and compare the similarities and differences between the two graphs. What type of graphs are they? Why would these types of graphs be used for this information?

Water usage (pg 47) • Look at a family’s water usage and interpret the column graph. In which month was the most water used? Write two statements about the column graph.

Weather graph • Which is the best display/graph to show a range of temperatures? (Line graph.) What features do you need to include on a line graph? For example: title, numbers along the vertical axis, times or days along the horizontal axis, accurate plots etc.

• Locate a weather line graph in a newspaper or on the internet and interpret what it is showing.

• Plot the following temperatures recorded over a week onto a line graph.

Sunday 28 °C

Monday 31 °C

Tuesday 32 °C

Wednesday 35 °C

Thursday 38 °C

Friday 21 °C

Saturday 24 °C

• Ask students to find out the temperatures in their local city over the past week and plot them onto a line graph they draw or create using a computer.

Favourite sport (pg 48) • Look at the results shown from a survey about a group of student’s favourite sport. The information has been presented three different ways. Which is the easiest to read and interpret? Why? Write three statements about the information using the display they find easiest to read.

Student survey • Survey your classmates on which mode of leisure travel they like using the best: skateboard, bike, scooter or rollerblade?

• Use a table (drawn by hand or computer) to record their results.

• Present the information in two different displays; for example, column graph, pie chart or dot plot.

• Compare displays and discuss which they feel works better for this information.

• Why wouldn’t you use a line graph for this information?

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

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

43

Year 5—Sub-strand: Data representation and interpretation—DR&I – 3

LINKS TO OTHER CURRICULUM AREAS English • Procedure writing: Ask students to write their own set of instructions on how to carry out a survey or how to display information in a graph.

• Grammar – ‘Nouns’: Nouns are used to label and identify a person, place, animal or thing. Make a list of possible nouns that could be used to label a display or graph. A graph or display normally needs a title and labels at each axis.

Information and Communication Technology • Choose a country that interests you and search for its current weather. How is this presented? Have they used a graph?

Look at the country’s population—has this been presented in a graph or display and, if so, what type? Is any other information about this country presented within a graph? If so, what is it telling you?

• Using a computer go to <www.ixl.com> Go to Year 5, then scroll down to ‘Data and graphs’. Investigate the different sections entitled interpret line graphs, interpret bar graphs, interpret pictographs, interpret line plots and choose the best type of graph.

Health and Physical Education • What house team colour do your classmates belong to? Show this information in a pie chart.

• Have races or activities in your house colours; for example, running races, relay races, team sports such as tunnel ball etc.

• What type of graph is commonly used to depict a person’s height or weight? Look at graphs on the internet that show the height and weight development of a child who is of a healthy and unhealthy weight range.

Economics • Comparing charts and graphs often help families and individuals budget their spending. For example, if they want to choose a new mobile phone plan or a new electricity company, they will read and interpret information commonly represented in graphs in order to decide which the best deal to choose is.

• Ask students to compare two bills or deals showing prices and allow them to comment on the best choice for a budget.

44

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

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

Year 5—Sub-strand: Data representation and interpretation—DR&I – 3

RESOURCE SHEET Interpreting displays Copy and distribute.

Melbourne weather 12–19 April 30 25 20 15

Night

10 5

Day

Sa tu rd ay

Fr id ay

Th ur sd ay

ne sd ay W ed

Tu es da y

on da y M

Su nd ay

0

House teams

Red

blue

CONTENT DESCRIPTION: Describe and interpret different data sets in context (ACMSP120)

green

gold

Gina’s fashion house sale 40 35 30 25 Shoes

20

Clothes

15 10 5 0

Day 1

Day 2

Day 3

Day 4

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

Day 5

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

45

Year 5—Sub-strand: Data representation and interpretation—DR&I – 3

RESOURCE SHEET Comparing displays Copy and distribute.

Amelia’s mobile phone 100 90 80

Usage

70 60

Calls

50

Texts

40

Data

30 20 10 0

January

February

March

70 60

Usage

50 40

Calls Texts

30

Data 20 10 0

46

January

February

March

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

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

CONTENT DESCRIPTION: Describe and interpret different data sets in context (ACMSP120)

Liam’s mobile phone

Year 5—Sub-strand: Data representation and interpretation—DR&I – 3

RESOURCE SHEET Water usage Copy and distribute.

Average water usage in litres per month 1200

Litres used

1000

800

600

400

200 0 October

November

December

CONTENT DESCRIPTION: Describe and interpret different data sets in context (ACMSP120)

September

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

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

47

Year 5—Sub-strand: Data representation and interpretation—DR&I – 3

RESOURCE SHEET Favourite sport Copy and distribute.

Favourite sport football soccer

hockey basketball netball tennis

Favourite sport

cricket 30

volleyball Number of students

25 20 15 10 5

= Students

Favourite sport basketball football soccer

hockey netball tennis cricket volleyball

48

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

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

CONTENT DESCRIPTION: Describe and interpret different data sets in context (ACMSP120)

l al yb le

Vo l

Cr

ick

et

s

l al

ni Te n

tb

et sk Ba

Ne

ba

ll

ey ck Ho

al

l

So

tb Fo o

cc er

0

Assessment 1

Year 5—Sub-strand: Data representation and interpretation—DR&I – 3

NAME:

DATE: Melbourne weather 12–19 April Temperature °C

30 25 20 15

Night

10 5

Day

Sa tu rd ay

Fr id ay

Th ur sd ay

W ed ne sd ay

Tu es da y

on da y M

Su nd ay

0

1. Look at the graph shown above and answer the following questions: (a) What type of graph is this? (b) What is the title of the graph? (c) Describe what information this graph is showing.

(d) What does

tell us?

(e) What does

tell us?

(f)

Do you think is the best method of displaying this information?

No

Explain why.

2. Look at Liam’s mobile phone usage and answer the following questions: (a) How does he use his phone the most? (b) How does he least use his phone? (c) In which month did he make the most calls?

70 60 50

Usage

CONTENT DESCRIPTION: Describe and interpret different data sets in context (ACMSP120)

Yes

40

Calls Data

30

Texts 20 10 0

(d) In which month did he send the least texts? (e) What type of graph is this? (f)

January

February

March

Do you think this is a good method to display this information?

Yes

No

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

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

49

Assessment 2

Year 5—Sub-strand: Data representation and interpretation—DR&I – 3

NAME:

DATE: = 2 students

How Year 5 travel to school

walk

skateboard

bike

scooter

car

bus

1. Look at the display above and answer the following questions: (a) What type of graph is this? (b) What information is it showing? (c) How many students ride a bike to school? (d) Which way do 4 students travel to school? (e) Which is the most popular way to travel to school?

2. Present the information above in a different graph of your choice on a separate piece of paper or using a print-out of a computer generated display/graph. (a) What type of graph is it?

(b) Which sport is the most popular?

Favourite sport 30

(c) Which sport is the least popular?

Number of students

25 20

(d) Which sport did 19 people choose?

15 10

(e) Is this a good method to present this information?

5

(f)

l al

Ho ck ey Ba sk et ba ll Ne tb al l Te nn is

So

Fo ot b

cc er

0 Students

Name one other method you could use:

4. Survey your classmates by asking them what their favourite sport is or how they travel to school and present the information in an appropriate display of your choice. You may use paper or the computer to create your display.

50

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

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

CONTENT DESCRIPTION: Describe and interpret different data sets in context (ACMSP120)

3. Look at the favourite sports graph and answer the following questions:

Checklist

Year 5—Sub-strand: Data representation and interpretation—DR&I – 3

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

Can compare different data displays

Can interpret different types of data displays

STUDENT NAME

Can identify different types of data displays

Describe and interpret different data sets in context (ACMSP120)

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

51

Year 6—Sub-strand: Chance – 1

Describe probabilities using fractions, decimals and percentages (ACMSP144)

TEACHER INFORMATION

RELATED TERMS Chance (Probability)

What this means

• The likelihood of an event occurring.

• A decimal numeral that includes a decimal point, representing whole numbers and part of whole numbers.

• Students will investigate and participate in some popular games of chance, games they are familiar with and also games from other cultures such as the Japanese game Pachinko, which is a mix of a slot machine and pinball. They will predict the outcome of these games using their knowledge of fractions, decimals and percentages. For example, if you were to toss a coin you would have 50% or 0.5 chance of it landing on heads. Students will then be able to test their predictions by carrying out these chance games and experiments.

Percentages

Teaching points

• Numbers that are part of 100 or ‘hundredths’.

• Allow students to discuss and predict the possible outcome of simple chance experiments and relate chance words to fractions, decimal or percentage amounts.

Decimals

Fractions

• A fraction is part of a whole. A fraction is obtained by dividing a whole or given amount into a certain number of equal parts and taking a certain number of them; for example, 2⁄3 refers to 2 of 3 equal parts. In a fraction the top number is referred to as the numerator (or number of parts you have) and the bottom number is the denominator (or the number of parts the whole is divided equally into).

Student vocabulary chance/probability

• Encourage students to use fractions, decimals and percentages as another means to represent the likelihood of an outcome in a game of chance.

• Allow students to be involved in a variety of simple chance experiments and games and then comment on their predictions and outcomes.

• Introduce some chance games from other cultures.

What to look for • Students who have difficulty predicting possible outcomes prior to an experiment.

• Students who have difficulty understanding fractions, decimals and percentages.

Proficiency strand(s): Understanding

likelihood

Fluency

outcome

Problem solving

fractions

Reasoning

decimals percentages

52

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

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

Year 6—Sub-strand: Chance – 1

HANDS–ON ACTIVITIES Probability games and situations (pg 55) • Give students examples of probability games and situations and ask them to use chance words to describe their outcome. For example, sometimes, always, impossible, possible, uncertain, certain, likely, highly likely, unlikely, could happen, will happen, probably, probably not.

• Use the chart provided and relate the chance words above with fractions, decimals and percentages. For example, certain would be the same as 100% or 1.0 and even chance would be 50%, 5⁄10 or 0.5.

• Suggest and place five chance events that could happen at school on a number line from 0 to 1.

0

0.5

1

Coin toss • Use chance words, fractions, percentages and decimals to predict what would happen if you were to toss a coin in the hope that it lands on heads.

• Ask students to use fractions, decimals or percentages to predict the following coin toss situations (out of 10 tosses): – 1 head and 9 tails – 5 heads and 5 tails – 9 heads and 1 tail – 2 heads and 8 tails – 6 heads and 4 tails – 10 heads – 3 heads and 7 tails – 7 heads and 3 tails – 10 tails – 4 heads and 6 tails – 8 heads and 2 tails • Ask students to carry out the experiment and compare and comment on their results with others.

Pea under the cup/Shell game • The pea under the cup or shell game (also known as ‘Thimblerig’) is an old army game where you have to guess which cup or shell the pea is hiding under after the cups/shells have been moved around. Ask students to predict their chances of guessing where the pea is on the first guess.

• Working in pairs, allow students to take it in turns to play the game.

• Discuss the results and ask students what fractions, decimals or percentages could they use to describe their outcomes.

Card games • Ask students to predict using words, fractions, decimals and percentages what chance they would have of choosing a hearts card form a deck of shuffled cards.

• Ask students to draw out 20 cards from a deck and see how many of each suit came out—discuss and compare the results with others.

• Snap: Predict what are the chances of winning a game of snap. Working in pairs, allow students to play snap. Discuss how is this a game of chance.

Pachinko (Japanese) • Pachinko is a Japanese mechanical game of chance that is a mix of a slot machine and pinball. It is played recreationally in arcades and also used for gambling. A player fires a ball into the machine which then moves down through a forest of pins. If the balls go into certain locations they can be captured and sequences of events may be triggered to release more balls. The object of the game is to capture as many balls as possible, as the balls can be exchanged for prizes.

• Relate this game to pinball. What chances do you have of winning pinball? Is it a game of chance or skill?

Lu–lu game (pg 56) • Early Hawaiians played ‘Lu-lu’ with disks of volcanic stone to replace a stone dice. The word Lu-lu means ‘to shake’. Each of the four playing pieces are marked on one side only (1 dot, 2 dots, 3 dots and 4 dots). The pieces that land dots side up are counted.

• Ask students to make their own playing pieces using cardboard, buttons, stones or coins. Then follow the game instructions and play Lu-lu in pairs.

• Discuss using words, fractions, decimal and percentages what their chances of winning were.

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

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

53

Year 6—Sub-strand: Chance – 1

HANDS–ON ACTIVITIES (CONTINUED) Board games • Make a list of board games and other games of chance students know; for example, Snakes and ladders, card games, Uno™, Pick-up sticks, Trouble™ etc. What are their chances of winning these games? What do their chances depend on?

• If they have access to these games, allow students to work in small groups playing one of these games of chance.

LINKS TO OTHER CURRICULUM AREAS English • Procedure writing: Ask students to devise their own game of chance and to write a set of rules for the game. Include an aim, equipment, procedure, results and conclusion.

• Reading: Choose a culture students are interested in and investigate, using nonfiction books or the internet, games that this culture play. Focus on games of chance. Write about at least one game you find interesting.

Information and Communication Technology • Using a computer investigate other games of chance from various cultures. Use a search engine to help you or go to <http://www.wfu.edu/~mccoy/mgames.pdf>

Health and Physical Education • Card game: Place four card symbols in each corner of a playing field or hall—heart, spade, club and diamond. The aim of the game is to be the last one left in the game. Ask students to run to a corner/symbol of their choice. The teacher then draws the top card from a deck of cards and holds it up. All those students standing in that corner/symbol are out and have to sit down. Students then choose the same or a different symbol. The game continues until there is only one person who is left; they are the winner.

The Arts • Spinning hexagon: Make a spinner using a hexagon shape and a tooth pick. Decorate each section of the hexagon with colours and/or numbers. Then carefully push the tooth pick through the centre of the hexagon. Create a game of chance using your spinning hexagon.

54

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

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

Year 6—Sub-strand: Chance – 1

RESOURCE SHEET Probability games and situations Copy and distribute.

Game or situation

Chance word

Fraction

Decimal

Percentage

Someone in the class will win $100 today We will use the classroom computers today A dice lands on 6 on the first roll I will get all my schoolwork completed today A coin will land on tails on the first toss I will have dessert tonight

CONTENT DESCRIPTION: Describe probabilities using fractions, decimals and percentages (ACMSP144)

My teacher will smile today Someone famous will visit the school today I will win a sport/board/ computer game this week I will be able to choose what we have for dinner tonight I will play with my friends at lunchtime today I will go home from school by car today I will go waterskiing this weekend I will visit my grandparents this weekend One of my classmates will appear in a music video this year Australian Curriculum Mathematics resource book: Statistics and Probability (Years 5 & 6)

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

55

Year 6—Sub-strand: Chance – 1

RESOURCE SHEET Lu-lu game Copy and distribute.

Origin: The game ‘Lu-Lu’ originated in Hawaii. The word Lu-lu means ‘to shake’.

The early Hawaiians played the game using discs of volcanic stone approximately 2.5 cm in diameter. They used these discs as stone dice called ‘Lu-lu’.

Equipment needed: To play Lu-lu you need four playing discs or pieces which are marked on one side only—the first piece has one dot, the second has two dots, the third has three dots and the fourth has four dots. Only the dots on the pieces that land face up are counted. The discs/pieces can be made from similar sized stones, wood, shells, clay, buttons or plastic discs.

•

Each player takes it in turn to shake all four playing pieces and toss them onto the ground or playing area. Each player has two tosses per turn.

•

If all four playing pieces land face up then the player scores ten points.

•

If all four playing pieces do not fall face up, the player only scores and counts the dots they can see. They then toss only the facedown stones on their second toss.

The dots that show on the second toss are added to the first score.

•

The player with the highest score after one turn wins. Players may wish to continue until someone reaches a chosen number, such as the first to 50 or 100.

Questions for discussion (probabilities): •

What are all the possible outcomes a player could score after one toss?

•

What possible outcomes could you have from only two or three discs/pieces being tossed?

•

What is the most amount of points you could score after two tosses?

•

What is the least amount of points you could score after two tosses?

•

What is the least number of tosses you would have to make to score 100?

•

What is the probability of all the discs/ pieces landing face up on the first toss?

•

What is the probability of each score?

56

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

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

CONTENT DESCRIPTION: Describe probabilities using fractions, decimals and percentages (ACMSP144)

Game rules:

Assessment 1

Year 6—Sub-strand: Chance – 1

NAME:

DATE:

1. Suggest a chance word, fraction, decimal and percentage to match these games or situations.

Game or situation

Chance word

Fraction

Decimal

Percentage

(a) I will have a sandwich for lunch today. (b) I will toss a coin and it will land on heads. (c) My family will win 1 million dollars this week. (d) I will complete my work at school today. (e) The principal will visit my classroom today.

CONTENT DESCRIPTION: Describe probabilities using fractions, decimals and percentages (ACMSP144)

(f) I will watch TV after school today.

2. Suggest something that you have 100% chance of doing today: 3. Suggest something that you have 5 ⁄10 chance of doing today: 4. Suggest something that you have 0.1 chance of doing today: 5. If you were to toss a coin 10 times, suggest your chances of getting the following: (You can describe your chances using words, fractions, decimals or percentages.) (a) 5 heads and 5 tails: (b) 2 heads and 8 tails: (c) 4 heads and 6 tails: (d) 3 tails and 7 heads: (e) 1 tail and 9 heads: (f)

10 heads:

6. Try the coin experiment above; what results did you get?

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

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

57

Assessment 2

NAME:

Year 6—Sub-strand: Chance – 1

DATE:

1. Using a deck of cards, predict what may happen if you were to draw out 20 cards. (Hint: Which suit may come out the most/least?)

2. Carry out the experiment above (make sure you shuffle the cards first) and record your results on the table below using ticks or tally marks.

Clubs Spades Hearts Diamonds

3. Looking at your results answer the following questions: (a) What did you find?

(c) Would the results be the same or different if you were to repeat the experiment?

(d) What decimal, percentage and fraction do you have of drawing out a heart from a full deck of cards?

(e) What decimal, fraction and percentage do you have of drawing out a black card from a full deck of cards?

4. Name and describe a game of chance you have learnt about that comes from another culture.

Name: Materials: Description: 5. Name a game that you play that involves chance.

58

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

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

CONTENT DESCRIPTION: Describe probabilities using fractions, decimals and percentages (ACMSP144)

(b) Were your predictions correct?

Checklist

Year 6—Sub-strand: Chance – 1

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

Carries out simple chance games and experiments

Uses fractions, decimals and percentages to describe chance outcomes

STUDENT NAME

Predicts possible outcomes from situations or games of chance

Describe probabilities using fractions, decimals and percentages (ACMSP144)

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

59

Year 6—Sub-strand: Chance – 2

Conduct chance experiments with both small and large numbers of trials using appropriate digital technologies (ACMSP145)

TEACHER INFORMATION

RELATED TERMS Chance (Probability)

What this means

• The likelihood of an event occurring.

• Students will be given the opportunity to repeatedly conduct chance experiments so that they may predict outcomes from larger trials. For example, if they were to roll a dice 10 times to see the results, predict what the results may be like if they were to roll a dice 100 or 1000 times. Students will start to realise that many of these games of chance can have outcomes and probability they can predict. Students will experience a variety of chance experiments and games including those they can set up and play themselves, those they can create and even those that can be played electronically.

Trial

• A process of investigation or experimentation to achieve a result.

Teaching points • Encourage students to discuss and predict the possible outcome of simple chance experiments.

• Allow students to be involved in a variety of simple chance experiments and games and then comment on their predictions and outcomes.

• Predict what may happen if these chance experiments were conducted on a larger scale.

• Expose students to some electronic chance experiments/games.

What to look for • Students who have difficulty predicting possible outcomes for a larger chance experiment trail.

• Students who have difficulty following instructions.

Student vocabulary chance/probability

Proficiency strand(s): Understanding

likelihood

Fluency

outcome

Problem solving

trial

Reasoning

experiment investigate

60

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

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

Year 6—Sub-strand: Chance – 2

HANDS–ON ACTIVITIES Dice roll combinations • If you were to roll a dice 10 times, what are your chances of rolling a 6? What if you were to roll a dice 20 times; does this increase the chances of rolling a 6? Ask students to try out this experiment.

• Predict what the chances are of rolling a 6 if you were to roll the dice 100 times. Students may guess how many 6s they think they may roll out of 100 rolls then trial this experiment.

• If you had two dice, what possible number combinations could you get? Make a list. For example: 1 + 1 = 2, 1 + 2 = 3, 1 + 3 = 4, 1 + 4 = 5, 1 + 5 = 6, 1 + 6 = 7 and so on.

• Predict and carry out the following experiment: How many rolls of two dice does it take you to reach the total of 100?

Compare answers between students; what was the least number of rolls? What was the most number of rolls?

Heads and tails (pg 63) • Ask students to predict the possible outcomes of a coin tossed 10 times. Then carry out the experiment recording outcomes on the table provided.

• Ask students to then predict the possible outcome if they were to toss a coin 100 times or 1000 times. Carry out this experiment.

• What possible combinations would you get if you were to toss two coins? Try it out and make a list. For example: H and H, T and T, H and T, T and H. • What possible combination would you get if you were to toss three coins?

Raffle tickets • Ask students what fraction of a chance would they have if they purchased 1 raffle ticket out of 100 tickets sold? What if they bought 10 tickets or 50 tickets? Would this increase their chances?

• Ask students to devise their own raffle. Imagine a raffle ticket cost $1.00; what prizes might they have if they had 100 tickets to sell?

• If every student in your class had one ticket in a raffle, what chance would a student have of winning?

Games of chance (pgs 64 and 65) • Allow students to play a variety of chance games such as Snakes and ladders, Uno™, Operation™, Trouble™ or any other board games available. Play in small groups then report back to the whole class what their chances of winning were.

Was there more chance or skill involved in winning? Operation™ is a game that if you touch the sides while removing a body organ it buzzes—is this a game of chance or skill?

• Ask students to devise their own board game of chance. Include the title, rules and aim of the game and any equipment needed, such as playing pieces. They may wish to use the template provided. Also use the spinner template provided in place of a dice.

Jelly bean jars (pg 66) • Look at the different jelly bean jars and guess how many jelly beans there may be in each one. Which is the easiest to guess? Which is the hardest?

• Create your own jelly bean jar experiment using a jar and jelly beans, buttons, counters or whatever you have available in the classroom. Ask classmates to guess how many are in the jar. How can a student increase their chances of winning or guessing correctly?

Electronic games of chance • Ask students to investigate and report back to the class electronic games of chance they have played, such as those available on a computer, on a iPod™, on an Xbox™ or PlayStation™ etc. Discuss in each case what is involved, what chance there is of winning etc. Allow students to play some of these chance games if you have access to them.

• Discuss chance and the topic of gambling. How are casino owners so wealthy? Is gambling a good way to win money?

What are the chances of winning and losing?

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

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

61

Year 6—Sub-strand: Chance – 2

LINKS TO OTHER CURRICULUM AREAS Information and Communication Technology • Investigate games of chance using a computer and the internet. What games come up when you search ‘games of chance’? If your school has access to ‘Study ladder’, there are some probability games and exercises you could try. Or go to <www.ixl.com>, click Year 6 and scroll down to locate ‘Probability’. Explore some of the suggested probability activities.

The Arts • Spinner (see Games of chance pg 65): Create your own spinner that shows the order of your favourite colours. Use the template provided or create your own. Divide your spinner in as many sections as there are colours that you like. The largest section should be your favourite colour; the next largest section should be your next favourite colour and so on.

Health and Physical Education • Ask students to suggest some fair ways that two teams could be chosen for a team sport. Test some of these ideas out.

For example, drawing names out of a hat, giving students numbers then splitting them into odd and even numbers for the two teams. Deicide the fairest method then carry out the selection. Choose a team game to play as a class such as T-ball, football, basketball, rounders etc.

62

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

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

Year 6—Sub-strand: Chance – 2

RESOURCE SHEET Heads and tails Copy and distribute.

H or T (out of 10)

CONTENT DESCRIPTION: Conduct chance experiments with both small and large numbers of trials using appropriate digital technologies (ACMSP145)

1

2

3

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6

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10

H or T (out of 100)

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

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

63

Year 6—Sub-strand: Chance – 2

RESOURCE SHEET Games of chance/game board part 1

CONTENT DESCRIPTION: Conduct chance experiments with both small and large numbers of trials using appropriate digital technologies (ACMSP145)

Copy onto card and distribute.

64

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

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

Year 6—Sub-strand: Chance – 2

RESOURCE SHEET Games of chance/game board part 2 Copy onto card and distribute.

CONTENT DESCRIPTION: Conduct chance experiments with both small and large numbers of trials using appropriate digital technologies (ACMSP145)

Equipment needed: split pin and scissors

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

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

65

Year 6—Sub-strand: Chance – 2

RESOURCE SHEET Jelly bean jars

CONTENT DESCRIPTION: Conduct chance experiments with both small and large numbers of trials using appropriate digital technologies (ACMSP145)

Copy and distribute.

66

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

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

Assessment 1

Year 6—Sub-strand: Chance – 2

NAME:

DATE:

1. Use fractions or percentages to predict the chance of rolling a number 6 on a dice: (a) 1 out of 6

(b) 2 out of 6

(c) 3 out of 6

(d) 10 out of 60

(e) 100 out of 600

(f)

1000 out of 6000

2. Roll a dice six times and see how many times you get a 6: 3. Repeat the experiment 5 times. What happened?

CONTENT DESCRIPTION: Conduct chance experiments with both small and large numbers of trials using appropriate digital technologies (ACMSP145)

A

B

blue

C

green

yellow

D

red

4. Look at the spinner above and answer the following questions: (a) On which spinner do you have an equal chance of landing on red? (b) On which spinner do you have the greatest chance of landing on blue? (c) On which spinner do you have the least chance of landing on yellow? (d) On which spinner do you have the greatest chance of landing on red? (e)

On which spinner do you have the greatest chance of landing on green?

(f)

Which spinner would be the fairest to use in a game?

(g) On which spinner do you have the least chance of landing on blue? (h) On which spinner do you have no chance of landing on green?

5. Explain why spinner A would be the fairest to use in a game.

6. When you are playing a game of chance like Snakes and ladders, do you have an equal chance of winning or is their skill involved?

7. Name a game of chance you enjoy playing.

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

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

67

Assessment 2

Year 6—Sub-strand: Chance – 2

NAME:

DATE:

Jackie – 5 tickets Marcus – 1 ticket Harry – 10 tickets Mia – 20 tickets Trang – 1 ticket

Ben – 1 ticket Dylan – 1 ticket Milka – 2 tickets Jake – 2 tickets Liam – 5 tickets

Lucas – 10 tickets Faith – 4 tickets Evan – 1 ticket Melinda – 5 tickets Jess – 10 tickets

Lilia – 5 tickets Taylah – 2 tickets Kayla – 10 tickets James – 5 tickets

(a)

Were all 100 tickets sold?

(b)

Who has the greatest chance of winning the raffle?

(c)

Which students have the least chance of winning?

(d)

Which students have a 10% chance of winning?

(e)

What fraction out of 100 would Liam have of winning?

(f)

Which students would have 2/100 or 1/50 chance of winning?

(g)

What chance does Faith have of winning?

(h)

Isla was absent and didn’t get to buy a ticket; what chance does she have of winning?

2. What would happen if students were only allowed to purchase 1 ticket in the Easter raffle?

3. Answer true or false to these statements: (a)

The more tickets you purchase the greater chance you have of winning.

(b)

If you only purchase one ticket in a raffle you cannot win.

(c)

Mia has an equal chance of winning compared to Jake and Taylah.

(d)

If you were to buy all 100 tickets you will win.

(e)

If you don’t buy a raffle ticket you can still win.

(f)

If there were 1000 tickets and you bought 10%, you would have 100 tickets.

4. Devise a chance experiment using counters, raffle tickets, a dice or coins and explain the rules on the back of this sheet. (Hint: It may help to draw it.)

5. Name a game of chance you can play electronically.

68

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

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

CONTENT DESCRIPTION: Conduct chance experiments with both small and large numbers of trials using appropriate digital technologies (ACMSP145)

1. At a school Easter raffle 100 tickets were sold. Look at the tickets that were purchased and answer the following questions:

Checklist

Year 6—Sub-strand: Chance – 2

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

Uses digital technologies to play games of chance

Conducts chance experiments and comments on predictions

STUDENT NAME

Predicts possible outcomes from small and large chance experiments

Conduct chance experiments with both small and large numbers of trials using appropriate digital technologies (ACMSP145)

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

69

Year 6—Sub-strand: Chance – 3

Compare observed frequencies across experiments with expected frequencies (ACMSP146)

TEACHER INFORMATION

RELATED TERMS Chance (Probability)

What this means

• The likelihood of an event occurring.

• Students will be involved in observing and conducting a variety of chance experiments that have certain expected results. Students will come to realise that if a trial is repeated over and over again that they will be able to predict the results. Occasionally they will experience some surprising results; however, these will depend on the experiment. Trials such as coin tosses, dice games and student’s pulse rate will provide the basis for these expected frequencies. They will have the opportunity to record some of these frequencies onto a table and graph so that they can see common results.

Experiment

• A test or trial to examine a prediction.

Frequencies

• The number of times an event occurs.

Teaching points • Encourage students to discuss and predict the possible outcome of a repeated chance experiment.

• Have students observe and record the frequencies occurring from simple chance experiments such as coin or dice tosses.

• Allow students to be involved in a variety of chance experiments and comment on their expected frequencies and outcomes.

What to look for • Students who have difficulty predicting expected frequencies from simple chance experiments.

• Students who have difficulty recording and plotting experiment results.

Student vocabulary chance/probability experiment outcome trial

Proficiency strand(s): Understanding Fluency Problem solving Reasoning

investigate frequencies

70

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

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

Year 6—Sub-strand: Chance – 3

HANDS–ON ACTIVITIES Coin toss experiment (pg 73) • Play a game of coin toss – last man standing. To start the game all students stand up and choose a coin side by placing their hands on their heads for heads and their hands on their behinds for tails. Toss a coin and those who choose the correct coin side stay standing; those who didn’t sit down. Continue the game until only one person is left standing.

After the game discuss if this is a game of skill or chance? The person who won—what did they do? Did they choose the same side each time or change if there had been too many frequencies of the same side in a row? Repeat the game and ask students to change their strategy. Did this help?

• Ask students to predict how many heads and how many tails you would get if you were to toss a coin 10 times. (They should use their knowledge of the coin game and frequency to make their prediction.) Is it correct to assume that out of 10 at least 40% will be heads?

• Ask students to predict using percentages or fractions what might happen if you were to toss a coin 100 times.

• Carry out the experiment (100 coin tosses) in front of the class and ask students to record the results on the resource sheet provided. Stop every now and again after there are more than two of the same side tossed in a row and ask students to predict the next toss.

• If you were to toss two coins, what would be the possible outcomes? (H and H, T and T, H and T, and T and H.) What percentage or fraction would you have of getting each outcome? For example you would have 25% or 1⁄4 chance of getting H and H. You would have 50% chance or 1⁄2 of getting H and T or T and H. Ask students to test out these outcomes by tossing two coins 10 times.

• Transfer this information onto a frequency graph (see resource sheet).

4-sided dice (pg 74) • Ask students to make their own 4-sided dice using the template. Colour each side a different colour; for example red, green, blue and yellow. What is this shape called? (triangular pyramid) • Predict what might happen if you were to roll this triangular dice 10 times. Ask students to carry out the experiment and record the colours.

• Repeat the same experiment 4 more times. Is there a pattern? Can you predict the next roll?

• Ask students to look at their results and predict what would be the frequency of each number occurring out of 10. Out of 50? Out of 100?

Card game • Play a card game in groups of 4 where you have to discard all of your suits (similar to Uno™). The player to get rid of all his/her 7 cards is the winner.

• Discuss what chance out of 4 you have of winning. Do all four players have an equal chance or does it depend on the cards you are dealt?

• If you were to play 10 rounds of this game what chance would you then have of winning?

Coloured beads in a bag • If you were to place 20 each of five different coloured beads into a bag that you cannot see through, what chance do you have of drawing out each of the colours?

• Ask students to draw out 20 beads from the bag and record their results. Is it what they expected? Predict what the next 20 colours might be.

• What would happen if there were 60 red beads, 20 blue, 10 yellow and 5 green—what would you expect may happen if you were to draw out 20 beads from the bag? Make your prediction and guess the frequency of red beads then carry out the experiment recording the results on a table such as the example provided below.

• Can there be surprising results?

1

2

3

4

5

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9

10

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12

13

14

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16

17

18

19

20

Colour R, B, Y, G

Can-labelling machine • Imagine there is a factory that labels cans of sliced fruit. It has been discovered that 2% or 2⁄100 of the cans are labelled incorrectly. What would this mean if 100 cans were labelled; how many would be incorrect? Ask students to work out the frequency of incorrectly labelled cans out of 200, 300, 400, 500, 600, 700, 800, 900, 1000 and even 10 000 cans.

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

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

71

Year 6—Sub-strand: Chance – 3

HANDS–ON ACTIVITIES (CONTINUED) Dice frequency (pg 75) • If you were to roll two dice, what possible totals could you get?

• Ask students to roll two dice 20 times and record their totals in the chart provided. Then transfer these frequencies into the column graph.

• Which totals did students find came up most frequently? Less frequently?

Pulse rate (pg 76) • Show students how to locate their pulse on their wrist or neck (show graphic example).

• Ask students to record their pulse over 20 seconds then multiply this amount by 3, which would give them the total in one minute. Alternatively they can count their pulse rate over 1 minute, over 30 seconds and double it or over 10 seconds and multiply by 6. Try different ways but remember the average pulse rate.

• Record every student’s pulse rate on a frequency graph using a computer or draw a column or line graph by hand. Ask students to look at which pulse rates were the most common. Any surprising results?

• Investigate what things can effect pulse rates using the internet.

LINKS TO OTHER CURRICULUM AREAS English • If you were to play a game of hangman where one student has to guess a word by guessing letters, which are the most popular letters that are suggested? Ask students to predict the most popular or common letters to be chosen during hangman. Then, working in pairs, play a game of hangman recording letters that are suggested during play.

• As a class, ask students to raise their hand as to which letters were chosen and record these on a simple alphabet table like the one below. What letters were the most popular, least popular or never chosen? Why are some letters more commonly chosen than others? What about the vowels?

a

b

c

d

e

f

g

h

i

j

k

l

m n

o p q

r

s

t

u

v w x

y

z

Information and Communication Technology • Use the internet to investigate pulse rates of elite athletes, people of different ages and those who may be unfit or overweight (also see below in Health and Physical Education/Science).

• Play a probability game online: see <www.kidmathgamesonline.com> ‘Probability’ and <www.nrich.maths.org> and select ‘primary activities’.

Health and Physical Education/Science • Ask students to record their pulse rate over one minute at rest and after 10 minutes of exercise such as skipping. Look at the frequency of pulse rates across the class; which rates are most common at rest and after exercise?

• Investigate what pulse rates can be at complete rest, such as while we are asleep. Students may use the internet or a nonfiction book to further investigate pulse rates at rest and after exercise then compare them to their own. What would be the resting pulse rate of an athlete? Or someone overweight? Do pulse rates differ between males and females? Does age affect pulse rates?

72

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

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

Year 6—Sub-strand: Chance – 3

RESOURCE SHEET Coin toss experiment Copy and distribute.

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100

Two coin toss 10 9 8 7 Frequency

CONTENT DESCRIPTION: Compare observed frequencies across experiments with expected frequencies (ACMSP146)

Key: H = Heads T = Tails

6 5 4 3 2 1 0 Heads, heads

Tails, tails

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

Heads, tails or Tails, heads R.I.C. Publications® www.ricpublications.com.au

73

Year 6—Sub-strand: Chance – 3

RESOURCE SHEET 4-sided dice

CONTENT DESCRIPTION: Compare observed frequencies across experiments with expected frequencies (ACMSP146)

Copy and distribute.

74

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

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

Year 6—Sub-strand: Chance – 3

RESOURCE SHEET Dice frequency Copy and distribute.

1

2

3

4

5

6

7

8

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19

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Totals chart 2

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17 16 15 14 13 12 Frequency

CONTENT DESCRIPTION: Compare observed frequencies across experiments with expected frequencies (ACMSP146)

18

11 10 9 8 7 6 5 4 3 2 1 0 4

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6

7

8

9

10

11

12

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

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

75

Year 6—Sub-strand: Chance – 3

RESOURCE SHEET Pulse rate Copy and distribute.

Check and record the rate, strength and rhythm. Use a watch or clock with a second hand. Make a note of the rate of the pulse, which is the number of beats per minute.

Check the strength of the pulse to see if it is strong or weak and if the rhythm is regular or irregular.

Your pulse is X (beats in 15 seconds) x 4 = Y (your pulse). You can also count the beats for 30 seconds and multiply by 2.

For children under age 18, a normal heart rate is 70–100 beats per minute.

For adults, a normal heart rate is 60–100 beats per minute.

(Taken from the website <www.wikihow.com/Check–Your–Pulse>) 76

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

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

CONTENT DESCRIPTION: Compare observed frequencies across experiments with expected frequencies (ACMSP146)

Use your fingers when finding a pulse. Don’t use your thumb when finding it, as it has its own pulse.

Assessment 1

Year 6—Sub-strand: Chance – 3

NAME:

DATE:

1. What possible outcomes do you think you would get if you were to toss one coin 20 times? Make your predictions using a range of percentages: (a) Tails: between

and

%

(b) Heads: between

and

%

2. Carry out the experiment tossing a coin 20 times and record your results below.

Key: H = Heads T = Tails 1

2

3

4

5

6

7

8

9

10 11 12 13 14 15 16 17 18 19 20

3. What percentage or frequency occurred? Heads:

%

Tails:

%

4. Predict what four possible outcomes you could get if you were to toss two coins.

CONTENT DESCRIPTION: Compare observed frequencies across experiments with expected frequencies (ACMSP146)

5. Toss two coins 20 times and record the frequencies below: 1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

6. Use percentages and fractions to record your outcome: (a) Heads and heads: (b) Tails and tails:

/20 or /20 or

% %

(c) Heads and tails or tails and heads:

/20 or

%

7. Do you think these percentages would change much if you were to toss two coins 100 times? (Try it out, if you have time.)

Yes No Explain why.

8. Name another chance experiment where the frequency/percentage would remain the same no matter how many times you were to carry out the experiment.

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

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

77

Assessment 2

Year 6—Sub-strand: Chance – 3

NAME:

DATE:

1. If you were to roll one dice 20 times the number you would get the most would be a 1.

Do you agree or disagree with this statement?

2. Test out the statement above by carrying out the experiment of rolling a dice 20 times and recording the results below.

1

2

3

4

5

6

7

8

9

10 11 12 13 14 15 16 17 18 19 20

3. (a) What was the most common number? (b) Would this be the case again if you were to repeat the experiment? Yes No Why? 4. If you were to roll two dice the most frequent total to occur would be 6.

5. Test out this statement by rolling two dice 20 times and use the table and tally marks to record the totals. Transfer this onto the frequency graph.

Agree Disagree

9 8

2

3

4

5

6

Frequency

7

1

6 5 4 3

7

8

9

2 1

10

11

12

0 2

3

4

5

6

7

8

9 10 11 12

Totals

6. (a) Was 6 the most common total?

Yes

No

Yes

No

If no, which number was the most common total? (b) Is this what you expected? (c) If you were to repeat the two-dice experiment again, do you think the results would be the same or different?

Why?

78

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

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

CONTENT DESCRIPTION: Compare observed frequencies across experiments with expected frequencies (ACMSP146)

10

Checklist

Year 6—Sub-strand: Chance – 3

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

Carries out chance experiments to prove or disprove expected frequencies

Observes frequencies occurring from chance experiments

STUDENT NAME

Predicts possible outcomes from a chance experiment

Compare observed frequencies across experiments with expected frequencies (ACMSP146)

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

79

Year 6—Sub-strand: Data representation and interpretation—DR&I – 1

Interpret and compare a range of data displays, including side-by-side column graphs for two categorical variables (ACMSP147)

TEACHER INFORMATION

RELATED TERMS Data

What this means

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

• Students will be exposed to a variety of data displays to identify and interpret including tables, column graphs, picture graphs, dot plots, line graphs and pie charts. They will also realise the benefit in presenting two categories of information side-by-side in column graphs in order to compare and comment on the information.

They will be asked to plan and prepare information is the best suited display according to the gathered data and so that the information will be the easiest for others to interpret. Students will explore a variety of ways to present data and will also be given the opportunity to compare their displays with their fellow students.

They will be encouraged to not only interpret the various displays but also comment on their effectiveness and usefulness according to the information gathered.

Side-by-side column graph

• Two column graphs displayed side by side so that information can be compared.

Dot plot

• A set of data represented by using dots over a number line.

Picture graph

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

Teaching points • Expose students to a variety of student and computer generated displays to comment on and interpret.

Line graph

• Allow students to explore and present gathered data in a variety of ways.

• A graph formed by line segments and connecting points to represent certain data.

• Introduce students to the concept of side-by-side displays such as column graphs in order for them to compare two categories of information.

Pie chart

• Encourage students to create data displays using a computer.

• A chart in which the sectors of a circle are used to show a whole in terms of its parts, with each sector often representing a category.

• Ask students to comment on the suitability of data displays according to the data.

What to look for • Students who have difficulty interpreting a variety of graphs, particularly side-by-side graphs.

Variable

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

Student vocabulary interpret data side-by-side column graph line graph

• Students who find constructing graphs and displays by hand difficult.

• Students who have difficulty using a computer to create a variety of data displays.

Proficiency strand(s): Understanding Fluency Problem solving Reasoning

dot plot pie chart variables

80

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

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

Year 6—Sub-strand: Data representation and interpretation—DR&I – 1

HANDS–ON ACTIVITIES Naming and identifying graphs (pg 83) • Show students a variety of different types of graphs including those provided on the resource page and graphs from newspapers, magazines, books and the internet. Ask them to identify and name each type, then have them interpret what information each graph is showing.

• In each of the graphs ask students to comment whether it is the most effective way to display the gathered information.

• Ask students to locate three different types of graphs or displays from newspapers, magazines or the internet. Cut or print them out and paste them into their book. Name each graph type, then write at least two statements explaining what the graph is showing.

• Present one of the graphs to the class and explain what information it is giving us.

Pie charts • Discuss when and why pie charts are most commonly used. Brainstorm and list all the information students can think of that could be displayed in a pie chart.

• Brainstorm and list student’s favourite leisure time activities. Ask students to survey their classmates about what their favourite leisure activity is and create a table similar to the one below to record their responses.

Play sport Watch TV Play Xbox™, PlayStation™ or Wii™ Play with friends Ride bike Reading Other: • Give students the opportunity to then present this information in a pie chart or using the charts tool in a program on a computer.

• Allow students time to compare and interpret their pie charts with fellow students.

Line graph (pg 84) • Discuss how line graphs are easy to construct; therefore, sometimes they are commonly used but not always appropriately used. Line graphs should be mainly used to show data that can change over time. For example, line graphs are good at showing weather changes over time, height development, weight over time, sales figures over time etc.

• Look at the example of a line graph (page 84) and interpret what it is showing.

• Ask students to construct their own line graph that shows their estimated height growth from the age of 1 to current age (11–12 years). It may help to measure their current height and work back from there. Tell students that the average 1 year old’s height is between 70–80 cm.

Picture graph (pg 85) • Look at the picture graph provided (page 85) and discuss what is showing. Why does it have a key and what does each symbol represent?

• Ask students to construct a picture graph showing what items they have in their pencil cases; for example, pencils, markers, pens, eraser, sharpeners and scissors. Use a key that shows one symbol represents two or three items.

• Allow students to compare their picture graphs with fellow classmates and comment whether or not their graph is easy to read and interpret.

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

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

81

Year 6—Sub-strand: Data representation and interpretation—DR&I – 1

HANDS–ON ACTIVITIES (CONTINUED) Side-by-side column graphs (pg 86) • Side-to-side column graphs are useful when presenting two pieces of categorical data so that they can be compared.

For example, side-by-side graphs can be used to compare height, weight and age; the weather in different states of a country; livestock at two farms etc.

• Look at the side-by-side graph provided (page 86) and discuss what it is showing. Is this an effective way of showing this information?

• Survey students about how they travel to and from school each day and display this information. Nominate a couple of students to survey another class as to how they travel to and from school each day. Using both sets of information, ask students to construct a side-by-side column graph. Allow students to interpret and compare the information.

Computer generated graphs/charts • Run through the process of producing computer generated graphs/charts with the students.

• Allow students the opportunity to experiment and create a variety of graphs and charts using the computer.

• Ask students to print out one of their graphs and swap with classmates so they can interpret and comment on the information and effectiveness of the graph.

LINKS TO OTHER CURRICULUM AREAS Information and Communication Technology • Investigate and interpret a variety of graphs found on the internet, in newspapers, magazines etc. Print or cut them out and paste them into students books and ask them to write 1–2 statements about the information they are displaying.

• Investigate a variety of data displays on <www.mathsisfun.com> Go to ‘Data’ and select the sub-heading ‘Data index’.

Look at and interpret the many different data displays including bar graphs, pie charts, line graphs, scatter plots, pictographs, histograms, frequency distribution, stem and leaf plots, cumulative tables, and graphs and relative frequency.

• Interpret a variety of graphs — go to <www.ixl.com>, select Year 6 skills, scroll down to ‘Data and graphs’ and try interpreting the following; 0.1: Interpret pictograph, 0.4: Interpret line plot, 0.7: Interpret bar graphs, 0.9: Interpret double bar graphs, 0.13: Interpret line graphs, 0.15: Interpret double line graphs.

• Try creating your own graphs using <www.mathsisfun.com> Go to ‘Data’ and find the section titled ‘Graphs index’. Try creating at least two different types of graphs. Print them out and see if they are easy to read and interpret.

Health and Physical Education • Investigate the height, weight and age of a willing sample group of 5 to 10 students. (The information can be collected anonymously if students prefer.)

• Present the information in side-by-side bar graphs. Is this the best way to present the information?

• Ask students to record their pulse rate at rest and after exercise. Use a double line graph to record this information. (For example, a blue line would reflect the resting pulse rate and the red line would be the pulse rate after exercise.)

82

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

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

Year 6—Sub-strand: Data representation and interpretation—DR&I – 1

RESOURCE SHEET Naming and identifying graphs Copy and distribute.

9 8

2nd Quarter

3rd Quarter

4th Quarter

Number of students

1st Quarter

7 6 Boys Girls

5 4 3 2 1 Maths

English

Sport Subjects

The Arts

Social Studies

Book sales 2013 80 Number of books sold

CONTENT DESCRIPTION: Interpret and compare a range of data displays, including side-by-side column graphs for two categorical variables (ACMSP147)

0

70 60 50 40

Fiction

30

Non fiction

20 10 0 January

April

July Sale period

October

Class pets

dog

cat

fish

bird

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

rabbit

guinea pig

horse

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

83

Year 6—Sub-strand: Data representation and interpretation—DR&I – 1

RESOURCE SHEET Line graph Copy and distribute.

Melbourne’s average temperature

35

Temperature °C

30 25 20 15 10 Winter Spring

5

Summer 0

Autumn 2010

2011

2012

2013

Year

84

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

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

CONTENT DESCRIPTION: Interpret and compare a range of data displays, including side-by-side column graphs for two categorical variables (ACMSP147)

40

Year 6—Sub-strand: Data representation and interpretation—DR&I – 1

RESOURCE SHEET Picture graph Copy and distribute.

CONTENT DESCRIPTION: Interpret and compare a range of data displays, including side-by-side column graphs for two categorical variables (ACMSP147)

McDonald’s Farm

Key 1 graphic = 4 animals

cow

sheep

goat

chicken

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

horse

dog

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

85

Year 6—Sub-strand: Data representation and interpretation—DR&I – 1

RESOURCE SHEET Side-by-side column graphs

Student

140

145

150

155

160

165

170

k Lu

e

k Ja

e

Co

e nn

Height

r

S

ge er

Height

Weight in kgs Height in cm

86

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

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

CONTENT DESCRIPTION: Interpret and compare a range of data displays, including side-by-side column graphs for two categorical variables (ACMSP147)

Student

0

10

20

30

40

50

60

70

k Lu

e

Ja

ke

Weight

nn Co

er

Se

e rg

Weight

Copy and distribute.

Assessment 1

Year 6—Sub-strand: Data representation and interpretation—DR&I – 1

NAME:

DATE:

Favourite sport shoes Favourite sport shoes

0

Sport shoes

4

con y®

Asics®

Sau

6

5

Asi cs®

Adidas®

Ad ida s®

8

10

e®

Nike®

10

Favourite sport shoes 15

N ik

12

Number of students

Number of students

14

Saucony®

0

CONTENT DESCRIPTION: Interpret and compare a range of data displays, including side-by-side column graphs for two categorical variables (ACMSP147)

Nike®

Adidas® Asics®

Saucony®

Sport shoe brands

1. Look at the three graphs above and answer the following questions: (a) Name the three types of graphs: (b) What information are the graphs giving us?

(c) Which sports shoe brand is the most popular? (d) Which sports shoes brand is the least popular? (e) How many students choose Adidas®? (f)

Which graph/s do you think shows the data best?

Why?

2. Using these four sports shoe brands, survey at least 10 of your classmates to find out their favourite sports shoe brand. Record their responses below.

Nike® Adidas® Asics® Saucony®

3. Now present this gathered data in a graph you think best displays this information. You may draw your graph by hand or use a computer to create it.

4. Make a statement about your results.

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

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

87

Assessment 2

Year 6—Sub-strand: Data representation and interpretation—DR&I – 1

NAME:

DATE: A group of Year 6 students recorded their height on the table below.

Kelly

1.32 m

Amy

1.31 m

Tracey

1.28 m

Rachael

1.49 m

Luke

1.53 m

Seth

1.41 m

Michael

1.45 m

Sarah

1.36 m

Marco

1.49 m

Trent

1.58 m

Lily

1.52 m

Joey

1.50 m

Frank

1.46 m

Sasha

1.39 m

Maria

1.44 m

Fabio

1.47 m

Siena

1.29 m

Kyle

1.60 m

Caleb

1.39 m

Scarlet

1.42 m

1. Present this information in the boys and girls side-by-side column graph outline below.

GIRLS

6

6

5

5

4

4

3

3

2

2

1

1

0

0 1.21 to 1.3 m

1.31 to 1.4 m

1.41 to 1.5 m

1.51 to 1.6 m

1.21 to 1.3 m

1.31 to 1.4 m

1.41 to 1.5 m

1.51 to 1.6 m

2. Look at the information and answer the following questions: (a)

Which height category was the most common for the boys?

(b)

Which height category was the most common for the girls?

(c)

Which height category was the least common for the boys?

(d)

Which height category was the least common for the girls?

(e)

How many girls are taller than 150 cm?

(f)

Which was the most common category overall?

3. Does this type of graph suit this data the best?

Yes

No

Why?

4. Name another type of graph you could have used to display this data.

5. Transfer the data from the table onto a graph of your choice using the computer.

Print it out and attach it to this sheet.

88

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

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

CONTENT DESCRIPTION: Interpret and compare a range of data displays, including side-by-side column graphs for two categorical variables (ACMSP147)

BOYS

Checklist

Year 6—Sub-strand: Data representation and interpretation—DR&I – 1

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

Constructs graphs using the computer

Interprets and constructs side-by-side graphs to compare data

STUDENT NAME

Names, interprets and compares a variety of data displays

Interpret and compare a range of data displays, including side-by-side column graphs for two categorical variables (ACMSP147)

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

89

Year 6—Sub-strand: Data representation and interpretation—DR&I – 2

Interpret secondary data presented in digital media and elsewhere (ACMSP148)

TEACHER INFORMATION

RELATED TERMS Primary data

What this means

• Data that has been collected by the person conducting and presenting the survey results.

• Students will be able to look at data displays and survey samples presented in the media and be given the opportunity to look at and comment on their worth and value. Some of the data that is presented is from a secondary source; students should be able to question if this information is enough to validate certain studies and samples. For example, if a media survey claims that children in Australia eat too much junk food judging from a census taken out of 200 children, then is this study enough to be able to make this comment? Whereas the Australian Bureau of Statistics conducts a population census every 5 years, which is very costly but more likely to show correct information that a smaller sample taken of the population. This outcome will lead students to examine both primary and secondary data sources. It will allow students to interpret and question the information gathered in the various data displays and decide whether or not enough information has been gathered to form a conclusion.

Secondary data

• Data that has been collected by an outside company or researcher which is then used by a second person.

Digital media

• Computer-generated information that is presented via the media (newspapers television, radio).

Sample/census

• The collection of data from a small group rather than the whole population.

Teaching points • Expose students to a variety of data displays and surveys in the media, using the internet, newspapers, magazines, television and radio. Define the difference between primary and secondary data.

• Allow students to comment on the data collected; how well has it been presented? Is the information from a primary or secondary source? How many were in the sample group?

• Ask students to locate their own digital media display using a suggested topic and the internet, print it out and comment on the effectiveness of the display.

• Encourage students to find examples of poorly presented surveys/ data displays and comment on their information.

• Allow students the opportunity to survey the whole school about a topic and comment on the differences age groups have on the information gathered.

What to look for • Students who have difficulty interpreting data displayed in the media.

• Students who have difficulty understanding the difference between primary and secondary data.

Student vocabulary interpret primary data secondary data digital media

Proficiency strand(s): Understanding Fluency Problem solving Reasoning

sample census

90

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

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

Year 6—Sub-strand: Data representation and interpretation—DR&I – 2

HANDS–ON ACTIVITIES Data in the media (pg 93) • Discuss how there are a wide variety of data displays and surveys available in the media. Some are from primary data and some from secondary data sources. Define the difference between the two types: – Primary data: Data that has been collected by the person conducting and presenting the results.

– Secondary data: Data that has been collected by an outside company or researcher which is then used by a second person.

• Look at some of the examples showing population growth in Australia (taken from the internet) and ask students to interpret and comment on the content and if the information is easy to read.

• Show students examples of data displays in the media; locate some on the internet. For example, the Australian Bureau of Statistics has a list of surveyed topics including housing, health, travel, population etc. Students can also look at weather statistics. Look for samples in newspapers and magazines too.

Interpreting a data display • Ask students to locate a survey or data display in the media, print or cut it out and paste it into their books. Write at least 3 statements about the information provided.

• Ask students to comment on whether or not the display was presented well and if students feel enough people were surveyed for the study.

• Allow students the opportunity to sit with a classmate and compare data displays.

Primary data (pg 94) • Locate a survey or data display in the media (newspaper, internet, magazine) that has been created using primary data.

Identify what the source is (who was surveyed) and how well the information has been presented.

• A group of Year 6 students were asked should they be allowed to wear casual clothes instead of a uniform. Look at the results on the resource sheet provided, discuss how they were displayed and comment on how well the information was presented. How many students were surveyed?

• Ask students to carry out their own investigation as to whether or not Year 6 students should be able to wear casual clothes instead of the school uniform and present the results in a display which students think best show the gathered information. Allow students to compare their data displays with other class members.

Secondary data (pg 95) • Look at an example of secondary data presented in the media claiming that the average amount of time 11–12 year olds spend playing video games each day is 2 hours. Comment on the graph and how it is presented. Ask students to comment on how many students were surveyed and whether or not that is enough to draw conclusions.

• Ask students to survey their own classmates as to the amount of time they spend each day playing video games.

Explain to students that this survey would be a sample if a presenter was commenting on all 11–12 year olds in the suburb they live in.

• Present the gathered data to the class and compare students data with the original data display provided.

Census or sample • If you wanted to find out how much time students spend travelling to and from school each day at your school, how would you go about it? Make a list of steps you would need to take. Do you survey the whole school or survey a sample group from each age/year level?

• Carry out the survey (whole school or sample) and present the information in a suitable table or graph.

• Allow students the opportunity to present their study to the class.

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

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

91

Year 6—Sub-strand: Data representation and interpretation—DR&I – 2

LINKS TO OTHER CURRICULUM AREAS English • Informative writing: Choose a data display from a media source (computer/internet, newspaper, magazine) and write an informative piece that would go with the data display; that is, comment on the information within the display as though you were a newspaper reporter.

• Gather these informative pieces and put them together to create a class newspaper.

Information and Communication Technology • Use the internet to locate a variety of data displays and comment on the information they are giving us. Search for the Australian Bureau of Statistics and look at the studies and surveys they are involved in. Look at how they present their gathered data.

• Look at the weather statistics in the newspaper and on the internet. How are weather statistics presented?

• Go to <www.mathsisfun.com> and investigate the data section. What sort of data displays are there and what information are they giving us? Is the information from primary of secondary data?

Health and Physical Education/Science • There is a great deal of information in the media about healthy eating and exercise for adults and children. Investigate data displays in newspapers, magazines and the internet about healthy exercise and eating habits in Australia—how accurate and trustworthy are these results/surveys?

• Look at the Australian Bureau of Statistics about this area of health and exercise—what information are they giving us?

Is this more accurate than magazines?

• Survey your classmates or a sample group from your school covering all ages and ask students ‘How much exercise/ physical activity they have done in a week?’ Use a table to record your results such as the one shown below.

Sample groups

Under 1 hour

1–2 hours

2–3 hours

3–4 hours

4–5 hours

More than 5 hours

Junior school (5–7 year olds) Middle school (8–10 year olds) Senior school (10–12 year olds) The Arts • Media: Make a list of all the graphs, tables and surveys that can be represented in the media.

• Create a poster showing a variety of data displays used in the media. Label each type of display. Comment on each representation. Notice how some are better presented than others. What makes a good data display?

• Watch the news show for children, ‘Behind the news’. Did they comment on any surveys or use any graphs to represent information? Was the source primary or secondary data?

92

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

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

Year 6—Sub-strand: Data representation and interpretation—DR&I – 2

RESOURCE SHEET Data in the media Copy and distribute.

Source: Australian Bureau of Statistics Australian Demographic Statistics (cat. no. 3101.0)

AUSTRALIAN

million 23

ESTIMATED RESIDENT POPULATION

21 20 19 18

Number of people

22

17 16 Jun 1992

Dec 1994

Jun 1997

Dec 1999

Jun 2002

Dec 2004

Jun 2007

AUSTRALIAN ANNUAL GROWTH RATE

Jun 2009

% 2.5 2.0 1.5 1.0

0 Dec 1989

Jun 1992

Dec 1994

Jun 1997

Dec 1999

Jun 2002

Dec 2004

Jun 2007

Jun 2009

2003 2013

* Australian states population growth 2003 – 2013 8

Population (millions)

CONTENT DESCRIPTION: Interpret secondary data presented in digital media and elsewhere (ACMSP148)

0.5

Number of people

Dec 1989

7 6 5 4 3 2 1 0

NSW

Vic.

Qld

SA

WA

TAS

NT

ACT

States and territories * Information is approximate only.

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

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

93

Year 6—Sub-strand: Data representation and interpretation—DR&I – 2

RESOURCE SHEET Primary data Copy and distribute.

Should Year 6 students be allowed to wear casual clothes to school every day?

Yes

No

No

Yes

94

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

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

CONTENT DESCRIPTION: Interpret secondary data presented in digital media and elsewhere (ACMSP148)

Casual clothes

Year 6—Sub-strand: Data representation and interpretation—DR&I – 2

RESOURCE SHEET Secondary data Copy and distribute.

DAILY NEWS News scoop—Pre-teens are spending too much time playing video games …

This reporter has discovered that instead of playing outside, the average 11–12 year old is inside playing video games for up to 2 hours each day! Is this what is contributing to obesity in Australian children? The sample below, taken from a survey conducted by the local university, shows some alarming results; at least one quarter of their leisure time is devoted to playing video games!

Leisure activities

video games

playing sport

outside activity

Time spent on video games

16 7-8yrs

14 Number of students

CONTENT DESCRIPTION: Interpret secondary data presented in digital media and elsewhere (ACMSP148)

watching TV

12 10

9-10yrs

8 6 11-12yrs 4 2 0

0 hours

1 hour 2 hours Time

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

3 hours

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

95

Assessment 1

Year 6—Sub-strand: Data representation and interpretation—DR&I – 2

NAME:

DATE:

1. Look at the information about asthma and answer the following questions: (a)

What sort of graph is this?

(b)

What is the title of this graph?

Asthma by age and sex, 2004–05 % 20

15

10

(d)

Which age group recorded the highest percentage of asthma?

Which age group recorded the lowest percentage of asthma?

5

0

0–4

5–9 Age group

10–14 Males Females

Source ABS, National Health Survey, 2004–05

(e)

Did males or females record a higher percentage of asthma in each group?

(f)

What is the source of this information?

2. Answer true or false to these statements about the graph. (a)

Higher rates of asthma were reported in children over 5 years rather than under 5.

(b)

Over 15% of females between 5–9 years have asthma.

(c)

More males than females have asthma.

3. Where do you think this information was reported?

4. If this information was a result of a national survey, would it be considered primary or secondary information?

5. If a newspaper was to comment on one part of this survey, would that comment be considered primary or secondary information?

6. Name at least three places where you can locate data displays in the media.

96

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

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

CONTENT DESCRIPTION: Interpret secondary data presented in digital media and elsewhere (ACMSP148)

(c)

Assessment 2

Year 6—Sub-strand: Data representation and interpretation—DR&I – 2

NAME:

DATE:

1. ‘The amount of time students travel to and from school is, on average, more than half an hour each day.’ (a)

Looking at the graph below, is the statement true or false?

(b)

One quarter of those surveyed took 0–10 mins to travel to and from school.

(c)

Does this graph tell you the source of the information?

(d)

Which travelling time showed the largest area?

(e)

Is this a well-presented survey?

True

False

Yes

No

Why/why not?

2. If you wanted to carry out a sample survey of how long students take to travel to and from your school, would it be best to survey your class or the whole school?

Travelling to and from school

0–10 mins

10–20 mins

CONTENT DESCRIPTION: Interpret secondary data presented in digital media and elsewhere (ACMSP148)

20–30 mins

30 mins +

3. Survey a sample across your school of about 20 students per Year level and ask them how long it takes them to travel to and from school each day. Use the table below to record the responses. Write a statement about your results.

0–10 mins

10–20 mins

20–30 mins

30 mins +

Lower school Middle school Upper school

4. Write a statement about your results.

5. Locate a data display in the media (internet, newspaper, magazine), print or cut it out and paste it on the back of this page. Write at least two statements about the information it is giving us. Comment on whether or not the information is easy to interpret and a good sample.

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

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

97

Checklist

Year 6—Sub-strand: Data representation and interpretation—DR&I – 2

98

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

Recognises and interprets secondary data

Recognises and interprets primary data

STUDENT NAME

Locates and interprets data displays in the media

Interpret secondary data presented in digital media and elsewhere (ACMSP148)

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

Year 5 Answers

Year 5

CHANCE – 1 Page 9

Assessment 1

1. (a) 2⁄10 or 1⁄5 2. Less 3. (a) 2 (d) 1 4.

(b) 5⁄10 or 1⁄2

(c) 3⁄10

(b) 1 (e) 2

(c) 3 (f ) 1⁄3

2. (a) Most: sport/active, Least: social (b) Answers will vary. Teacher check (c) categorical (d) open 3.–4. Answers will vary. Teacher check Page 30

Assessment 3

1. Answers will vary. Teacher check 2. (a) O (b) C (c) C (e) O (f ) O (g) C 3.–5. Answers will vary. Teacher check

(d) O (h) C

DR&I – 2 Page 39 Page 10

Assessment 2

1. Answers may vary (rules include: scissors beats paper, paper beats rock and rock beats scissors).

2. Answers will vary. Teacher check 3. Answers will vary. Teacher check 4.–5. Teacher check 6. Answers will vary. Teacher check

CHANCE – 2 Page 19

Assessment 1

Page 20

DR&I – 3 Page 49

(d) 4⁄10 or 2⁄5

DR&I – 1 Page 28

Assessment 1

1. (a) numerical (b) categorical 2. (a) C & N (b) N (c) C (d) N (e) C (f ) C (g) C & N (h) C 3. Answers may vary e.g. ‘What snack do you have for recess today?’

4. Teacher check 5. Categorical 6. Answers will vary. Teacher check Page 29

Assessment 2

1.–4. Answers will vary. Teacher check

Assessment 2

1. Answers will vary. Teacher check 2. (a) 1⁄10 (b) 2⁄10 or 1⁄5 (c) 3⁄10 3.–4. Answers will vary. Teacher check

1. (a) Bar/column graph (b) The number of boys and girls in each year level. (c) Answers will vary. Teacher check (d) Year 3/4 (e) Year 5/6 (f ) Year 1/2 2. Answers will vary. Teacher check 3. (a) Dot graph/plot (b) 1 (c) 3 (d) 6 or more Page 40

1.–2. Answers will vary. Teacher check 3. (a) 3⁄10 (b) 1⁄10 (c) 6⁄10 or 3⁄5 4. Equal coloured balls in the bag.

Assessment 1

Assessment 2

1. Sport/Active: Ben, Sasha, Alex, Jake, Mike, Yang, George, Jess, Sienna, Marc Social: Lily, Helena, Faith, Kate Media: Nic, Gina, Riley, Kyle, Lachlan, Indy

Assessment 1

1. (a) Line (b) Melbourne weather 12–19 April (c) Melbourne’s daily and nightly temperature in degrees Celsius over 1 week in April (d) the daytime temperature (e) the night-time temperature (f ) Answers will vary. Teacher check 2. (a) texts (b) data (c) February (d) February (e) bar/column graph (f ) Yes Page 50

Assessment 2

1. (a) Picture graph (b) How Year 5 students travel to school (c) 8 (d) skateboard (e) car 2. Teacher check 3. (a) bar/column (b) basketball (c) hockey (d) netball (e) yes (f ) answer will vary 4. Teacher check

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

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

99

Year 6 Answers Page 78

CHANCE – 1 Page 57

Assessment 1

1.–6. Answers will vary. Teacher check Page 58

Assessment 2

1.–2. Answers will vary. Teacher check 3. (a)–(b) Answers will vary. Teacher check (c) different (d) 0.25, 25%, 1⁄4 (e) 0.5, 1⁄2, 50% 4.–5. Answers will vary. Teacher check

CHANCE – 2 Page 67

Assessment 2

(b) 2⁄6 or 33% 1. (a) 1⁄6 or 17% (c) 3⁄6 or 1⁄2 or 50% (d) 10⁄60 or 1⁄6 or 17% 100 1 (e) ⁄600 or ⁄6 or 17% (f ) 1000⁄6000 or 1⁄6 or 17% 2.–3. Answers will vary. Teacher check 4. (a) A (b) B and D (c) C (d) C (e) B (f ) A (g) C (h) D 5. The coloured sections are equal in size.

6. equal chance of winning 7. Answers will vary. Teacher check Page 68

Assessment 2

1. (a) Yes (b) Mia (c) Marcus, Trang, Ben, Dylan and Evan (d) Harry, Lucas, Jess and Kayla (e) 5⁄100 or 1⁄20 (f ) Milka, Jake and Taylah (g) 4⁄100 or 1⁄25 (h) 0% or 0/100 2. Everyone would have an equal chance of winning.

3. (a) true (b) false (c) false (d) true (e) false (f ) true 4.–5. Answers will vary. Teacher check

CHANCE – 3 Page 77

Assessment 1

Assessment 2

1. Disagree 2. Teacher check 3.–6. Answers will vary. Teacher check

DR&I – 1 Page 87

Assessment 1

1. (a) Column/bar, pie and line (b) The favourite sport shoes chosen by a group of students. (c) Asics® (d) Saucony® (e) 8 (f ) Answers will vary. Teacher check 2.–4. Answers will vary. Teacher check Page 88

Assessment 2

1. Teacher check 2. (a) 1.41 – 1.5 m (b) 1.31 – 1.4 m (c) 1.21 – 1.3 m (d) 1.51 – 1.6 m (e) 1 (f ) 1.41 – 1.5 m 3.–4. Answers will vary. Teacher check 5. Teacher check

DR&I – 2 Page 96

Assessment 1

1. (a) bar/column graph (b) Asthma by age and sex, 2004–05 (c) 10–14 years (d) 0–4 years (e) males (f ) ABS, National Health Survey 2004–05 2. (a) true (b) false (c) true 3. Answers may include: on the internet, in the media (TV or newspapers), brochures or magazines for health practitioners etc.

4. Primary 5. Secondary 6. Internet, newspapers, magazines, brochures etc.

Page 97

1.–3. Answers will vary. Teacher check 4. Heads and heads, tails and tails, heads and tails, tails and heads 5.–6. Answers will vary. Teacher check 7. No, because there are only 3 options; therefore, the percentages are unlikely to change much no matter how many times you toss the coins.

8. Answers will vary. Teacher check

100

Year 6

Assessment 2

1. (a) (b) (c) (d) (e)

false true no 10–20 mins No, it does not tell you the source or the number of students that were surveyed.

2. whole school 3.–5. Answers will vary. Teacher check

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

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