Maths - CHANCE & PROBABILITY Unit Plan Year 5/6

UNIVERSITY OF SOUTH AUSTRALIA

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Name: Brooke Matilda Parsons

Student ID 1 0 0 0 6 0 9 6 4

Email: parbm004

Course code and title: EDUC 3051 Mathematics Curriculum for Early years and Primary Years 2

School: Education Program Code: MBED

Course Coordinator: Anna Rogers Tutor:

Day, Time, Location of Tutorial/Practical: Workshop: Tues 11am, Maureen Hegarty. Seminar: Wednesday 4pm, Julie Grant

Assignment number: 1 Due date: 14/4/09

Assignment topic as stated in Course Information Booklet: Planning for two weeks of teaching maths

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Brooke Parsons Mathematics Curriculum for Early & Primary Years - 1 –100060964 Assignment 1

http://www.unisa.edu.au/ltu/students/study/integrity.asp

This unit of work has been designed to teach to a year five and six class. The students in the

class have a variety of Maths abilities and differing levels of knowledge about chance and data.

The year six students completed a chance and data unit when they were in year five, however it

was not as extensive as this unit because they were in a year four and five class. Children at this

school live in a middle to upper class area and therefore most of them fall into that socio-

economic status. Only three students in the class have a non-English speaking background.

One of these students receives extra School Services Officer (SSO) time because they still have

some difficulties with the English language, to date their Maths skills have not been greatly

affected by this and therefore no differing tasks have been required for this student during

Maths.

Please note that for the purposes of this assignment and to represent where the tasks fit into the

Maths/Science learning cycle (Rogers, 2002) some tasks appear to be broken up, however in

the classroom I would expect to complete the lesson/s through the learning cycle before moving

onto a new concept. For example, I would expect to complete the Heads or Tails game, tabling,

graphing and discussing results and subsequently, I would not move onto playing and collecting

data for the dice rolling game before graphing and discussing the results of the Heads or Tails

game.

It is necessary to acknowledge that the lessons detailed in this unit plan have been adapted

from a variety of resources including texts, books and websites.


Unit Plan…Chance, Data & ProbabilityLearning Area:

Maths

Year Level:

5/6 (Primary & Middle Years)

Strands:

Exploring, analysing & modelling data

Proposed Duration:

600 minutes (15 x 40 min lessons)

Key Ideas:

Year 5 - Students refine their understanding of chance and randomness by using data from their daily

activities to describe possible outcomes and their likelihood. They analyse trends and relationships and make

predictions about possibilities in the future.

Year 6 - Students engage with data to understand, analyse and apply notions of chance and probability in the

social and natural worlds.

Additional Key Ideas:

Year 5 - Students generate and analyse data from a diverse range of sources (including online) and

perspectives to investigate situations drawn from their personal lives and the world around them. They use

this data to explore patterns and relationships, and to inform their choices and actions.

Year 6 - Students engage with data by formulating and answering questions, and collecting, organising and

representing data in order to investigate and understand the world around them.

Standard Outcomes:

3.3 - Analyses data to search for patterns in events where the range of outcomes is generated by situations

where chance plays a role.

3.1 - Poses questions, determines a sample, collects and records data including related data, represents

sample data in order to investigate the world around them.

Essential Learnings:

Identity – a sense of personal and group identity

Thinking – a sense of creativity, wisdom and enterprise

Interdependence – a sense of being connected with others and

their world

Futures – a sense of optimism about their ability to shape their

futures

Communication – a sense of the power and potential of literacy,

numeracy and ICT

Key Competencies:

KC1 – using information

KC2 – communicating ideas

KC3 – planning & organising

KC4 – working in teams

KC5 – using maths

KC6 – solving problems

KC7 - using technology


Tasks for Enquiry:

Finding out about the Learner

Lesson 1

(Adapted from Bobis, Mulligan & Lowrie 2009)

Brainstorm words that could be used to describe

chance (examples: likely, unlikely, certain, possible,

impossible, probable, maybe)

Have students working in pairs; ask them to choose

four words that are brainstormed and plot them on a

“chance” line (with certain at one end and never at

the other). Discuss entering fractions and whole

numbers on the line

Determine students prior knowledge of the Maths

term probability

Lesson 2

(Adapted from Bobis, Mulligan & Lowrie 2009)

Play Heads or Tails as a class.

Students put hands on head if think a head will be

face up after the coin is tossed. Students will put

hands on bottom if think a tail will be face up after the

coin is tossed

Discuss why students chose to put their hands on

their heads/bottoms.

Explain that the possible outcomes (head or tail) are

called the sample space

Introduce students to the term random, where all

possible outcomes have an equal chance of

occurring

Lesson continued in ‘Explore’ phase

Lesson 10 & 11

(Adapted from Same or Different, Maths 300 2001)

Have a pair of students assist you demonstrate this

game.

Key Questions:

What words are used to describe when there is a

chance of something happening?

What do you know about probability?

Can you give me an example?

Do you know how to represent it?

If I flip a coin what are the possible outcomes?

Why did you put your hands on your head/bottom?

Did anyone keep their hands on their head/bottom for

every toss? Why?

Does anyone know what the probability is of getting a

head or a tail?

What is the sample space of this game?

Does the player who needs to choose the same

colour blocks have a fair chance of winning?


Have 2 red blocks and 1 yellow block in a bag.

Students chose one block at a time. Student who

chooses two blocks the same colour wins a point and

students who chooses two blocks that are different

colours wins a point

Lesson continued in ‘Explore’ phase

Explore

Lesson 2 cont’d

Have students collect data of when they

see/hear/read of information relating to

chance/likelihood

Share their findings and discuss as a class

Lesson 3 & 4

Students play Heads or Tails as a class again.

Record how many times a head is face up and how

many times a tail is face up. Ensure you flip the coin

a large number of times

Lesson continued in ‘Getting the Idea’ phase

Lesson 5 & 6

(Adapted from Fenichel 2001; Bobis, Mulligan &

Lowrie 2009)

Introduce students to chance and probability with

dice. Ask the students the probability of rolling a 5

and the probability of rolling an even number.

Discuss as a class.

Have the students work in pairs to roll and record

when they roll a 5 and when they roll an even

number. Ensure they keep track of how many rolls

Why? Why not?

Are the outcomes for this random?

What do you think it means when;

-the weather forecaster says there is a 50%

chance it will rain tomorrow?

-the newspaper says it’s very likely that the Crows

will beat Port Adelaide?

-mum says it’s highly unlikely that you will be allowed

to go to Sarah’s for a play?

-on your “chance” line, where would that word go?

Use other examples relevant to what the students

found?

Why did you put your hands on your head/bottom?

Did anyone keep their hands on their head/bottom for

every toss? Why?

Does anyone know what the probability is of getting a

head or a tail?

What is the probability of rolling a 5?

What is the probability of rolling an even number?

Why is that?

Why isn’t it the same as rolling a 5?

Are the outcomes of rolling a dice random?


they make. Ask the pairs to roll the dice 15 times

only.


Lesson 7

(Adapted from Bobis, Mulligan & Lowrie 2009; Reys

et al. 2007)

Introduce two 6-sided dice

Discuss students thoughts on which number will

come up most often if the numbers on the dice are

added together

Have students work in pairs and roll their two dice 15

times.

Ask the students to record their results


Lesson 10 & 11 cont’d

Have the students work in pairs to play and record

their findings of Same or Different

Lesson continued in ‘Getting the idea’ phase

Lesson 12 & 13

(Adapted from Cheng n.d.)

Students work in pairs with a pack of cards.

Have the students flip a card from the top of the

pack, starting a new pile.

For the purposes of this game have the students

predict they will turn over a king and have them

record their chance of doing so, along with the

outcome

Demonstrate to the whole class and then work in

pairs.

(Students may want to record the cards they have

flipped over or look back on those cards in the pile)


What number do you think will come up most often

when the two numbers are added together? Why?

What number do you think will come up least often?

Why?

What is the chance of pulling out the same coloured

blocks?

What is the chance of pulling out different coloured

blocks?

What is the chance that you flip over a king?

Why is it 1 in 13, when there are 52 cards?

Now that you have flipped this card what is the

chance now that you will flip over a king? Is it 1 in

12? Why? Why not? Would it be 4 in 51?

Why does keeping that card out of the pack make a

difference to the chance of flipping another card?

Do you think the outcomes of flipping cards are

random? Why? Why not?


Getting the Idea


Use the data collected from playing Heads or Tails,

table and graph the classes results.

Firstly table the first 10 flips.

Discuss how many of these 10 flips were heads and

how many were tails?

Table all of the flips

Discuss how many of the flips were heads and how

many were tails?

Explain the law of large numbers


Use the data collected from rolling the dice, table and

graph the results of each pair.

Discuss how many times each pair rolled a 5 and

how many times each pair rolled an even number.

Collate all of the pairs data and table and graph the

results of the class.

Discuss how many times the class rolled a 5 and

how many times they rolled an even number.

Introduce the students to the term independent event

How many of these were heads?

How many were tails?

If the chance of flipping a head/tail is 50% why don’t

our results show this?

Do the results represent that there is a 50% chance

of flipping a head or a tail when we look at all of the

flips?

If I flipped a coin and a tail was face up, when I

flipped the coin a second time will I flip a tail or a

head?

Why? Why not?

Why would the chance still be 50%?

Why wouldn’t the chance be 50%?

What is the probability of rolling any number on the

dice?

What about an odd number?

Why do you think that the results of the whole class

closely represent that there is a 1 in 6 chance of

rolling a 5? Or a 1 in 2 (or 50%) chance of rolling an

even number?

If the chance of rolling a 5 is 1 in 6. If I rolled the dice

and rolled a 5, what would be the chance that if I

rolled the dice again that it would be a 5?

Why? Why not?

Why would the chance still be 1 in 6?


Lesson 7 cont’d

Using the data collected from rolling the two dice,

table and graph the results of each pair

Discuss which number came up the most

Before tabling the classes results ask the students to

write down all of the possible sums and what

numbers on the dice could make that sum

Have the students predict what total number was

rolled the most by the class

Table and graph the classes results

Discuss how many times 7 was the total of the dice

rolled

Discuss how many times 2 & 12 were rolled

Lesson continued in ‘Practicing the Idea’ phase


Use the data collected from the students working in

pairs and discuss each pairs results.

Collate the class’s data and discuss.

Introduce students to the term conditional probability

Add a second yellow block into the bag and have the

students play again.

Ensure they record how many times the same or

different blocks were pulled from the bag.

Discuss some of the pairs results.

Collate the class’s results and discuss.

Why wouldn’t the chance be 1 in 6?

What number came up the most in your pair? Why

do you think that is?

What number came up the least? Why?

How many sums make …?

Do you think that there is an equal chance of rolling

one number against another number? Why? Why

not?

What number came up the most in the classes

results? Why do you think that is?

What number/s came up the least? Why?

How many times did the person who had to pull out

the same blocks win?

What about the person who had to pull out different

blocks?

How does pulling out a red block effect the chance of

who wins?

How does pulling out a yellow block effect the

chance of who wins?

Why do the class’s results show such a difference

between the same and different? Does anyone

remember what that is called? (Law of large

numbers)

Do you think the person that has to pull out the same

coloured blocks might win more times now?

Why? Why not?

Will there be a random outcome now that there are

the same number of each coloured block? Why?

Why not?



Use the data collected from the students flipping their

cards and share with the class

Lesson continued in ‘Practicing the Idea’ phase

Practicing the Idea

Lesson 7 cont’d

(Swan 1997)

Play The Great Car Race 1 (Appendix 1)

Lesson 8 & 9

(Original lesson idea)

Have students work in pairs or small groups to play a

variety of games that have independent events

Examples:

Twister

Snakes & Ladders (with a 10-sided dice or two 6-

sided dice)

Trouble

Beetle (Maths 300 2002)

Cut & Predict (Swan 1998; Cheng n.d.)

Using the game of choice have the students record

what their chance of flipping/rolling/spinning is?

Allow students to record a variety of different

combinations

Have the students play the game, recording the

If I pulled a red block out, what is left in the bag?

What coloured block is my opponent more likely to

draw from the bag? Why?

If that happens, what is the chance that I will pull out

a yellow or red block? What percentage is that?

What was your chance of flipping over a king once

you had flipped over two kings? One king? Three

kings? Four kings?

Why was your chance of flipping over a king different

to Robbie’s?

If you had flipped over three kings in 29 cards, what

would your chance be of flipping over a king?

Who do you think will win?

Is this a fair race? Why? Why not?

What is the chance of spinning a blue left foot?

What about a different combination?

What is the chance of rolling a 3 on the dice? What is

the chance of rolling a double number? What is the


number of flips, rolls, spins and their outcomes

Have each pair/group table and graph their results.

Lesson cont’d in ‘Applying the Idea’ phase


Have the students play the same game but this time

allow them to choose and predict which suit they will

flip over

Ensure students record as they go

Share their outcomes with the class

Discuss

Lesson 14 & 15

(Original lesson idea)

Have the students work in pairs or small groups to

play one of these games that have conditional

probability events.

Examples:

Fish

Snap

Uno

Using the game of choice have the students record

what their chance of flipping number/suit/colour is?

Allow students to record a variety of different

combinations

Have the students play the game, recording their

prediction, the number of flips and their outcomes

Have each pair/group record their results in a

manner so others can read the outcome/s.

chance of flipping over a king?

What is the chance of flipping over any card that is a

heart?

What is the chance of ….?

What is your sample space?

Is this random? Why? Why not?

What is the chance you will flip a card of the same

suit (heart, club, spade, diamond)?

Why is it 13 in 52? Could we represent this another

way?

What is the chance you will flip a different card?

What is the chance you will flip two 3’s over in a row?

Or two cards of the same suit?

At the beginning of the game what is the chance of

flipping over a yellow card? After 6 cards were

flipped over, what was your chance then?

After flipping over 20 cards, and one king, what

would your chance of flipping over a king be on the

next flip?


Lesson cont’d in ‘Applying the Idea’ phase

Applying the Idea


Share outcomes of playing games with class.

Describe why and how that happens


Share outcomes of playing games with class.

Describe why and how that happens

What was the chance/probability of

rolling/flipping/spinning a …?

What is the sample space of your game?

If you had three dice/ two ten sided dice, what would

the probability be then?

Did your game rely on independent events or

conditional probability?

If you had two packs of cards, what would the

probability be then?

Was the chance of flipping a particular card over

random? Why? Why not?

Maths Language: (Bobis, Mulligan & Lowrie 2009; Reys et al. 2007)

Likely

Possibly

Probably

Probability

Maybe

Unlikely

Certainly

Impossibly

Chance

Sample space

Random

Law of large numbers

Independent event

Conditional probability

Learning Outcomes:

Students are able to determine the chance of something happening when it is an independent event

Students are able to determine the chance of something happening when conditional probability plays a role

Students can describe when something is more likely/probable to occur and when it isn’t

Students are able to represent the chance or probability of something happening using fractions, decimals

and percentages

Students use Maths language

Students are able to explain to others why something does or doesn’t occur


Equipment/Resources:

Packs of cards

Dice – 6 sided and 10 sided

Coins

Twister

Trouble

Snakes & Ladders

Uno

Formative Assessment

Spinning the Wheel worksheet (Appendix 2)

Probability Problem Solving worksheet (Appendix

3)

Class Observation checklist

(Appendix 4)

Summative Assessment

Pair/group presentation about games played for both

independent events and events where conditional

probability plays a role.

Independent Events assessment rubric (Appendix 5)

Conditional Probability Events assessment rubric

(Appendix 6)


The students will be assessed throughout the unit of work as well as at the end of the unit of

work. A number of formative assessments should occur throughout the unit of work, these can

be found in appendices one, two and three. Two of these assessments are worksheets the

students can complete either individually or with another student. The intention of these

assessments is to share the student’s answers with the class. Appendix two would be used early

in the unit, whereas appendix three would be used later in the unit after the concept of

conditional probability is introduced to the students. Appendix four is a checklist to be used by

the teacher, the teacher can begin to use this checklist from the beginning of the unit of work. All

students should be able to complete the tasks listed on this checklist by the end of the unit of

work.

The final summative assessment tasks that the students need to complete are for their

independent events games and their games where conditional probability plays a role, the

rubrics for these assessments can be found in appendices five and six. The teacher must

complete these rubrics and assess whether the students demonstrated the skills in an excellent

manner, good, satisfactory or poor manner.

The appendices do not include a large number of worksheets because I would expect the

students to find their own ways of recording, tabling and graphing their results, and hence I

would not provide them with templates to do so.

There are no cross curricula links within this unit of work, however use of books that discuss the

chance or probability of something occurring (not within a Maths context) could be used

throughout the unit.

Learning about chance and probability in the classroom assists students to understand why

certain events occur. Chance and probability play a role in a number of everyday games as well

as games at side shows and the like, providing students with the opportunity to play these

games allows them to see for themselves just how the outcome can be, or is affected.


References

Beetle Game Plan 2002, Maths 300, viewed 5 April 2009,

<http://www1.curriculum.edu.au/maths300/m300bits/121pbeet.htm>.

Bobis, J, Mulligan, J & Lowrie, T 2009, Mathematics for children: Challenging children to think

mathematically, 3rd edn, Pearson Education Australia, Frenchs Forest, NSW.

Cheng, C n.d., Curriculum design for mathematics lesson – probability, TeAch-nology.com,

viewed 29 March 2009, <http://search.teach-nology.com/units/probability.pdf>.

Fenichel, M 2001, Understanding probability, Discovery Education, viewed 29 March 2009,

<http://school.discoveryeducation.com/lessonplans/programs/probability/>.

Reys, RE, Lindquist, MM, Lambdin, DV & Smith, NL 2007, Helping children learn mathematics,

8th edn, John Wiley & Sons, Inc., NJ.

Rogers, A 2002, Suggested mathematics learning sequence/cycle, University of South Australia,

viewed on 12 March 2009,

<http://www.unisanet.unisa.edu.au/learn/EDS/?PATH=/Resources/100679/

Online+study+resources/&default=Noticeboard.htm>.

Same or Different Plan 2001, Maths 300, viewed 5 April 2009,

<http://www1.curriculum.edu.au/maths300/m300bits/153psame.htm>.

Swan, P 1997, Dice dilemmas: Activities to promote mental computation and develop thinking

about chance processes, A-Z type, Woodvale, WA.

Swan, P 1998, Card capers: Developing mathematics from playing cards, A-Z type, Woodvale,

WA.


http://www1.curriculum.edu.au/maths300/m300bits/153psame.htm

http://www.unisanet.unisa.edu.au/learn/EDS/?PATH=/Resources/100679/Online+study+resources/&default=Noticeboard.htm

http://www.unisanet.unisa.edu.au/learn/EDS/?PATH=/Resources/100679/Online+study+resources/&default=Noticeboard.htm

http://school.discoveryeducation.com/lessonplans/programs/probability/

http://search.teach-nology.com/units/probability.pdf

http://www1.curriculum.edu.au/maths300/m300bits/121pbeet.htm

Appendix 1

Reproduced from Swan 1997, p. 37


Appendix 2

Reproduced from Fenichel 2001, p. 8


Appendix 3

Probability Problem Solving

Complete this worksheet alone or with a partner, but be sure to complete your own sheet. Each answer must be written as a fraction, decimal and a percentage.

1. Your sock drawer is a mess. There are 12 black socks and 6 red socks mixed together. What are the chances that, without looking, you choose a red sock from your drawer?

What are the chances you choose a black sock?

If you have chosen a black sock out of your drawer and kept it out, what are the chances that you will not wear an odd pair of socks today to school?

2. You are rolling a 6 sided dice, what are the chances of rolling a 6?

3. You are rolling the same dice, what are the chances of rolling an even number?

4. If you roll two dice, what is the chance of rolling a double number?

5. You randomly choose a card from a deck of cards, what is the chance you will select a jack?

6. Using the same deck of cards, if you have already selected a jack of clubs and kept that card in your hand, what are the chances that you select another jack?

Or another card that is a club?

7. You are visiting a kennel that has three German Shepherds, four Labradors, six Chihuahuas, five poodles and four Western Highland terriers. When you arrive the dogs are taking a walk, what is the probability of seeing a German Shepherd first?

What about a Western Highland terrier?

8. Two out of three students in Miss Parsons class prefer to bring their lunch, rather than buying it. If twenty students prefer bringing their lunch, how many students are in Miss Parsons class?

Adapted from Fenichel 2001, p.7


Appendix 4

Class ObservationChance, Data & Probability

Em

ma

Cla

udia

Pet

er

Rob

ert

Bro

oke

Bel

inda

Lean

ne

… … … … … … … … … .. .. .. .. … … … … ..

Is able to describe likelihood of something occurringCan describe the chance of flipping a head or tailCan describe the chance of rolling a number on the diceCan describe the chance of flipping a card in a pack of cardsCan describe an independent event Can record, table and graph data for independent eventsIs able to make predictions about why something may/ may not occur?Can record and make sense of data for conditional probability eventsCan describe a conditional probability eventIs able to represent the chance of something happening in fractions, decimals and percentages

© Parsons 2009


Appendix 5

Independent Events Assessment

Excellent Good Satisfactory Poor

Recorded, tabled and graphed

findings are easy to read and

interpret

Can describe the outcome of their

game

Can describe using Maths language

why certain things occurred

Can explain to the class so the

class understands

Uses examples to ensure the class

understands

Can answer questions from the

class about why things occurred?

© Parsons 2009


Appendix 6

Conditional Probability Events Assessment

Excellent Good Satisfactory Poor

Recorded findings are easy to read

and interpret

Can describe the outcome of their

game

Can describe using Maths language

why certain things occurred

Can explain to the class so the

class understands

Uses examples to ensure the class

understands

Can answer questions from the

class about why things occurred?

© Parsons 2009


Documents

Maths - CHANCE & PROBABILITY Unit Plan Year 5/6