Lesson Plan 19 Flipping Coins - · PDF fileLesson Plan 19 – Flipping Coins | Page 2 2008 | ABC Science Online Materials and equipment These quantities are for 6 separate groups Total

Lesson Plan 19 – Flipping Coins | Page 1

2008 | ABC Science Online

Lesson Plan 19

Flipping Coins

Brief description

Flipping a coin one hundred times might sound mundane but it always produces truly

astonishing results. You‟ll astonish your class by correctly identifying who really flipped a coin

one hundred times at home, and who faked their results. Your perplexed students will be

motivated to do some basic maths and graph their results on the accompanying worksheet to

find out how you did it.

Duration: 60 - 80 minutes

Year level: Upper primary (some maths ability required)

Topics: Probability, scientific method, mathematical average, graphing

Preparation: 5 minutes

Extensions: Write a short story about how a series of fortunate and/or unfortunate

random events can have serious impacts on our attitudes and daily lives

Overview

Whole class Distribute the '100 Coin Flip' homework task and discuss the

activity.

(15 – 20 min)

Homework Students flip a coin. If the result is heads, they flip a coin 100

times and record results. If the result is tails, they imagine

flipping a coin 100 times and record their imaginary results.

Whole Class Check each student‟s results and astonish the class by

correctly identifying whether the results are real or imaginary

(„faked‟).

Explain how you did it (see teacher notes). Return homework

sheets for further coin flips and analysis.

(30 – 40 min)

Small groups Students who 'faked' results pair up with a student who really

flipped coins. Students then complete their worksheets and

graphs individually.

(15 – 20 min)

Whole Class Discuss the activity

Students will be keen to astonish their family and friends with

this activity so it is worth discussing how best to do this.

Your students may be keen to tally the whole class‟s results

to see if the averages approach the predicted frequencies. If

so, use a spreadsheet (on the interactive whiteboard if

available) to calculate the class averages.

(30 – 40 min)



Materials and equipment

These quantities are for 6 separate groups

Total Quantity Description

30 Student Worksheets

30 10 or 20 cent coins

Preparation

Photocopy sufficient quantity of student worksheets for whole class.

This lesson requires the calculation of averages of data sets containing ten results. It is

strongly recommended that you read the student worksheet carefully before deciding whether

you will use this lesson to teach or reinforce a prior lesson on how to calculate averages.

Alternatively, you could calculate the averages of ten results on the whiteboard, or on an

interactive whiteboard for the students to copy onto their worksheets.

Objectives

Science skills

Students will: Follow worksheet instructions to generate a series of one hundred coin

flip results (Activity 1)

Tally up clusters of consecutive heads or tails (Activity 2)

Calculate average frequency of clusters from ten sets of one hundred coin

flips (Activity 3)

Graph the observed average frequency of clusters from ten sets of one

hundred coin flips (Activity 4)

Science concepts

Sufficiently large numbers of independent, random events can contain

surprising clusters

The frequency of clusters in a series with known probabilities can be

calculated using mathematical rules

Positive attitudes

Students will Develop an appreciation for statistics

Recognise the impact of sample size on the reliability of statistics

Work cooperatively with partners/group members when sharing results



Procedure

Day 1

Distribute and discuss Homework Activity (5 – 10 min)

Distribute the worksheet 'Homework Activity 1' and discuss.

Demonstrate how students should flip their coin (toss a coin with your thumb so that it

spins during flight - catch the coin in your palm, place it on top of your other hand to

reveal the result)

To speed up the process, students could ask a parent, guardian or sibling to record the

results on their 'Homework Task' worksheet

Demonstrate how to generate the imaginary results by pretending to flip a coin (mime

the action, placing the pretend coin on top of your other hand to reveal the pretend

result)

Emphasise that 'imaginary' data sets will be as important as the real results

It is worth admitting that you realise flipping a coin one hundred times is a fairly

mundane task. To motivate students to complete the task carefully, tell them that their

combined results will reveal astonishing facts about the science of chance and random

events in the next activity.

Day 2

Collect and discuss worksheets (15–20 min)

Identifying real and imaginary results is incredibly easy. See Teacher Notes (page 5) for samples

of real and imaginary (fake) results. You will be able to tell the difference at a glance.

Collect the Homework Activity worksheets

Examine each student‟s results and announce whether the data is real or imagined and

ask the student if your assessment is correct – repeat this for every student‟s data

Your students will be astonished by the accuracy of your assessments!

Ask if anyone knows how you were able to tell real and imaginary results apart

Ask two students to transcribe a set of imaginary results onto the whiteboard – one

student calls out each result while the other places a tick in the heads or tails column

Ask two other students to transcribe a set of real results onto the whiteboard

Ask students if they can see any clear difference between the two sets of results

Discuss how you were able to identify the real and imaginary results (see Teacher Notes

Page 5)



Procedure (continued)

Distribute and discuss remaining worksheet pages (30 – 45 min)

After distributing the remaining pages of the worksheet, discuss and demonstrate how to

complete each activity. Alternatively, distribute one page of the worksheet at a time but be

prepared for early finishers.

Discuss worksheet 'Activity 2 – Analysis' and demonstrate how to tally up clusters using

the real results transcribed on the whiteboard.

Demonstrate how to calculate the results in the 'Check' column. Be prepared for early

finishers – you may need to discuss the next step individually with these students.

When the majority of the class has finished 'Activity 2 – Analysis', discuss 'Activity 3 –

Combine Results'. Each student will need to share their checked results with nine others.

Demonstrate how to calculate Average Frequencies. You should decide in advance

whether students may use calculators or a spreadsheet for this step. Alternatively, you

could calculate the frequencies for ten sets of results on the interactive whiteboard

using a spreadsheet – students can then transcribe and use these results.

Discuss the graph and demonstrate how to plot the observed results (ie next to

predicted results on the graph).

Class discussion (10 – 15 min)

When all the students have finished plotting their results on the graph, lead a discussion about

the observed outcomes.

Were they surprised how often long series of consecutive heads or tails appeared?

Could these results teach us anything about life in the real world?

Can you think of situations when a series of unrelated or independent random events

might make you feel lucky or unlucky?

This discussion could lead into a creative writing task about the impact of chance events

on our daily lives and attitudes – a short story is provided as an example in the student

worksheet

Your students will be keen to repeat the experiment and astonish their own test group

of people – they can easily do this by asking several family members to perform Activity

1 while they are at school.



Teacher’s notes

Spot the difference!

Spotting the difference between real and imaginary coin toss results is incredibly easy.

To get a sense of how astonished your students will be by your ability to do this, take

a close look at the two sets of results below. One of the sets is real, the other is faked

and these are very similar to those your students will present to you for inspection, but

which is which? Can you see anything funny going on? Turn the page when you are

ready to find out how to determine the difference easily and quickly.

Real and Imaginary Results:

Can you spot the difference here?

# H T

# H T

1 51

2 52

3 53 4

54 5

55 6

56

7 57

8 58

9 59 10 60 11 61

12 62 13 63 14

64 15 65

16 66

17 67 18 68

19 69 20

70

21 71

22 72 23

73 24 74

25 75

26 76

27 77

28 78

29 79

30 80

31 81

32 82

33 83 34

84 35 85

36 86 37 87 38 88

39 89 40 90

41 91

42 92

43 93 44 94

45 95 46 96

47 97 48 98

49 99

50 100

# H T

# H T

1 51 2

52

3 53

4 54 5

55

6 56

7 57 8

58

9 59

10 60

11 61

12 62 13

63

14 64

15 65 16 66 17 67

18 68

19 69

20 70

21 71

22 72

23 73 24 74

25 75

26 76 27 77

28 78

29 79

30 80 31

81 32 82

33 83

34 84

35 85

36 86

37 87

38 88

39 89 40

90

41 91

42 92 43 93

44 94 45

95

46 96 47

97 48 98

49 99

50 100



How to spot the difference

You should have noticed that the results on the left side of the page contain several very long

runs of consecutive results. For instance, there were:

Five consecutive heads from #4 to #8

Seven consecutive heads from #43 to #49

Six consecutive tails from #73 to #79

These long runs seem so unlikely that most people would suspect this to be the fake results

but this is in fact the real set. The imaginary (fake) results on the right contain no more than

three consecutive heads or tails in a row.

You can differentiate real from fake results at a glance by simply looking for these long series

(clusters) of consecutive heads or tails.

Random doesn’t look so random!

Most people find these long series of consecutive results much less likely than they really are. A

string of four heads starts looking like a pattern when in fact, there isn‟t one. A string of eight

or nine will have a crowd looking for any cause other than random chance but in reality, there

is a very good chance that at least one of these long runs of consecutive results will appear if

you continue flipping a coin long enough. In fact, you are almost guaranteed to see at least one

series of six or more consecutive heads or tails in one hundred coin flips. This is why fake

results are so easy to spot.

We find this very surprising at first because we expect the outcome of consecutive coin tosses

to alternate between heads and tails much more than they really do. We easily mistake long

series of consecutive results, or clusters, as patterns when they are in fact truly random. To the

untrained eye, this makes random results appear to be 'fake', and fake results seem more 'real'.

Independent, random events

Our intuition about independent, random events like coin flips does not match reality because

we rarely look at large enough samples. We expect the 50/50 rule to apply on much shorter

time scales than it really does. In reality, the 50/50 rule takes much longer to surface. As a

result, we can easily suspect a long series of consecutive independent or unrelated events to be

significant when they are in fact inherent and quite natural. Public health and safety officials

therefore rely heavily on statistics in order to separate natural variations in population health

from those with specific and preventable causes.



Calculating probability

A simple diagram like the one below can be used to calculate the probability of any

outcome. The sum of the probabilities of all possible outcomes for a random event

must always add to 1. For a coin flip, there are two possible outcomes, either heads or

tails. So if the coin is unbiased, and the coin flipping technique is also unbiased, then

the probabilities are exactly half and half (½ or 0.5 or 50%).

So, using the diagram, there are four possible outcomes on the second flip. The

probability of getting HH on the second flip is ¼ (or 0.25). The probability of HT, TH,

or TT are all also ¼. The probability of HHH on the third flip is 1/8 (or 0.125) and HHHH

on the fourth is 1/16 (or 0.0625).

A faster way to calculate the probability of an outcome after any number of flips is to

multiply the probabilities of all the outcomes together. So the probability of HH is ½ ×

½ = ¼. The probability of HHH is ½ × ½ × ½ = 1/8 and of HHHH is ½ × ½ × ½ × ½ =

1/16.

Calculating the probabilities and expected frequencies of clusters is beyond the scope

of primary school mathematics but students should be able to grasp the concept of

their expected frequency and notice that their combined results match these

predictions almost perfectly.

The expected frequencies for each cluster size are provided in Table 5 in the Student

Worksheet. Each frequency in the table represents the average number of times you

would expect to see these clusters in a large number of sets of results from one

hundred coin flips.

HHH HHT HTH HTT TTT TTH THH THT

HH HT TT TH

H T

HHHH HHHT HHTH HHTT HTHH HTHT HTTH HTTT TTTH TTTT TTHH TTHT THHH THHT THTH THTT

1st Flip

2nd Flip

3rd Flip

4th Flip



Expected results

The table below contains ten sets of real results. The averages calculated in the table are

plotted in pink on the graph below.

Cluster

Size

Frequency

M

y R

esu

lts

2 S

uzie

3 Bra

d

4 Jane

5 Pa

ul

6

Tob

y

7

Karla

8

Emma

9 Ian

10

Tess

Average

Heads 46 43 49 55 51 51 43 52 49 49 48.8

Tails 54 57 51 45 49 49 57 48 51 51 51.2

1 29 26 26 24 24 29 26 23 21 16 24.4

2 14 7 10 9 10 12 7 13 12 14 10.8

3 5 4 4 8 8 8 4 7 7 9 6.4

4 1 5 6 0 3 3 5 1 7 2 3.3

5 2 3 0 3 1 1 3 4 0 3 2

6 0 1 0 2 0 1 1 1 1 1 0.8

7 2 1 0 1 1 0 1 0 0 0 0.6

8 0 0 0 0 1 0 0 0 0 0 0.1

9 0 0 2 0 0 0 0 0 0 0 0.2

10 0 0 0 0 0 0 0 0 0 0 0

1 2 3 4 5 6 7 8 9 10

5

10

15

20

25

30

YOUR RESULT

Cluster Size

(Number of consecutive heads and consecutive tails)

Averag

e Freq

uen

cy

Expected

frequency

Observed

frequency



Probability in the real world

The Gambler’s Fallacy

The Gambler‟s Fallacy is explained in the student worksheet. It arises when we know the

previous results of a series of random events like coin flips. Because we expect the 50/50 rule

to appear sooner or later, we incorrectly assume that the probability of getting either heads or

tails changes over time. After a long series of heads, many people assume that the probability

of tails on the next flip is higher than ½. In reality, the probability of tails is still exactly ½ every

time we flip the coin, no matter how many heads preceded it.

This fallacy can obviously get gamblers into very serious trouble. To make matters worse, the

odds of casino games are stacked slightly against the gambler (eg the inclusion of a green zero

on roulette wheels stacks the odds of black/red, or odd/even slightly in favour of the casino –

even though every result is independent of the last and truly random, the green zero

guarantees the casino will take more winnings than the gambler given sufficient time).

A second problem in addition to the Gambler‟s Fallacy is the tendency to remember large wins

and to forget small losses even though those small losses may add up to be significantly higher

in value than the occasional large wins.

“Littlewood’s Law of Miracles”

Renowned University of Cambridge mathematician John Littlewood once famously calculated

the expected natural frequency of strange coincidences. He defined a 'miracle' as being a one

in a million event we might believe to be so unlikely that we deem it to have 'real significance'.

He assumes we hear, see and think things at a rate of roughly one per second. In an eight hour

day, we experience around 30,000 such 'events' (60 seconds × 60 minutes × 8 hours =

28,800). At this rate, we experience around one million 'events' per 30 day month (864,000 to

be precise). Most of these events are so mundane or expected that pass by unnoticed. But

every now and then we experience some strange coincidence eg you‟re thinking about an old

friend seconds before they call, or a song you‟re humming comes on the radio.

A series of fortuitous events might make you feel especially lucky eg ten traffic lights turn

green as you approach, each giving you a clear run to an important appointment for which you

are running late, followed by a parking space 'magically' opening up just as you arrive. Less

fortunate ones could make you feel 'cursed', such as ten red lights, no parking spaces within

ten blocks for an appointment, followed by a toothache and an expensive parking ticket.

If we agree that events with probabilities around one in a million could be called 'miracles', then

we could expect one such 'miracle' around once per month. While 'Littlewood‟s Law of Miracles'

shines some light on their statistical probability, it shouldn‟t diminish our enjoyment of those

pleasant, quirky coincidences. It could however, help anyone who endures three or more

unfortunate events in succession to stay positive and motivated, rather than sink into mild

depression or suffer unwarranted anxieties.

Name ___________________

Activity 1 - Homework

Tossing a coin always results in either heads or

tails but never both. No surprises there! But

something very strange lurks beyond this

simple fact. To find it, you’d need to flip a coin

thousands of times. That would take ages but

by contributing just one hundred results each,

your class can discover this quirky fact of

nature together.

Step 1

Flip a coin. Do not record your result.

If the result is heads, follow the instructions

under HEADS in Step 2.

If the result is tails, follow the instructions

under TAILS in step 2.

Step 2

HEADS

Complete the table on this page by flipping a

coin one hundred times. For each toss, place a

tick in the H column if you flipped heads or the

T column if you flipped tails.

Please do not make any marks in the last

column. You will use the A column for analysis

in the next class activity.

TAILS

Complete the table on this page by pretending

to flip a coin one hundred times. There is no

'right' or 'wrong' way to do this. Just record the

result you would expect each time.

For each imaginary toss, mime the action of

tossing and catching the coin. Then place a tick

in the H column or in the T column.

Please do not make any marks in the last

column. You will use the A column for analysis

in the next class activity.

# H T A

# H T A

1 51

2 52

3 53

4 54

5 55

6 56

7 57

8 58

9 59

10 60

11 61

12 62

13 63

14 64

15 65

16 66

17 67

18 68

19 69

20 70

21 71

22 72

23 73

24 74

25 75

26 76

27 77

28 78

29 79

30 80

31 81

32 82

33 83

34 84

35 85

36 86

37 87

38 88

39 89

40 90

41 91

42 92

43 93

44 94

45 95

46 96

47 97

48 98

49 99

50 100

2008 | ABC Science

Online

Tab

le 1

– O

ne H

un

dred

C

oin

Flip

s

Activity 2 – Analysis

How did your teacher know whose results were real and whose were

faked? As you discovered, it was actually very easy! Flipping a coin

repeatedly usually results in surprisingly long sets of heads or tails.

These consecutive results are called clusters and they are much more

common than we expect. In this activity, you will count the number of

different sized clusters in your results.

Step 1 – Count the totals

First, count the total number of Heads and Tails you flipped. Record your

results in Table 2.

Step 2 – Circle the clusters

Draw circles around consecutive groups of ticks (clusters) in Table 1 as

illustrated. Be sure to group consecutive results for flip #50 and flip #51.

Step 3 – Count the ticks in each cluster

Count the number of ticks in each cluster and write this number in

column A. For example, write the number 1 in column A for single ticks.

Write the number 2 in column A for two consecutive ticks. Write the

number 3 in column A for clusters of three ticks, and so on.

Step 4 – Count the clusters

Count the number of single ticks you circled and write in column A.

Record this total row 1 of the Frequency column in Table 4. Next, count

the number of circles containing two ticks in column A. Record this

number in row 2 of the Frequency Column. Continue counting the

number of circles (clusters) containing 3, 4, 5 and up to 10 ticks until you

have completed Table 2.

Table 3– Cluster Frequency

Cluster

Size Frequency Check column

1 × 1 =

2 × 2 =

3 × 3 =

4 × 4 =

5 × 5 =

6 × 6 =

7 × 7 =

8 × 8 =

9 × 9 =

10 × 10 =

Check total =

# H T A

1

2

3 3

4

5 2

6 1

7 1

8

9 2

10

11

12

13 4

14

15 2

16 1

17 1

18

19 2

Circle and count the

crosses in each cluster like this

Step 5 – Check your results

This step will help you check that you

counted all the ticks and tallied all the

clusters correctly.

For each row, multiply the number in

the „Frequency‟ column by the number

indicated in the „Check‟ column.

Finally, add all the numbers in the

check column and write the result next

to „Check total‟. If your result is 100,

you have correctly counted all the

clusters.

If your „Check total‟ is not 100, you

made a mistake in Step 3 but don‟t

worry! Just go back to Step 3 and tally

the clusters again until you‟ve found

the problem.


Table 2 – Totals

Heads Tails

Activity 3 – Combine Results

Now that you have counted the clusters you recorded, it’s time to share your results. This

will increase your sample from one hundred results to one thousand results. Your

combined results will reveal just how common those unexpectedly long clusters really are.

Step 1 – Copy your results

Transcribe your results from Tables 2 and 3 into the column labelled 'My Results' in Table 4 below.

Step 2 – Share results

Share your results with nine other students. Write each person‟s name at the top of the remaining

columns in Table 4. Then copy their totals from Table 2 into the first two rows, and their results from

Table 3 in the rows labelled 1 to 10.

Step 3 – Average results

Add all the numbers in the Total Heads row and write the answer in your science journal. To calculate

the average number of heads observed in all 1000 results, simply divide this number by 10. Record

the result in the average column. Repeat for the Total Heads row.

Next, calculate the average frequency of each cluster size observed in your set of data. Again, simply

add all ten numbers in each row and divide the total by 10. Write these results in the Average column.

Table 4 – Combining 1000 Results

Cluster

Size

Frequency

1 M

y R

esu

lts

2

3

4

5

6

7

8

9

10

Average

Total

Heads

Total

Tails

1

2

3

4

5

6

7

8

9

10


Activity 4 – Surprisingly Predictable

The probability of getting heads or tails on a fair toss are exactly equal. So we can write the

probability of heads or tails as ½ (or 0.5). The probability of getting two heads in a row is ½ × ½ =

¼ (or 0.25). The probability of getting three heads in a row is ½ × ½ × ½ = 1

/8 … and so on. Using

these rules, mathematicians can calculate the expected frequency of any series of consecutive

results. The expected frequencies results for 100 coin flips are provided in Table 5 below.

Table 5 – Expected Cluster Frequencies for 100 Coin Flips

Cluster Size 1 2 3 4 5 6 7 8 9 10

Predicted

Frequency 25 12.5 6.25 3.13 1.56 0.78 0.39 0.19 0.10 0.05

This table tells you that if you flip a coin 100 times, you should expect to see 25 single (non-consecutive)

results. You should also expect 12.5 pairs of consecutive heads or tails, 6.25 triples etc.

Remember that real clusters are counted in whole numbers (integers) but their average frequency can be a

fraction.

Step 1 – Comparing your results

Plot your results from the Average column in Table 3 on the graph below. Use the blank space to the

right of each grey bar for each cluster size.

How closely did the average results of your combined results (representing 1000 coin flips) match the

expected average frequencies of each cluster size?

Do you think the results would match more closely if you combined even more results?

Random doesn’t look random

In this activity, you discovered that random results don‟t really look like random results to the

untrained eye. Most people are surprised to see five or six consecutive heads or tails in a row but in

reality, these clusters are actually quite common. Our intuition about independent, random events

does not match reality very well.

Everybody knows the probability of getting heads or tails when you flip a coin are exactly equal. So, in

a series of one hundred coin flips, we would expect to see fifty heads and fifty tails. This is what

people mean when they say fifty, fifty.

For one hundred coin flips, fifty/fifty is roughly what you get but we‟re not too surprised by results

like 42/58. The problem is that we expect the 50/50 rule to apply on much shorter time scales than it

actually does.

For ten coin flips, most people expect around five heads and five tails. But you know now that results

like seven heads and three tails are not unusual. Such results wouldn‟t bother you much unless there

was something riding on the outcome. When there is something valuable at stake however, we can

easily fall into a trap called “The Gambler‟s Fallacy”.

The Gambler’s Fallacy

fallacy

noun, plural fallacies.

1. a deceptive, misleading, or false notion, belief, etc.: a popular fallacy.

2. a misleading or unsound argument.

3. deceptive, misleading, or false nature.

4. Logic any of various types of erroneous reasoning that render arguments logically unsound.

5. Obsolete deception.

(From Macquarie Dictionary)

The Gambler‟s Fallacy is an incorrect belief about the probability of independent random events such

as coin flips. We all know the probability of heads is always exactly half, every time you flip a fair coin.

The problem arises after a series of three or more heads because we expect the fifty/fifty rule to

appear. As a result, we assume that the probability of tails on the next flip must be greater than

fifty/fifty. In reality, the probability of tails is still exactly the same no matter how many heads

preceded a flip. Even after ten consecutive heads, the probability of tails on the next flip is still fifty

per cent!

Over hundreds of consecutive flips, the fifty/fifty rule holds true but you can never predict the

outcome of an individual flip.

A coin toss doesn‟t mean very much unless we have something riding on the outcome. When there is

something valuable at stake however, we can easily become very sensitive about the result. If several

random events go the wrong way, we might start feeling „unlucky‟ or become depressed. In some

situations, this can even make us start feeling suspicious or acting completely out of character. To see how

easily this could happen, imagine how you would feel in the following situation:

A Random Story

One day, you invite a new friend home from school. You walk and chat and stop for a rest in

the park on the way. As you turn the last corner into your street, you both spot something small and

shiny lying on the footpath right in front of your house. You race to see what it could be lying there

on the grass. You arrive together to discover that the shiny object is a very expensive looking sports

watch. It has five separate dials controlling all kinds of high-tech functions including GPS, a depth

gauge, timers, alarms and even a heart monitor! The shiny stainless steel wrist band is made of

hundreds of intricate, inter-connecting links. It‟s by far the most amazing watch you have ever seen.

You pick it up and hurry to your room, close the door and start investigating how all the

buttons work together. The watch beeps and the display changes. The light button illuminates the

dial in a cool blue-green glow. Your mother brings you a sandwich and a glass of milk and asks to

see what you‟ve got. She takes a long look at the watch and realising how precious it, decides you

should take it to the police. She drives you and your friend to the local station straight away.

The police officer asks lots of questions. Where did you find it? At what time? Was there

anything else nearby? She completes an official form, records both your names and commends you

for your honesty. Then she offers you both a little ray of hope. Judging by the brand, she says she

wouldn‟t be surprised if the owner gave you a reward for returning the watch.

After three months, the officer calls and invites you to the station with your parents. Nobody

has collected the watch! To your surprise, your friend is there too. The officer asks who will be

signing for the watch. You look at each other and shrug.

“Well, I saw it first”, your friend says.

“No you didn‟t, we found it together!”, you reply. “And anyway, we found it at my house”, you

hasten to add. But the policewoman says where you found it makes no difference at all. Seeing your

dilemma, she suggests you should toss a coin to decide who will keep the watch. It‟s the only fair

way to decide. Your heart starts to race. Your eyes meet your friend‟s and suddenly, you don‟t like

such good friends anymore. Your friend‟s dad takes a coin out from his pocket.

“Here, best of three”, he says, handing you the coin. Your flip flies high in the air, the coin is a

blur.

“Heads”, your friend calls. Blast! It‟s heads. You flip again.

“Heads!”, your friend calls again. The coin seems to hover forever. You‟re already one down

and it‟s the best watch you‟ve ever seen. It just has to be tails this time! You slap the coin on your

wrist and slowly lift your hand but you can‟t believe your eyes. Heads again!

“Well that settles it, I guess?”, the policewoman says. Your face turns bright red and everyone

can tell how disappointed you are. But while your friend‟s dad is signing the release form, you

decide to toss the coin again out of sheer frustration. Heads again. That‟s odd, you think so you

toss it again and this time, you really can‟t believe your eyes. Heads again! That‟s four in a row. You

flip it once more to be sure. Heads again!!!

“Hey!”, you exclaim. “This coin is rigged!” Everyone turns to look at you.

“I just flipped this coin three more times. That‟s five heads in a row. I want a rematch. You

cheated!”

Your friend‟s father asks for the coin and flips it. Tails!

“You‟re cheating! I want a new coin”, you protest. The police officer asks for the coin and flips

it three times but says nothing. She just gives you a look that makes you sink. It‟s half pity, half

disappointment. Your mum has exactly the same expression on her face.

“But it‟s true. I got five heads in a row! That‟s impossible. Try it again!” This time, the police

officer just gives you a sad looking smile and hands the coin back to your friend‟s father. He slips

the coin back in his pocket and you watch it disappear. Now you‟ll never be able prove the coin was

a fake… or was it?


Documents

Lesson Plan 19 Flipping Coins - · PDF fileLesson Plan 19 – Flipping Coins | Page 2 2008 | ABC Science Online Materials and equipment These quantities are for 6 separate groups Total