The Showdown!

Warm up (10 minutes)

Lets start with reminding ourselves of the language of probability.

Check out this clip which looks at the basics:

Watch this clip until 2.40 and then complete the activity below:

https://www.youtube.com/watch?v=KzfWUEJjG18

Write an event that would match these words.

Be prepared to share your ideas with the class explaining how these words differ from each other.

Main Content (30-40 mins):

We are going to simulate a game of Australian Rules Football with a Showdown played between Adelaide and Port Adelaide. 

• Who are the well-known players?
• What have the past showdown results been?
• Which team is more likely to kick goals accurately?

Here is table of results on how accurate each team’s goal kicking is.

Table 1

Tally of Goals (6 Points) and Behinds (1 Point) from 

Think, pair, share and write down the results with your desk buddy 

Questions:

1. How many goals/behinds did Port Adelaide/Adelaide score?
2. Calculate goal kicking accuracy as a percentage (Formula: Number of Goals ÷ Total shots at goal = goal kicking accuracy as a percentage)
3. Which team performed better?
4. How many games do you think are included in these results? Why? 
5. What is the purpose of working out the shooting percentage?
6. Which team is more successful based on these results? Why?
7. Extension: If each team had ten shots on goal, how many would you expect to be goals? 

If you have any questions, please raise your hand and your teacher will come and help you.

Share your results with the rest of the class

We are going to simulate a game between Adelaide and Port Adelaide. In your desk buddy pairs make two six faced dice per pair.

Each blank dice will have: 

• faces labelled ‘goal’ 
• faces labelled ‘behind’

You will need to choose the number of dice faces that closely matches the performance of the teams over the past few games.

Help yourself to two blank dice and decorate them when you are ready. 

Share with the class how/why you chose to decorate the Port Adelaide and Adelaide dice

Conclusion/Reflection (5-10 minutes):

New vocabulary you have learnt today: goal, behind, face, percentage

Questions that the teacher will ask:

When rolling a dice - What are the chances I will roll an even number?  What are the chances I will roll an odd number?  What are the chances I will roll a 3?  

The teacher will now draw out random names on pop sticks to explain the meaning of these words and the answers to these questions so have a discussion with your desk buddy about what they mean and be prepared to share with the class.

You can use: http://www.amathsdictionaryforkids.com/dictionary.html if you need

Resources:

Named pop sticks

30 x Table 1 sheets for students 

Warm Up (15 mins): 

Have a go at creating some mystery spinners on the The Mystery Spinner Challenge game with your desk buddy.

http://www.scootle.edu.au/ec/viewing/L2384/index.html

How did you decide on the number of sectors for each spinner?

What happened when you tested your spinners? Did they match the results? Why/Why Not?

Share your observations with class

Main Content (30 mins):

Now we are going to explore the issues of short and long run frequency. 

Here we consider the difference between what happens with a small number of games, against what happens with a large number of games.  In this game Adelaide will take the same number of shots at goal as Port Adelaide. With your dice that you made in last lesson you are going to play a  a four shot game. Each dice will be rolled rolled twice.

Record on the chart below with how many wins/losses for Adelaide and how many for Port Adelaide.

After you've done this play a twenty shot game (each dice will be rolled ten times) then a twenty shot game,

Record the results as tally marks in Table 2.

Table 2

Short and Long run frequency

Look for patterns you see in the table of data

Why those patterns have occurred? 

Extension;

Add up the scores of both teams for the 10 shot and 20 shot games.  

Scores added are 6 points for a goal and 1 point for a behind.  

What is the minimum number of goals needed to be kicked in the 10 and 20 shot games to guarantee winning?

Conclusion/Reflection (10-15 minutes):

New vocabulary you have learnt today: short term frequency, long term frequency, patterns, trends 

The teacher will now draw out random names on pop sticks to explain the meaning of these words so have a discussion with your desk buddy about what they mean and be prepared to share with the class.

You can use: http://www.amathsdictionaryforkids.com/dictionary.html if you need

Have another turn of the Mystery Spinner Challenge with your desk buddy to see if you can get more accurate results. 

Online Resources:

Mystery Spinner Challenge: http://www.scootle.edu.au/ec/viewing/L2384/index.html

Maths Dictionary: http://www.amathsdictionaryforkids.com/dictionary.html

Warm Up (10 minutes): 

Coin Flipping

The teacher will ‘flip a coin’ https://www.online-stopwatch.com/chance-games/flip-a-coin/ twice

You need to predict what the coin will land on.  If you think:

two heads – two hands on heads (H, H)

one head one tail – one hand on head, one hand on bum (H, T)

one tail one head - one hand on bum, one hand on head (T, H)

two tails – two hands on bum (T, T)

Enjoy looking at the different combinations!

Check out this clip to see how we write up the probabilities of tossing two coins:

https://www.youtube.com/watch?v=cXNDqOJD5b4

Main Content (30-40 minutes):

You are now going to investigate what happens in sports betting. Before we start you need to understand that gambling is a serious addiction and can have extremely negative effects on peoples lives.  The purpose of this exercise is to show how organisations like the TAB develop odds in relation to the likelihood of a sports team winning.

We will imitate what happens when sports bets are placed.

We will use the Port Adelaide/Adelaide dice that you made yesterday to find the outcome of the game.

Each student will have $1.00 to place on as bets. The TAB is paying $1.40 for Adelaide to win and $2.80 for Port Adelaide to win. 

Discuss with your desk buddy and then with your table group: Why do you think the amounts being offered are different? 

Now, write down the team you would like to place your bet on.  The teacher will record these on the board.

No play the Showdown using the dice from the previous lesson using fixed number of shots - 20.  

Record the score in a tally chart like the one below.

Table 3

Using the results from your game you need to work out how much the TAB will pay out to winners for the game.

Compare this with the total amount of money they collected ($1.00 for each student).

For example:

$1.00 from thirty students, twenty students invested in Adelaide @ $1.40.  

TAB has to pay out $1.40 x 20 = $28.00.

Discuss as a class 

• What profit, break-even and loss mean? (profit – make money, break-even – to finish at the same amount that you started with, loss -lose money)
• What probability language/vocabulary best matches these terms (profit – likely, break-even – equal chance 50/50, loss – unlikely)
• How many games has the TAB made a profit/break-even/loss? 

Focus on which betting proportions would cause the TAB to make a profit or a loss. Given the odds at $1.40 and $2.80 and a class of thirty students the outcomes for the TAB can be shown as:

TAB Key:

Sometimes no matter who wins the TAB will make a profit if the betting proportions fall into a particular zone.  

Ask your teacher for a sheet like the one below.

Student Name:                                                                                                                                               Date:

TAB Profit and Loss Table 

Task: Colour in the zones

- where the TAB can’t lose blue

- the remaining squares red (the red squares will indicate a loss for the TAB)

Ask your teacher if you need help.

Be prepared to share your findings with the class

What zones show the person betting winning?

What zones show the TAB winning?

Is it an equal chance of winning against the TAB?

Resources:

30 x TAB Profit and Loss Table sheets 

30 x Table 3 sheets

Online Resources:

Flip a Coin: https://www.online-stopwatch.com/chance-games/flip-a-coin/

Random name picker: https://www.online-stopwatch.com/random-name-pickers/name-picker-wheel/

Maths Dictionary: http://www.amathsdictionaryforkids.com/dictionary.html

Conclusion/Reflection (5-10 minutes):

New vocabulary you have learnt today: 50/50, equal chance, profit, loss, break-even 

The teacher will spin the online random name picker https://www.online-stopwatch.com/random-name-pickers/name-picker-wheel/ to randomly select the person who will explain the meaning of these words so have a discussion with your desk buddy about what they mean and be prepared to share with the class.

You can use: http://www.amathsdictionaryforkids.com/dictionary.html if you need

Warm Up (15 minutes): 

Welcome back to the Showdown.  We are now going to learn a little bit more about Probability.  Please go through slides 1-17 of Probability and Chance Power Point and discuss with your desk buddy

https://www.slideshare.net/cbsroscommon/probability-chance

Come up with 3 challenging questions from the information given to you to ask the rest of the class.

Share questions and answers with class.  Discuss new vocabulary. 

Main Content (35-40 minutes):

This was the table that we completed in Lesson 1

Table 1:

This table shows that Port Adelaide have more shots at goal than Adelaide, they just aren’t as accurate.

The same dice that you have made will be used for this Showdown.  

Using an online spinner https://wheeldecide.com/index.php?c1=20&c2=21&c3=22&c4=23&c5=24&time=5 you are going to spin to see the number of shots (long term frequency) at goal for Port Adelaide and Adelaide.  

• Port Adelaide's range will be higher: 20-24 (based on total shots at goal from table 61/65) 
• Adelaide's range will get less: 16-20. 

This should ensure that the end result will be 50/50 (both teams have equal chance of winning)

• Why will the end result now be 50/50 even though Adelaide still has more sides of the dice labelled goal

Discuss your reasons with your desk buddy and then your table group.

Play the simulation game (as a whole class)

• Spin the online spinner https://wheeldecide.com/index.php?c1=20&c2=21&c3=22&c4=23&c5=24&time=5 to determine the amount of shots on goal for each team Eg. Port Adelaide will have 21 shots and Adelaide will have 18 shots
• Using Multiple Dice Roller https://www.online-stopwatch.com/chance-games/roll-a-dice/full-screen/– spin to see goals and behinds 

Dice 1 Adelaide            

if you roll a 1,2 = behind          if you roll a 3, 4, 5 or 6 = goal

Dice 2 Port Adelaide     

if you roll a 1,2, 3 = behind      if you roll a 4, 5 or 6 = goal

The teacher will now demonstrate how to play.  

1. Roll both dice and record the results as tally marks in the attached table.  

2. After 18 rolls (Adelaide allocated shots) we only record the results of dice 2 (Port Adelaide allocated shots) for 3 more rolls.

This is because this experiment we are trying to create conditions for Port Adelaide and Adelaide to have an equal change of winning.

3. Calculate your total scores for each team

4. Calculate the goal kicking accuracy as a %

Table 4:

Online Resources 

Online Spinner: https://wheeldecide.com/index.php?c1=20&c2=21&c3=22&c4=23&c5=24&time=5

Multiple Dice roller: https://www.online-stopwatch.com/chance-games/roll-a-dice/full-screen/  (under settings add 2 dice) 

Probability and Chance PowerPoint:https://www.slideshare.net/cbsroscommon/probability-chance

Maths Dictionary: http://www.amathsdictionaryforkids.com/dictionary.html

Conclusion/Reflection (5 minutes):

Discuss with your table group

- What you enjoyed about the lesson?

- What worked/didn't work well?

- What could be improved for next time

One speaker reports back to the class for discussion.

The teacher will record this information and use for next lesson.

Warm Up (15 minutes):

Please go through slides 24-46 of Probability and Chance Power Point and discuss with your desk buddy

https://www.slideshare.net/cbsroscommon/probability-chance

Come up with 3 challenging questions from the information given to you to ask the rest of the class.

Share questions and answers with class.  Discuss new vocabulary. 

Your teacher will now discuss and look at examples of Theoretical and Experimental Probability from the Power Point Slides.

Main Content (25-30 minutes):

Looking at yesterdays results from the Simulation game:

Think, pair, share and write down the answers to these questions with your desk buddy: 

Would the TAB odds still be $1.40 vs $2.80? Why/Why not?

1. What odds you would set for an 18 vs 21 shot game

Share the results of your discussions with your class

Pairs  will need to calculate the TAB profit/break even for each team is and what a TAB loss will be for each team.  

Formula to help you work out the profit/break even:

 (number of students at $1 each) ÷ (odds) = (TAB Profit/Break Even

Example:

30 ÷ 2.10 (Adelaide odds) = 14.3

This means that less than 15 students bet on Adelaide for the TAB to make a profit or break even

Whole Class Activity

Your teacher will now record the correct Profit, Break-Even and Loss amounts as a class and record on the whiteboard. 

What team you will invest your imaginary $1 on?

Now we can start the Showdown.  

Your teacher will lead this from IWB 

• Adelaide will have 18 shots and Port Adelaide will have 21 shots
• Using Multiple Dice Roller – spin to see goals and behinds 

Play the simulation game (as a whole class)

• Spin the online spinner https://wheeldecide.com/index.php?c1=20&c2=21&c3=22&c4=23&c5=24&time=5 to determine the amount of shots on goal for each team Eg. Port Adelaide will have 21 shots and Adelaide will have 18 shots
• Using Multiple Dice Roller https://www.online-stopwatch.com/chance-games/roll-a-dice/full-screen/– spin to see goals and behinds 

Dice 1 Adelaide            

if you roll a 1,2 = behind          if you roll a 3, 4, 5 or 6 = goal

Dice 2 Port Adelaide     

if you roll a 1,2, 3 = behind      if you roll a 4, 5 or 6 = goal

Students to keep the results on their own online scoreboard https://panaaj.bitbucket.io/keepscore/ updating it after each roll. 

At the end of the game:

With your desk buddy

1. Work out if the TAB made a profit, loss or broke even using the odds the class decided on

Student Name:                                                                                                                                               Date:

TAB Profit and Loss Table 2

Using the new odds from our class discussion for Port Adelaide and Adelaide calculate the TAB Profit, Break Even or Loss

Task: Colour in the zone where the TAB can’t lose blue and the remaining squares red, the red squares will indicate a loss for the TAB

Online Resources: 

Online Spinner: https://wheeldecide.com/index.php?c1=20&c2=21&c3=22&c4=23&c5=24&time=5

Multiple Dice roller: https://www.online-stopwatch.com/chance-games/roll-a-dice/full-screen/  (under settings add 2 dice) 

Online scoreboard: https://panaaj.bitbucket.io/keepscore/

Probability and Chance PowerPoint:https://www.slideshare.net/cbsroscommon/probability-chance

Maths Dictionary: http://www.amathsdictionaryforkids.com/dictionary.html

Resources:

30 x TAB Profit and Loss Table 2 sheets 

Conclusion/Reflection (5 minutes):

Revisit new vocabulary introduced: variables, odds 

The teacher will spin the online random name picker https://www.online-stopwatch.com/random-name-pickers/name-picker-wheel/ to randomly select the person who will explain the meaning of these words so have a discussion with your desk buddy about what they mean and be prepared to share with the class.

You can use: http://www.amathsdictionaryforkids.com/dictionary.html if you need

From your TAB Profit and Loss 2 Table Results

What zones show the person betting winning?

What zones show the TAB winning?

Is it an equal chance of winning against the TAB?

Table 1 Answers

Tally of Goals (6 Points) and Behinds (1 Point) from 

Expected responses from Table 1 Discussion 

1. Use the table to extract information 
2. See formula in table 
3. The Adelaide team are more accurate at goal kicking, even though the Port Adelaide team have more shots on goal.
4. Three games played to gather these results, due to there being just over 10 goals kicked a game.  You could argue 2 games in good playing conditions or 4 games in wet, muddy conditions.  It will be interesting if any groups mention this
5. The percentages are 63.9% for Adelaide and 47.7% for Port Adelaide.  Percentages give a common base of one hundred so comparisons can be made.  As the teams didn’t have the same amount of shots on goal to compare, you can use shooting percentage to see which team is more accurate.
6. Adelaide is the more successful team as they more accurate when kicking for goal. 
7. If each team had ten shots on goal, Adelaide would kick 6 and Port Adelaide 5.  This is simple once goal kicking accuracy has been worked out.

Expected Dice solution (Student discussion) 

The best solution is (based on the shooting percentage): 

Adelaide: four faces showing goal, two faces showing behind.                                                                                  

Port Adelaide: three faces goal, three faces behind.  

Students may use different reasoning to find their solutions:

One way could be that 39 of 61 shots on goal were successful for Adelaide.  Rounding to the nearest 10 makes 40 of 60.  As there are six faces on a dice, you could divide this number down to 4 of 6.  Adelaide’s dice will have four faces marked as goal and the other two will be marked behind.

Port Adelaide kicked 31 goals and 34 behinds.  This is very close to 50% accuracy looking at those numbers so students would mark three sides as goal and three sides as behind. 

Another way might be  that students recognise that both teams had close to 60 scoring shots each.  With a dice having 6 sides, students may value 10 shots per face of the dice, rounding to the nearest 10.  This gives Adelaide four faces saying goal and two saying behind whilst Port Adelaide have three saying goal and three saying behind. 

Look for patterns they see in the table of data and why those patterns have occurred? 

The more shots taken, the more likely Adelaide will win. This shows that the greater the number of shots, the closer the results of the experiment will match to the expected outcome.

Students should become aware that the results for a small number of shots are random and do not match the expected outcome. This is called short run variability where it is difficult to predict the result from a short number of games.

Think, pair, share and write down the results with their desk buddy 

Questions for desk buddies to discuss:

1. Would the TAB odds still be $1.40 vs $2.80? Why/Why not?
2. Discuss what odds you would set for an 18 vs 21 shot game

Share the results of their discussions

Expected responses:

1. No. As Adelaide are now having less shots than Port Adelaide taking away their advantage of having one more dice face (saying goal) .