The Mathematics of Lotto - 2014 MAWA Secondary Convention Mathematics Education: Teaching for Understanding and Growth
←
→
Page content transcription
If your browser does not render page correctly, please read the page content below
2014 MAWA Secondary Convention
Mathematics Education: Teaching for Understanding and Growth
The Mathematics of Lotto
Gregory Hine, Ph.D.
The University of Notre Dame Australia
Some light humour to start us off... http://dubbed-scene.com/the-simpsons-season-3-episode-19-dog- of-death
Let’s have a play...
On your Lotto card, complete 10 games by selecting any 6 numbers for each game.
When you’re finished, turn to your partner and discuss your ‘selection strategy’.
The winning numbers from last Saturday’s Lottery were:
42 31 23 14 5 1 Supp#1 10 Supp#2 44
How well did you go in your 10 games?
Do you think that players understand the true chances of winning a prize when they play Lotto?
Do you think that this is fair, or are people being exploited?
How do you think a lack of understanding affects the amount of money people spend?
A Modified Game
Let’s play a modified version of Lotto 6:2 Lotto
This means for every 6 numbers in the draw only two will be drawn out
A winner is determined if the preselected those two numbers are drawn out
Complete Activities in 1) and 2) with a partner
As a class, let’s calculate:
(i) the total number of games played
(ii) the total number of games won
(iii) the winning percentage of the class
Look back to Activity 1c) on p.1 How do our results compare?
Let technology work for us
Using Maths 300 software, let’s try to determine a ‘long term’ winning percentage for
the 6:2 game by playing:
(i) 10 games_____________
(ii) 50 games_____________
(iii) 100 games____________
(iv) 1000 games___________
What value do you think the winning percentage will approach as we play more games?
I played 10 000
games here!Applying mathematical thought
In the 6:2 game, how many ‘pairs’ of numbers can be drawn from the 6 cards available?
Let’s list them here.
1,2 1,3 1,4 1,5 1,6 2,3 2,4 2,5 2,6 3,4 3,5 3,6 4,5 4,6 5,6
Looking back to Activity 2, let’s create a tally to find the most commonly occurring
‘pairs’ from our class.
Pair Number of Times Selected
How can we explain why these ‘pairings’ were so popular?Mathematics + Technology
Since there are 15 pairs of numbers that can be chosen from the 6:2 game, each pair should appear
_______times if we play 1500 games.
Do you think that this prediction is realistic? What do you predict if 1500 games are actually played?
Using Maths 300, let’s test our predictions by playing 1500 games and recording the results in the
table found p. 3 Activity 5c)
What can we conclude about the likelihood of any pair of numbers being drawn?Extension Work
Consider other scenarios for games, and hypothesise which would give better odds
(a) 8:2 or 7:3? (b) 5:3 or 6:2?
Investigate how the chance of winning varies by changing the number of cards available
e.g. Compare games of 6:2, 7:2, 8:2.
Dispel popular myths through technological exploration
Numbers in a row never turn up
Even numbers are better than odd numbers
If you increase the numbers in a row, your chances of winning worsen
The longer you play the better your chances of winning
Conduct some field research: Do people who play Lotto overestimate their chances of winning?What about Saturday Lotto?
How do these activities link in with the ?
Year 7
List outcomes of chance experiments involving equally likely outcomes and represent probabilities of those outcomes using fractions (ACMSP116)
Recognise that probabilities range from 0 to 1 (ACMSP117)
Pose questions and collect categorical or numerical data by observation or survey (ACMSP118)
Construct displays, including column graphs, dot plots and tables, appropriate for data type, with and without the use of digital technologies (ACMSP119)
Year 8
Investigate techniques for collecting data, including census, sampling and observation (ACMSP284)
Explore the practicalities and implications of obtaining data through sampling using a variety of investigative processes (ACMSP206)
Explore the variation of means and proportions of random samples drawn from the same population (ACMSP293)
Investigate the effect of individual data values , including outliers, on the mean and median (ACMSP207)
Year 9
List all outcomes for two-step chance experiments, both with and without replacement using tree diagrams or arrays. Assign probabilities to outcomes and
determine probabilities for events (ACMSP225)
Calculate relative frequencies from given or collected data to estimate probabilities of events involving 'and' or 'or' (ACMSP226)
Year 10
Describe the results of two- and three-step chance experiments, both with and without replacements, assign probabilities to outcomes and determine
probabilities of events. Investigate the concept of independence (ACMSP246)
Use the language of ‘if ....then, ‘given’, ‘of’, ‘knowing that’ to investigate conditional statements and identify common mistakes in interpreting such
language (ACMSP247)
Evaluate statistical reports in the media and other places by linking claims to displays, statistics and representative data (ACMSP253)What are the chances of this happening?
These workmen are installing bollards to stop nurses from parking on
the pavement outside the Royal Hospital in Belfast.
They are cleaning up at the end of the day.
How long do you think it will be before they realise that they can't go home?You can also read
