Roundabout Rugby
This is a level 4 probability and measurement activity from the Figure It Out theme series. It is focused on finding all possible combinations for a round robin tournament and creating a timetable. A PDF of the student activity is included.
About this resource
Figure It Out is a series of 80 books published between 1999 and 2009 to support teaching and learning in New Zealand classrooms.
This resource provides the teachers' notes and answers for one activity from the Figure It Out series. A printable PDF of the student activity can be downloaded from the materials that come with this resource.
Specifc learning outcomes:
- Find all possible combinations for a round robin tournament.
- Create a timetable.
Roundabout Rugby
Achievement objectives
GM4-4: Interpret and use scales, timetables, and charts.
S4-3: Investigate situations that involve elements of chance by comparing experimental distributions with expectations from models of the possible outcomes, acknowledging variation and independence.
Required materials
- Figure It Out, Levels 3-4, Theme: Sport, "Roundabout rugby", page 12
See Materials that come with this resource to download:
- Round about rugby (.pdf)
Activity
The students first need to establish which games need to be played, given the condition that each team plays each other team only once.
Below are some ways of doing this.
An arrow diagram:
An organised list:
AB, AC, AD, AE, AF, BC, BD, BE, BF, CD, CE, CF, DE, DF, EF.
All of these methods reveal that 15 games must be played. The students can also use multiplication to work out the total number of games. There are six teams. Each team plays each other team once, so each team will play five games. Six teams playing five games is 6 x 5 = 30 games. But this counts each game twice (it counts the Cats playing the Eagles and the Eagles playing the Cats, but this is actually only one game), so half of 30 is the number of games played: 30 ÷ 2 = 15 games.
The students then need to make up a timetable in which no team has more than two consecutive games. A table is a useful way to do this.
The students will need to work systematically to ensure that their draw meets all the requirements. Many different draws are possible. The students will not always be able to have a game on both fields at the same time. The minimum time is eight games of 30 minutes, a 30 minute lunch break, and six 10 minute breaks between games. This is a total of 330 minutes or 51/2 hours.
1.
15 games
2.
a. A suggested timetable could be:
9:00 – 9:30 |
A vs B |
C vs D |
9:40 – 10:10 |
A vs E |
B vs F |
10:20 – 10:50 |
E vs C |
D vs F |
11:00 – 11:30 |
A vs D |
B vs C |
11:40 – 12:10 |
E vs F |
|
12:10 – 12:40 |
Lunch |
|
12:30 – 1:10 |
F vs C |
B vs E |
1:20 – 1:50 |
A vs C |
B vs D |
2:00 – 2:30 |
A vs F |
D vs E |
Many other draws are possible.
b. This would take a total of 5 hours 30 minutes (51/2 hours), the minimum possible
time.
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