# Random or not: open investigations

TLF ID L5835

Test a machine that randomly packages two or three types of fruit jubes: penguin, fish and frog. Choose the ratio that each jube type is likely to be produced within a packet of 12 jubes. For example, choose a 2:1 ratio so that penguin jubes are twice as likely to be produced as fish jubes. Look at numbers of the most common jube type, patterns in sequences of one jube type or alternating sequences of jube types. For example, look at patterns such as penguin, fish, penguin, fish (alternating run of 4). Analyse the results of large samples. Compare the numbers of the most common jubes or longest runs of jube types. Identify the most likely number of the most commonly occurring jube type or the longest run most likely to occur in a packet. This learning object is one in a series of 17 objects.

#### Educational details

Key learning objectives
• Students observe and analyse data about random events to test conjectures about variation.
• Students interpret frequency graphs illustrating experimental results.
• Students observe the shape of experimentally derived data distributions.
• Students relate the shape of data distributions to statements about sample variation and sample size.
Educational value
• Provides sampling scenarios for students to explore relationships between proportions, sample size and random variation in even and uneven distributions.
• Demonstrates that conclusions based on small sample sizes can be wrong due to random variation.
• Automatically collates experimental results and displays them as frequency graphs.
Year level

7

Learning area
• mathematics
Strand
• Mathematics/Statistics and probability
Concept
• Mathematics/Investigation
• Mathematics/Graphs
• Mathematics/Experiments
• Mathematics/Random events
• Mathematics/Sampling
• Mathematics/Statistics
• Mathematics/Data interpretation
• Mathematics/Conjectures
• Mathematics/Number patterns
• Mathematics/Probability
Skill
• Analysis;
• Application;
• Comprehension;
• Knowledge
Student activity
• Interactives;
• Experiment;
• Estimation;
• Analysis;
• Modelling
Learning design
• Experiential learning;
• Independent learning;
• Problem solving;
• Visual learning

#### Other details

Contributors
• Technical implementer
• Script writer
• Name: Erica Dale
• Organisation: Tungaroo Software
• Address: Manly NSW 2095 Australia
• Subject matter expert
• Name: Howard Reeves
• Address: Lindisfarne TAS 7015 Australia
• Educational validator
• Name: Graham Jones
• Publisher
• Date of contribution: 20 Sep 2013
• Organisation: Education Services Australia
• Address: Melbourne VIC 3000 Australia
• URL: http://www.esa.edu.au/
Access profile
• Colour independence
• Device independence
• Hearing independence
Learning resource type
• Interactive Resource
Browsers
• Microsoft Internet Explorer - minimum version: 8.0 (MS-Windows) - maximum version: 9.0 (MS-Windows)
• Firefox - minimum version: (MS-Windows)
• Safari - minimum version: 5.1 (MacOS)
Operating systems
• MacOS - minimum version: 10.6
• MS-Windows - minimum version: XP - maximum version: 7
Rights
• © Education Services Australia Ltd, 2013, except where indicated under Acknowledgements.