# Biscuit factory: complex ratios

TLF ID L2372

Examine a pair of gears that drives a conveyor belt to an oven, including cases where the belt gear is larger than the driver. Notice that the number of rotations for each gear depends on the gear size (number of teeth). Explore the relationship between the number of teeth and the number of rotations. Build a table to compare rotations for a range of gear sizes. Look for a pattern in the number of rotations. Choose a gear to adjust the speed of a conveyor belt. For example, choose a belt gear size (15 teeth) that will complete half a rotation for every turn of the driver wheel (30 teeth). This learning object is the third in a series of six objects that progressively increase in difficulty.

#### Educational details

Key learning objectives
• Students use knowledge of factors and multiples to solve problems.
• Students apply ratios to solve multiplicative problems.
Educational value
• Demonstrates that factors, multiples and common multiples are integral to solving problems involving ratios.
• Provides opportunities for students to practise multiplication and division operations in ratio situations.
• Encourages students to use multiplicative strategies and ratios to interpret and describe relationships between objects.
• Provides data tables for students to record observations and predictions.
• Automatically collates data tables and displays number patterns on line graphs.
Year level

8

Learning area
• mathematics
Strand
• Mathematics/Number and algebra
Concept
• Mathematics/Number patterns
• Mathematics/Multiples
• Mathematics/Multiplication
• Mathematics/Rates
• Mathematics/Ratio and proportion
• Mathematics/Algebra
• Mathematics/Arithmetic
• Mathematics/Computation
• Mathematics/Factors
• Mathematics/Graphs
• Mathematics/Fractions
Skill
• Analysis;
• Application;
• Comprehension;
• Knowledge
Student activity
• Interactives;
• Experiment;
• Analysis;
• Modelling
Learning design
• Experiential learning;
• Independent learning;
• Problem solving;
• Visual learning

#### Other details

Contributors
• Technical implementer
• Script writer
• Name: Rod Rees
• Organisation: Rees Films Pty Ltd
• Address: Blackburn VIC 3130 Australia
• Subject matter expert
• Name: Howard Reeves
• Address: Lindisfarne TAS 7015 Australia
• Educational validator
• 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.