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# Biscuit Factory

Students focus on the mathematical skills and mental calculations (recall of multiplication and division facts, recognition of common factors and multiples) associated with using ratios in a problem-solving context.

### Teacher notes

• In the context of a biscuit making factory, students determine the properties of gear wheels (size, number of gears, direction of rotation) in order to successfully operate the biscuit factory conveyor belt.
• Students are progressed from counting techniques to the important aspects associated with multiplicative thinking. Feedback is designed with this transition in mind.

### Learning objects

 Biscuit factory: ratiosIn a two gear system, using a driver gear with 60 teeth, students vary the number of teeth on the belt gear and identify the resulting ratio of rotations between the two gears. They build a table showing the ratios. The results are also displayed in a graph. Students then determine the correct gear size to achieve the rotation required to cook gingerbread biscuits. Biscuit factory: complex ratiosIn a two gear system, using a driver gear with 30 teeth, students vary the number of teeth on the belt gear and identify the resulting ratio of rotations between the two gears. They build a table showing the ratios. The results are also displayed in a graph. Students then determine the correct gear size to achieve the rotation required to cook gingerbread biscuits. Biscuit factory: gear directionStudents use simple gear chains to investigate the impact on rotational direction of having an even or odd numbers of gears. Biscuit factory: two-gear systemIn a two gear system, students vary the number of teeth on each gear and build a table of the resultant ratios between the number of teeth and the number of rotations. Students then determine the correct gear size to achieve the rotation required to cook gingerbread biscuits. Biscuit factory: three-gear systemIn a three gear system, students vary the number of teeth on each gear and build a table of the resultant ratios between the number of teeth and the number of rotations. Students encounter the impact of a second driver gear. Students determine the correct gear size to achieve the rotation required to cook gingerbread biscuits. Biscuit factory: gearsStudents select the required number of teeth on each of the gears in a two gear system to run the conveyor belt at the required speed.