7: Advanced Multiplicative - Proportions and Ratios

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A large bag of lollies has 15 raspberry, 18 banana, and 21 orange lollies. The mixture is the same for a medium sized bag that has 10 raspberry lollies in it. How many banana and orange lollies will be in the medium sized bag?


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Student: If you double a big pack you get thirty raspberry, thirty-six banana, and forty-two orange lollies. The medium pack only has ten raspberry lollies so you divide everything by three. So there are thirty-six divided by three, or twelve banana and forty-two divided by three, or fourteen orange lollies in the medium pack.

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Students at the Advanced Multiplicative stage are learning to choose appropriately from a range of part-whole strategies to solve and estimate the answers to problems involving multiplication and division. These strategies require one or more of the numbers involved in a multiplication or division to be partitioned, manipulated, then recombined.