1. NZ Maths
  2. Supporting professional practice
  3. Numeracy project PLD
  4. Representational Framework
  5. 8: Advanced Proportional - Proportions and Ratios

8: Advanced Proportional - Proportions and Ratios

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Relevant and up-to-date teaching resources are being moved to Tāhūrangi (tahurangi.education.govt.nz). 
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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: The numbers are all multiples of three. The medium sized bag has two thirds as many raspberry lollies, so it will have two thirds as many of the others too. Two thirds of eighteen is twelve and two thirds of twenty-one is fourteen.

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Students at the Advanced Proportional stage are learning to select from a repertoire of part-whole strategies to solve and estimate the answers to problems involving fractions, proportions, and ratios. These strategies are based on finding common factors and include strategies for the multiplication of decimals and the calculation of percentages.