In Chapter 11, percentages were related to decimals and fractions in an attempt to show the pattern of relationships between these concepts and, it is hoped, to make them mutually supportive in the development of the concept of numbers less than one. In this chapter, the work will be extended to all numbers, including those greater than one, but the key reference values of 50%, 20%, 10%, 5%, 2% and 1% will be used to build pre‐and post‐estimates and to check if an answer and/or the process used to solve the problem make sense. The main objective of this chapter is to provide concrete and visual images of percentages so that the formulae and algorithms are understood and that the understanding acts as an anchor for memory. This is achieved by focusing on a hundred and on one.

An Image of Percentage

Since percentage relates to 100, the image presented to the learner should involve a clear demonstration of 100. Further, it should demonstrate dividing the quantity up into 100 parts, thereby identifying one part out of the hundred parts. The 100 square (Figure 14.1) has been used throughout this book in several applications.

Illustration of a grid.

Figure 14.1 100%.

This chapter will deal with three types of percentage problems:

  • Type 1 is ‘What is x % of N ?’ This is finding the percentage of a quantity.
  • Type 2 is ‘What percentage of y is x?’ This is expressing one quantity ...

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