# Number Strategies and Knowledge: Level 6

The key idea of number strategies and knowledge at level 6 is that multiple operations can be applied to solve real problems involving real numbers.

The key idea of number at all levels is that much of our world can be quantified and these quantities can be combined by certain rules. By the time students reach Level 6 they have been exposed to a great deal of number work and hopefully have begun to form a sense of how numbers can be combined and how useful this is. At level 6, they further extend their understanding of numbers and learn a few more applications. In particular, they learn to use direct and inverse relations as well as powers with integers and fractions. They also encounter irrational numbers, which are numbers that can not be expressed as a fraction, for example, pi, and the square root of 2. On the applications side they learn about compound rates and how to numerically find the optimum value of certain functions.

This key idea develops from the key idea of number strategies and knowledge at level 5 and all previous experience with number.

Level 6 is the last time that Number occurs as a thread in the Curriculum. However, there is very little mathematics and statistics that can be done without at least a passing knowledge of number. Number especially underpins and is generalised by algebra. Students without a good understanding of number are lost in algebra. The key idea of calculus at level 7 and 8 takes the idea of numerical methods for optimisation and shows how functions may be optimised by the use of derivatives. At level 8, calculus goes back to using numerical techniques for finding area. At a higher level, numerical techniques are an essential part of the subject because much of what occurs in real situations is currently too complicated for analytical methods.