The key idea of number strategies and knowledge at level 5 is that proportional thinking can be applied to solve real problems involving rational numbers.

Many real world problems require the use of proportional thinking to solve. Proportional thinking is the ability to interpret and compare ratios, or to operate on more than one number simultaneously. A ratio is a comparison between quantities or measures describing the relative amounts of each. They can appear in a wide variety of contexts and there are several different types of ratio:

**Part-to-whole ratios:**These compare one part of a whole with the whole. For example, in a class with 12 boys and 13 girls the ratio of the number of boys to the number of students in the class is 12:25**Part-to-part ratios:**These compare parts of a whole. In the example above the ratio of boys to girls is 12:13. This type of ratio can also be used to compare more than two values. For example a fruit salad could be described as having banana, apple and pineapple in the ratio 2:3:1.**Rates:**Both types of ratio above compare measures of the same type of thing. A rate is a type of ratio which compares two different measures or quantities. Common examples of rates include dollars per kilo, kilometres per hour, etc.

This key idea develops from the key idea of number strategies and knowledge at level 4 where students could apply a variety of strategies to operating on rational numbers.

This key idea is extended in the key idea of number strategies and knowledge at level 6 where students are able to apply multiple operations to solve problems.