The dual scale number line can be used for any proportional calculation where zeroes of both quantities align.
In other words, it is not suitable for converting between Celsius and Fahrenheit as 0°C is 32°F.
Discuss with students that it is useful to look for easy numbers to use in calculations, but that a unitary method (i.e. consider 1% or 1 unit of quantity) will work for any example.
For example, to find 17% of a quantity a student might use a unitary method, first determining 1% of the quantity and then finding 17%.
For diagrams, students will need to be aware of the particular terminology that is useful for discussing the diagram. In this case, the terms 'proportional' and 'unitary' are useful. Students should be encouraged to record these words and describe their meaning.
The teacher should provide further examples of more complicated, multi-step problems.
For example, if a student is asked to find 23% of $125, they can set up the dual scale number line showing the given information and then use the unitary method to find 1% of $125 (i.e., $1.25).
Multiplying both sides by 23 then shows that 23% of $125 is $28.75.
The Dual Scale Number Line can be useful for finding more than 100%.
For example, when increasing a quantity by 30% it is useful to find 10% (by dividing 100% and the given quantity by 10) and then multiplying by 13 to give 130%. Alternatively it is possible to use the unitary method and divide by 100 to give 1% and then multiply by 130.
This approach, focussing on multiplication and division only, is different to determining 30% and adding to the 100%.
The reason for focussing on multiplication and division only on this diagram is that students will need to eventually recognise that these two steps (i.e. dividing by 10 and multiplying by 13) can be carried out as one step: "multiply by 1.3"; namely, that a 30% increase can be found by multiplying by 1.3.