Adding and subtracting directed numbers

This lesson develops the concept of adding and subtracting directed numbers. The activities address common misconceptions about the addition and subtraction of directed numbers. Students explain their reasoning using diagrams.

The activities use the ‘charge’ model of directed numbers. For example, a diagram showing 6 positive charges and 2 negative charges is interpreted as being positive 4.

The calculation 4 + (–2) is represented by starting with a diagram showing 4 positive charges, then placing 2 negative charges on the diagram. The result is a diagram that can be interpreted as positive 2.

The calculation 2 – (–1) is represented by starting with a diagram showing 3 positive charges and 1 negative charge. This can be interpreted as showing positive 2. The act of taking away negative 1 is shown by crossing out the negative charge. This results in an answer of positive 3.

There is a collaborative activity in which students must match pictures showing calculations using the charge representation with written calculations.

There are pre-lesson and post-lesson formative assessment tasks. Detailed teacher notes give suggestions on questioning and how to use the resources. Full solutions are given for each of the sections.

This is a concept development lesson from the Mathematics Assessment Resource Service, a collaboration between UC Berkeley and the Shell Centre team at the University of Nottingham. Further information on the collection is given here.