Using standard algorithms for number operations

This lesson develops the concept of making sense of the standard algorithms for addition, subtraction, multiplication, and division of positive integers. In particular students will work on the following areas:

• Improving conceptual understanding of why and how the algorithms work.
• Developing procedural fluency in carrying out the algorithms.
• Becoming more able to spot unreasonably sized answers and to debug errors in procedures.

An initial activity involves students peer assessing some work that has been completed incorrectly. They must spot where a mistake has been made and suggest how to improve the work. The activity addresses some common misconceptions, such as forgetting to add a ‘carry’ digit.

The main activity involves looking at the work of six students and assessing what mistakes they are making. Students must write some advice for each student to help them improve their work.

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.