Consecutive sums

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Can all numbers be made in this way? For example 9=2+3+4, 11=5+6, 12=3+4+5, 20=2+3+4+5+6

Lesson idea. This resource provides a detailed consecutive sums activity with extension work.

Teaching approach. By definition, a problem is something that you do not immediately know how to solve, so learning how to solve something unfamiliar is not straightforward. Tackling an extended problem is difficult.

This lesson gives pupils an opportunity to engage in mathematical thinking(ta) and develop their higher order(ta) thinking skills on a problem that is accessible but which has interest. For example, the problem is presented in diagrammatic and numerical ways.

The plan suggests several visualisation(ta) methods to present the same underlying task. It should be useful for teachers to compare these different presentations and either to select the one that they feel will be most useful for their pupils or explore ways for the pupils to see the links between the different methods. The assessment(ta) ideas, using other pupils' solutions from the NRICH website are widely applicable to other problems too. (edit)

Resource details
Title Consecutive Sums
Topic Investigation
Teaching approach
Learning Objectives

Allowing pupils to:

  • explore different ways of approaching a problem,
  • make links between different representations,
  • explain their approaches and what they have noticed,
  • notice features of the problem and gage whether these are important,
  • be able to generalise,
  • reflect on which methods helped to get close to a solution to the problem.
Format / structure

Word document and wiki page and an extension activity.

Age of students / grade

KS4,  Secondary,  KS3

Files and resources to view and download

Consecutive sums activity (on the wiki) or File:Consecutive sums Activity.doc (as a downloadable Word document) and File:Steps activity.doc


This resource was adapted from resources contributed by Mark Dawes