Consecutive sums

Can all numbers be made in this way? E.g. 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.

Resource details
Title	Consecutive Sums
Topic	[[Topics/Investigation|Investigation]]
Teaching approach	[[Teaching Approaches/Assessment|Assessment]],  [[Teaching Approaches/Higher order|Higher order]],  [[Teaching Approaches/Mathematical thinking|Mathematical thinking]],  [[Teaching Approaches/Visualisation|Visualisation]]
Learning Objectives	To allow pupils to explore different ways of approaching a problem For pupils to make links between different representations For pupils to explain their approaches and things they have noticed For pupils to notice features of the problem and to appreciate whether these are important For pupils to be able to generalise To reflect on which methods helped to get close to a solution to the problem
Format / structure	wiki text, and .doc download
Subject	[[Resources/Maths|Maths]]
Age of students / grade	[[Resources/Secondary|Secondary]],  [[Resources/KS4|KS4]],  [[Resources/KS3|KS3]]
Files and resources to view and download	Consecutive sums activity (extension work is linked from the main resource)