# Mathematics problem: Consecutive sums

Page 3 of 16 Previous | Next 1 Problems to develop mathematical processes and applications 2 Mathematics problem: All in a Jumble 3 Mathematics problem: Consecutive sums 4 Mathematics problem: Got It! 5 Mathematics problem: Harmonic triangle 6 Mathematics problem: Isosceles triangles 7 Mathematics problem: More number pyramids 8 Mathematics problem: Odds and evens 9 Mathematics problem: Reaction timer 10 Mathematics problem: Route to infinity 11 Mathematics problem: Seven squares 12 Mathematics problem: Speeding up, slowing down 13 Mathematics problem: Square it 14 Mathematics problem: Squares in rectangles 15 Mathematics problem: Tilted squares 16 Mathematics problem: Triangles in circles Mathematics problem: Consecutive sums

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Problem outline

This problem investigates the sums of consecutive numbers. The aim is to identify patterns and relationships and explain them, for example, why all odd numbers can be written as the sum of two consecutive numbers, or identifying a rule for determining the number of ways a particular number can be represented as the sum of consecutive numbers.

Why do this problem?

This problem can provide high quality activity for all pupils by offering an accessible context in which to explore the structure of numbers at a wide range of levels. First, through experimentation, learners might discover relationships, then they might begin to pose their own problems and finally, produce convincing arguments or proofs for what they have discovered.

For the problem itself and some associated teachers' notes

Consecutive Sums (link opens in new window) from NRICH (link opens in new window) .

Curriculum references: process

The guidance sections ‘What teachers might do' offer suggested actions that can help to draw out pupils' skills in representing. There is, however, a breadth of opportunities to develop a range of process skills including:

Simplify a situation or problem to help identify and classify patterns.

Pose problems, making and beginning to justify conjectures and generalisations.

Appreciate that there are a number of different techniques and approaches that can be used to analyse a situation.

Form convincing arguments based on findings, and make general statements.

Curriculum references: content

Number: Number operations; Integers, powers and roots

Understand addition, subtraction, multiplication and division as they apply to whole numbers and decimals; know how to use the laws of arithmetic and inverse operations. Construct and simplify linear expressions.

Useful links

Other useful links including problems and articles from the NRICH website can be found in the 'Related links'.

Mon, 02/02/2009

Mathematics problem: Consecutive sums

Mathematics exemplification 'How the problem might be focused': Consecutive sums

Mathematics exemplification 'How the problem might unfold': Consecutive sums

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dc.title Mathematics problem: Consecutive sums dc.description Mathematics problem: Consecutive sums. dc.identifier nsonline.org.uk~234601~161243 dc.subject English, Unpublished dc.date 2009-02-02 15:45:00