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Prompt Cards

These two group activities use mathematical reasoning - one is numerical, one geometric.

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Consecutive Numbers

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

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Exploring Wild & Wonderful Number Patterns

EWWNP means Exploring Wild and Wonderful Number Patterns Created by Yourself! Investigate what happens if we create number patterns using some simple rules.

Calendar Patterns

Stage: 2 Challenge Level: Challenge Level:1

Anil (Irmak Primary School, Turkey) explored some adding patterns:

$1 + 8 = 9$
$2 + 9 = 11$
$3 + 10 = 13$
$4 + 11 = 15$
$5 + 12 = 17$
$6 + 13 = 19$
$7 + 14 = 21$
$8 + 15 = 23$

Alice from Perse School for Girls spotted a pattern:


There is a pattern, it's that the two numbers diagonal to each other added together make the same number as the other pair of diagonal numbers make.

Chris found another pattern using multiplication:

If you cross multiply the set of four numbers, their difference is always $7$.
$1 \times 9 = 9$ and $2 \times 8 = 16$, difference $= 7$
$3 \times 11 = 33$ and $4 \times 10 = 40$, difference $= 7$
$15 \times 23 = 345$ and $16 \times 22 = 352$, difference $= 7$ etc...

If you discovered any other patterns, then do let us know. Please don't worry that your solution is not "complete" - we'd like to hear about anything you have tried.


The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities can be found here.
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NRICH is part of the family of activities in the Millennium Mathematics Project.