### Prompt Cards

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

### Consecutive Numbers

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

### 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.

# Magic Triangle

##### Stage: 2 Challenge Level:

Michael and Robert from Necton Middle School in Norfolk sent the following solution, where the sides all add up to 17:

Simone from Stroud Green Primary School sent us another solution where the sides all add up to 17.

In fact, there are lots more solutions. Here's a list of them (including the two shown above). Each group of four numbers makes up a side of the triangle. Of course, within a side you can switch round numbers that aren't on a corner, but that doesn't really give any new solutions.

17 = 1 + 5 + 9 + 2 = 2 + 4+ 8+ 3 = 3 + 6 + 7 + 1
17 = 1 + 6 + 8 + 2 = 2 + 5 + 7 + 3 = 3 + 4 + 9 + 1

19 = 1 + 5 + 9 + 4 = 4 + 2 + 6 + 7 = 7 + 3 + 8 + 1
19 = 1 + 6 + 8 + 4 = 4 + 3 + 5 + 7 = 7 + 2 + 9 + 1
19 = 2 + 5 + 9 + 3 = 3 + 1 + 8 + 7 = 7 + 4 + 6 + 2
19 = 2 + 6 + 8 + 3 = 3 + 4 + 5 + 7 = 7 + 1 + 9 + 2

20 = 1 + 6 + 8 + 5 = 5 + 2 + 4 + 9 = 9 + 3 + 7 + 1
20 = 2 + 4 + 9 + 5 = 5 + 1 + 6 + 8 = 8 + 3 + 7 + 2
20 = 2 + 6 + 7 + 5 = 5 + 3 + 4 + 8 = 8 + 1 + 9 + 2
20 = 3 + 4 + 8 + 5 = 5 + 2 + 6 + 7 = 7 + 1 + 9 + 3
20 = 4 + 2 + 9 + 5 = 5 + 1 + 8 + 6 = 6 + 3 + 7 + 4
20 = 4 + 3 + 8 + 5 = 5 + 2 + 7 + 6 = 6 + 1 + 9 + 4

21 = 3 + 5 + 7 + 6 = 6 + 2 + 4 + 9 = 9 + 1 + 8 + 3
21 = 3 + 4 + 8 + 6 = 6 + 1 + 5 + 9 = 9 + 2 + 7 + 3
21 = 3 + 2 + 9 + 7 = 7 + 1 + 5 + 8 = 8 + 4 + 6 + 3
21 = 3 + 5 + 6 + 7 = 7 + 2 + 4 + 8 = 8 + 1 + 9 + 3

23 = 7 + 2 + 6 + 8 = 8 + 1 + 5 + 9 = 9 + 3 + 4 + 7
23 = 7 + 3 + 5 + 8 = 8 + 2 + 4 + 9 = 9 + 1 + 6 + 7