Triangle numbers investigation | KS3 maths | Teachit - Free Printable

1. The first 3 triangle numbers are 1, 3, and 6.
2. The pattern of triangle numbers is formed by adding consecutive natural numbers: 1, 1+2=3, 3+3=6, 6+4=10, etc.
3. To find the next triangle number after 6, add 4 (the next natural number) to 6: 6 + 4 = 10.
4. The number of cubes added each time increases by 1: 2 (from 1 to 3), 3 (from 3 to 6), so the next addition is 4.
5. The first 10 triangle numbers are calculated as follows:
- 1st: 1
- 2nd: 1 + 2 = 3
- 3rd: 3 + 3 = 6
- 4th: 6 + 4 = 10
- 5th: 10 + 5 = 15
- 6th: 15 + 6 = 21
- 7th: 21 + 7 = 28
- 8th: 28 + 8 = 36
- 9th: 36 + 9 = 45
- 10th: 45 + 10 = 55

a) 10 cubes will be needed to make the next triangle number.
b) You are adding 4 cubes each time.
c) The first 10 triangle numbers are: 1, 3, 6, 10, 15, 21, 28, 36, 45, 55.