Question

Ben's class were making number tracks and cutting them up.

number track of 0 to 12 ... ... ...

First they cut them into twos. Ben started with zero

Pairs of numbers: 0,1 2,3 4,5 etc ... ... ...

but Miles started with one:

numbers in pairs: 1,2 3,4 5,6 etc ... ... ...

Then they both added up the numbers on each piece.

Ben wrote: 0+1=1, 2+3=5, 4+5=... ... ...

Miles wrote: 1+2=3, 3+4=7, 5+6= ... ... ...

What patterns could they see?

Alice cut her number track into 3s and added up the numbers on each one.

numbers in threes: 0,1,2 3,4,5 6,7,8 etc ... ... ...

Winston made a longer number track which he cut into 5s and he added up the numbers on each one.

numbers in fives: 0,1,2,3,4 5,6,7,8,9 10,11,12,13,14 etc ... ... ...

What could they discover about the sum of the numbers on their strips of number track?

What other patterns can you find?

Answer 1

1. the pattern is that of arithmetic progression with a common difference between each no. of the pattern.
2. there is common difference between each no. of the pattern .  

other pattern 0+1+2, 3+4+5, 6+7+8 ......
                           3      ,     12   ,   21     
                            3*1 ,       3*(1+3) , 3*(4+3)