You will have noticed that $36$ is both a triangular number and a square number! That is, $36$ dots can be arranged perfectly both in a triangle and in a square. Make pictures in your notebook illustrating this! This shows that the same number can be represented differently, and play different roles, depending on the context. Try representing some other numbers pictorially in different ways!

What would you call the following sequence of numbers $?$

That’s right, they are called hexagonal numbers! Draw these in your notebook. What is the next number in the sequence $?$

What happens when you start to add up hexagonal numbers, i.e., take $1,1+7,1+7+19,1+7+19+37, \dots ?$ Which sequence do you get$?$Can you explain it using a picture of a cube$?$

Find your own patterns or relations in and among the sequences in Table $1.$ Can you explain why they happen with a picture or otherwise$?$

Can you recognise the pattern in each of the sequences in Table $3?$