Can you find a similar pictorial explanation for why adding counting numbers up and down

Can you find a similar pictorial explanation for why adding counting numbers up and down Class 6

Question 1.

Can you find a similar pictorial explanation for why adding counting numbers up and down, i.e., 1, 1 + 2 + 1, 1 + 2 + 3 + 2 + 1, …, gives square numbers? Class 6

Solution:

These squares give 1, 4, 9, 16, 25, 36.

Question 2.

By imagining a large version of your picture, or drawing it partially, as needed, can you see what will be the value of 1 + 2 + 3 + ... + 99 + 100 + 99 + ... + 3 + 2 + 1? Class 6

Solution:

Yes, 100 × 100 = 10000.

Question 3.

Which sequence do you get when you start to add the All 1’s sequence up? What sequence do you get when you add the All 1’s sequence up and down? Class 6

Solution:

1, 2, 3, ... (1, 1 + 1, 1 + 1 + 1, ...),

1, 3, 5, ... (1, 1 + 1 + 1, 1 + 1 + 1 + 1 + 1, ...).