Developing reasoning and language
Pyramid activity
Lines of enquiry – Year 5
Quickly complete the grid
Identify patterns and relationships between numbers
e.g.

In the second row all the numbers are odd; in the third and fourth
rows, all the numbers are even.

The total at the top of the grid is twice the total of the numbers
on the bottom row.

The difference between adjacent numbers on the bottom row is 1,
between adjacent numbers on the second row is 2 and between
numbers on the third row is 4.

The middle number in the second row is scaled up by 4 to give the
total at the top.

The total of the first and fourth numbers on the bottom row is
equal to the total of the middle numbers on the bottom row.

The top total is equal to the total of the two outer numbers on the
bottom row multiplied by 4
Investigate the calculations within the pyramid rather than the totals.
What patterns can you see in the pyramid now?
What happens if I add 1 to each number on the bottom row? (The total
increases by 8.When we have increased by 1 each of the numbers in
the first row, the total increases by 8 because we have added: 1 + (1 
3) + (1  3) + 1 OR 8 numbers at the top, I have added 1 to each
number so 8 x 1 = 8)
Suppose we add 5 to each number in the first row, what will happen to
the top number?

Given all four numbers in the bottom row, is there a way I can find
the top total without completing second and third rows?

Does this method work for other sets of four consecutive numbers
along the bottom row?

Will it work for any set of four numbers?

If all the numbers in the bottom row were odd numbers, would the
total be an odd number too? What about other combinations of odd
and even numbers?

Suppose we used the letters a, b, c and d in the bottom row in place
of numbers. Could you fill in the rows to show how to get the top
number?

What if we had a bottom row with five numbers – is there a similar
method we might use?

Can we find a way of stating the 4 consecutive numbers in the
bottom row, given the top number, without working out any of the
numbers in between first?
What will the top calculation look like?