Consecutive Numbers

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

Pair Sums

Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?

Negative Dice

If the odd numbers on two dice are made negative, which of the totals cannot be achieved?

Consecutive Negative Numbers

Age 11 to 14Challenge Level

Do you notice anything about the solutions when you add and/or subtract consecutive positive numbers?

You could start by considering four consecutive positive numbers before moving on to consider four consecutive negative numbers.

If you have looked at several sets of consecutive numbers and noticed some similarities in the solutions, you may be wanting to explain why they occur. An algebraic representation of the situation might help you with this:

if $a$ is your smallest number, the four consecutive numbers are $a$, $a+1$, $a+2$, $a+3$