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

Take, for example, four consecutive negative numbers, say

^-7, ^-6, ^-5, ^-4

Now place + and / or - signs between them.

e.g.

^-7 + ^-6 + ^-5 + ^-4

^-7 - ^-6 + ^-5 - ^-4

There are other possibilities. Try to list all of them.

Now work out the solutions to the various calculations.

e.g.

^-7 + ^-6 + ^-5 + ^-4 = ^-22

^-7 - ^-6 + ^-5 - ^-4 = ^-2

Choose a different set of four consecutive negative numbers and repeat the process.

Take a look at both sets of solutions. Notice anything?
Can you explain any similarities?

Can you predict some of the solutions you will get when you start with a different set of four consecutive negative numbers?
Test out any conjectures you may have.

Try to explain and justify your findings.