Negative numbers may seem an obscure concept, until you bring in examples from life. The best one I know of is the example of debt vs. savings.
Use the following method using both a number line and a balance sheet (such as a checkbook log).
It works this way. Explain that if I have no money at all, and owe nothing, I am at zero in my bank account.
If I owe you ten dollars, but have no money in my pocket, the scale would read – negative 10. It may help to write the negative numbers in red ink, showing that you are “in the red” by so much. If I have $10, and owe $10, on a number line would move forward ten, then back ten, showing a total of zero at the end. Use different values to practice addition and subtraction on the number line.
A negative/positive number exercise that is quite effective, uses real money. Having your child physically add or subtract the amount from their own “bank” by earning or spending (keeping their own funds in a shoebox that says “bank account”) and paying you dollar by dollar for purchases, makes quite an impression. Not only will they understand the concept of positive and negative numbers (and balances), but it may motivate them to become more frugal!
Another way to emphasize this concept is to have them work off a debt (of a reasonable amount) after buying them a small item (on credit). They didn’t have the money to pay for it themselves so they owe it and have a negative balance. After paying it off fully, they may expect to have money in their pocket, but will realize that they have only gotten back to zero, and need to work more without spending it, to have a positive balance!
This is a hard math lesson. Not because the numbers are difficult to compute, but because reality is hard!