This is a difficult concept for children to understand.

I normally relate it to temperature, which is something that they are familiar with and a thermometer is basically a vertical number line.

On a hot summer day, the temperature might be 25°C and at night the the temperature might fall to 15°C.

As the temperature decreases, the numbers decrease

(because so far the numbers have all been positive).

On a cold winter day, the temperature might be 10°C and at night the the temperature might fall to 0°C.

Again as the temperature decreases, the numbers decrease

(because the numbers are still positive).

On a really cold winter day, the temperature might be 0°C and at night the temperature might fall to -10°C.

Now as the temperature decreases, the numbers increase.

(because the numbers are now negative).

It is common for children to think that -10 has a greater value than -5, because the 10 is higher than 5.

These worksheets from Mathsblog should help:

Negative Numbers Missing Numbers

Order Negative Numbers 1 Order Negative Numbers 2

Negative Number Quiz from BBC Bitesize

Working with Negative numbers

Another way of explaining this is in terms of money in a bank account - if you have -10 pounds in your account, you are overdrawn and owe the bank £10.