The scale carries on below zero
Zero is not the end of the scale. On a cold night the temperature can fall below 0°, and the thermometer keeps going down past zero. The numbers below zero are the negative numbers.
Negative numbers turn up wherever there is a zero to go below: a floor below the ground floor, a diver below sea level, or money that is owed.
The scale runs from 10° down through 0° to −10°. The line across the tube is zero, and every mark under it is below zero.
The minus sign names the side
A temperature 3 degrees below zero is written −3°, and it is read as "negative 3" or "minus 3". The 3 says how far the number is from zero, and the minus sign says which side of zero it is on: −3 is 3 below zero, and 3 is 3 above it.
The level reads −3°: three degrees below the zero line.
On a number line
A number line carries on past zero in the same way. Laid flat, the negative numbers sit to the left of zero and the positive numbers to the right. −3 and 3 are both 3 steps from zero, on opposite sides of it.
−3 is 3 steps to the left of zero, and 3 is 3 steps to the right.
Adding moves up, even past zero
Start at −3 and add 4. Adding moves up the scale, so the temperature rises. 3 steps up reach 0, and 1 more step lands on 1. So −3 + 4 = 1.
Subtracting moves down the scale in the same way. A temperature of 2° that falls by 5° ends at −3°: 2 steps down reach 0, and 3 more go below it, so 2 − 5 = −3.
From −3°, a rise of 4 passes zero and stops at 1°.
Walk the marker from −3. Each step to the right adds 1: four steps pass zero and land on 1.
The usual mistakes
Moving the wrong way. −3 + 4 is not −7. Adding moves up the scale, even from below zero, and −7 is 4 steps further down.
Dropping the minus sign. −3 + 4 is not 7. That starts from 3 above zero, but −3 is 3 below it.