Look at this thermometer. The red line has dropped below the zero mark and it reads −3 °C.

What is that little minus sign in front of the 3 telling us? Is −3 °C warmer or colder than a frosty 0 °C morning?

−7 on the number line

Here is a number line that runs from −10 all the way up to +10, with zero right in the middle. Watch where −7 sits: seven steps to the left of zero. The further left we go, the colder, the deeper, the more below-zero we are.

0 in the middle

Now look at zero itself. Everything to the right of it is positive; everything to the left is negative. Zero is the dividing line — like the ground floor of a building, with upstairs floors above and basement floors below.

+5 on the number line

And here is +5, five steps to the right of zero. Notice how +5 sits five steps to the right of zero, while −7 sits seven steps to the left — the same idea of stepping out from zero, just in opposite directions.

Counting a change that crosses zero

Here is a real question. One night in Galway the temperature was +4 °C, then it dropped to −2 °C. How many degrees did it fall? Have a first guess — there is no wrong answer yet, because we are about to count it out together.

Watch the line. First we count from +4 down to zero: that is 4 steps. But we are not there yet — the temperature kept falling below zero, so we count on from 0 down to −2: that is 2 more steps. Add them: 4 steps and then 2 more steps makes 6 degrees. That is the trick with negative numbers — when a change crosses zero, count down to zero first, then keep counting below.

Now we count some changes across zero together on the −10 to +10 line, using the trick we just saw: count down to zero first, then keep counting below. We will work through two changes in order. First, the temperature falls from +3 °C to −1 °C — place a marker on +3, another on −1, then count the steps out loud. Next, a bigger fall from +2 °C to −5 °C. Predict how many steps each change is before we count it, then we'll check together.

Today we work through these temperature-change problems together, each one a little trickier than the last. Every one asks the same question — by how many degrees did it change? — so we spot the action words and count the size of the fall: the freezer that fell a few degrees, the basement carpark that dipped below zero, the Mullingar cold snap that crossed zero, and finally a deep fall that goes right down below −5.