About this video
Sal works backwards from a final temperature of -9 degrees Celsius in Fairbanks, Alaska, to find the starting temperature. He uses a vertical number line to undo each change: a 5-degree drop means the earlier temperature was 5 above, and a 2-degree rise means it was 2 below. He then checks the answer by running the changes forwards.
You'll be able to
- work backwards through temperature changes to find a starting temperature.
- use a vertical number line to add and subtract with negative numbers.
- check my answer by applying the changes forwards from the start.
Key words
- Degrees Celsius
- A unit for measuring temperature; 0 degrees Celsius is where water freezes.
- Vertical number line
- A number line drawn up and down, like a thermometer, with bigger numbers higher up.
- Working backwards
- Starting from the end result and undoing each change to find where you began.
Transcript
- Amanda lives in Fairbanks, Alaska. The table below shows the temperature changes in Fairbanks over a two-hour period. So when we went from 3pm to 4pm the temperature increased by two degrees Celsius, and then from four to five the temperature decreased by five degrees Celsius.
Amanda notices the temperature at 5pm is negative nine degrees Celsius. What was the temperature in Fairbanks at 3pm? So they're essentially telling us the temperature at the end of these changes, and they want us to figure out the temperature at the beginning of these changes.
So let's see if we can do that. Let me draw. Since, in thermometers we're used to thinking vertically. So I'll draw a vertical number line here to think about this a little bit. So here we go. Alright, so at 5pm we end up at negative nine degrees Celsius, so let's just say this is zero, negative one, two, three, four, five, six, seven, eight, nine.
So we end up at negative nine degrees Celsius. This is zero degrees Celsius right over here. So from zero... Sorry, from 4pm to 5pm the temperature dropped by five degrees Celsius and that got us to negative nine. So we drop by five to get to negative nine, so we must've started five above negative nine.
So one, two, three, four, five... Right over here. So this is that drop. This is that five degree drop. Like we said, one, two, three, four, five. So that's that five degree drop right over here. This is a negative five degrees Celsius. So at 4pm, right at 4pm, we must've had a temperature of...
Well, five above negative nine is going to be negative four. Negative four degrees Celsius. This is what the temperature was at 4pm. So this is at 4pm. And then, to figure out 3pm, remember when we go from 3pm to 4pm our temperature increased two degrees Celsius.
So we increased by two degrees Celsius from that hour to get to negative four degrees Celsius. So we increased by two degrees Celsius. So if we increase by two degrees Celsius to get to negative four, that means at 3pm we must've been two below that. So this is what we did from three to four.
>From three to four we increased by two to get to negative four. So this right over here is the plus two degrees Celsius right over there. So we must've started right here at 3pm. We must've started right there at 3pm. All I did is underline this. If you know we're at negative nine to end with, and from four to five we dropped negative five to get there, that means at four we must've been five above negative nine.
So we're at negative four, and then from three to four, if we increased two degrees to get there, that means at three we must've been two degrees below negative four. So this right over here is negative six degrees Celsius. So what was the temperature in Fairbanks at 3pm?
It was negative six degrees Celsius. And you can verify that. If you start at negative six, you add two, you get to negative four, and then you subtract five, you get to negative nine, which is exactly what we had here.
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