Unit 4 · Topic 01 · Integers
A mountain weather station reported a summit temperature of -8 degrees while the base camp read 15 degrees, the same morning.
Pixel needed to tell hikers exactly how many degrees colder the summit was — not just "a lot colder."
Whole numbers alone couldn't describe the summit's reading at all.
Pixel was building a weather display for a trekking app. The base camp thermometer read 15 degrees Celsius, comfortably warm. The summit station, radioed in separately, read "8 degrees below zero." Pixel tried entering just "8" for the summit, but that made it look warmer than some cold days at base camp, which was clearly wrong — 8 below zero should be far colder than 15 above zero, not a plain 8.
Anaya, watching over Pixel's shoulder, suggested a minus sign: -8. That fixed it instantly. Any number below zero needed the minus sign to show it wasn't just small, but actually the opposite direction from zero compared to positive numbers. Pixel drew a number line for the app: zero in the middle, positive numbers stretching right for warm readings, negative numbers stretching left for below-freezing readings.
Kabir tested the display by asking how many degrees colder the summit was than base camp. Counting from -8 up to 15 on the number line, he counted 23 steps. "Fifteen minus negative eight is twenty-three," he said, surprised the gap was so large. Pixel confirmed it: the distance between a positive and a negative reading always adds their sizes together, since they sit on opposite sides of zero.
The app went live the next day, and a hiker messaged asking why a reading of -2 was described as WARMER than a reading of -10. Anaya explained using the same number line: -2 sits further right than -10, closer to zero, so it really is the warmer of the two — even though both numbers have minus signs, the one closer to zero on a negative number line is always the larger value.
Integers are whole numbers together with their negatives: ...-3, -2, -1, 0, 1, 2, 3... They include zero, all positive whole numbers, and all negative whole numbers, but no fractions or decimals.
On a number line, positive integers sit to the right of zero and negative integers sit to the left, with zero in the middle. Moving right always increases the value; moving left always decreases it, even among negative numbers.
Comparing two negative integers can feel backwards at first: -2 is GREATER than -10, because -2 sits closer to zero, further right on the line. The number with the larger digit isn't automatically the larger value once a minus sign is involved.
Check a weather app or thermometer for today's temperature. If it's above zero, imagine and write down what -5 degrees colder would read, and where that sits on a number line.
Draw a number line from -10 to 10. Mark two negative numbers and explain out loud which one is larger and why, using the number line.
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