Tuesday
Tuesday: Order and Distance
Raven unrolls the weather log along the Numbers Desk. "Four readings: -3, 2, -7 and 0. Which was coldest?"
"Negative 7 has the biggest number," Rocket says, "so it is the warmest?"
"Find it on the number line," says Raven. "What do you notice about where it sits?"
Rocket slides his finger left past 0, past -3, all the way to -7. "It is the farthest left. The coldest."
Nova hovers over the line. "Left is less," she says. "Right is greater. On every number line, always."
"So -3 is greater than -7," Rocket says slowly, "even though 3 is less than 7."
"And -7 is farther from 0," Raven adds. "Seven away. That is its absolute value." Nova hums. "Two different questions."
Order on the number line
Numbers grow as you move right. Any number to the right is greater than any number to its left.
-3 > -7 because -3 is to the right of -7. Read it as "-3 is warmer than -7" on the weather log.
Every negative number is less than 0, and less than every positive number. -1/2 and -2.5 sit between the whole numbers.
Absolute value: distance from 0
The absolute value of a number is its distance from 0, with no sign. We write it with bars: |-7| = 7 and |7| = 7.
Distance is never negative. A reading of -7 is colder than -3, but |-7| is greater than |-3|: it is farther from freezing.
Order and absolute value answer different questions. "Which is less?" looks left. "Which is farther from 0?" looks at distance.
- Read the question.
- Tap your answer.
- Read the question.
- Tap your answer.
- Read the question.
- Tap your answer.
- ?-7
- ?-3
- ?0
- ?-1/2
- ?4
- ?2.5
| Sentence | True or false? |
|---|---|
| -3 > -7 | ? |
| -2.5 < -2 | ? |
| 0 > -1/2 | ? |
| -4 > 3 | ? |
Lay them in order on a strip of tape with 0 in the middle. Say which is farthest from 0.
Order and distance, sorted. Tomorrow is Numbers Lab: your own weather log and a game played above and below par.