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Week 06 · Below Zero

Monday

Above and below zero
// Negative numbers, opposites, absolute value and the four-quadrant map
⏱ about 20 min

Monday: Above and Below Zero

Frost edges the window above the Numbers Desk. Rocket taps the glass. "The thermometer outside says 4. But the red line is under the zero."

"Then it is not 4," says Raven. "What do you notice about the marks below the 0?"

"They count up going down," Rocket says. "One below, two below, three below, four below."

Nova hovers beside the window, her light soft against the frost. "Four below zero has a name," she says. "Negative four."

"So zero is not the bottom," Rocket says. "It is the middle."

"The middle of the Field Day weather log," says Raven, pulling out a tall paper strip. "Above zero up here, below zero down here."

Nova hums. "Every number has a partner on the other side. Find them."

Rocket and Raven at a frosty window with a thermometer below zero, Nova hovering, a tall number line on the wall.

Opposite directions, opposite signs

Positive and negative numbers describe quantities with opposite directions. Above zero and below zero. Won and lost. Forward and back. Up and down.

The sign tells the direction. 4 means four above zero. -4 means four below zero. Zero itself is neither: it is the starting point.

In every situation, ask what 0 means. On a thermometer, 0 is the freezing mark. In a game, 0 means no points won or lost yet.

SituationPositiveNegativeWhat 0 means
Thermometer6 above zero: 66 below zero: -6The freezing mark
Game points3 points won: 33 points lost: -3No change in score
Steps5 steps forward: 55 steps back: -5The starting line
Elevator2 floors up: 22 floors down: -2The ground floor

Opposites

A number line from -6 to 6 with points at -4 and 4

Two numbers are opposites when they sit the same distance from 0 on opposite sides. 4 and -4 are opposites.

The opposite of the opposite brings you back: the opposite of -3 is 3, and the opposite of 3 is -3. So -(-3) = 3.

Zero is its own opposite. It is the only number that is.

WRITE THE NUMBER
  • Read the question.
  • Tap your answer.
The thermometer reads 4 degrees below zero. Which number says that?
Raven won 7 points in the ring toss. Which number says that?
Rocket took 5 steps back from the starting line. Which number says that?
The elevator went 2 floors below the ground floor. Which number says that?
OPPOSITES
  • Read the question.
  • Tap your answer.
What is the opposite of -4?
What is the opposite of 7?
What is the opposite of -12?
What is the opposite of the opposite of -3?
StatementTrue or false?
Four below zero is written -4.?
Zero is the lowest number on a thermometer.?
The opposite of -9 is 9.?
The opposite of the opposite of 5 is -5.?
WHY THIS EXERCISEFlipping a sign twice brings a number back to itself, so -(-5) = 5.
What is the opposite of 9? Type the number with its sign.
WHY THIS EXERCISEWriting the sign is the whole point: 9 and -9 are different numbers.
Try it
Find a thermometer, a game score or an elevator button with a number below zero or below ground.
Write what 0 means in that situation, and what one number above and one number below it mean.
Draw a tall number line from -10 to 10. Mark 0 in red, then mark 4 and -4 and connect them with an arc.

A good first step below zero. Tomorrow you put negative numbers in order and measure their distance from 0.