Week 06 · Below Zero
Data Day
Data Day: Treasure map
// Negative numbers, opposites, absolute value and the four-quadrant map
⏱ about 20 min
Data Day: Treasure Map
Saturday morning Raven draws a cross on a big sheet of graph paper. "Data Day. The kitchen table is (0, 0)."
"Everyone hides a counter somewhere in the room," Rocket says, "and gives the coordinates. We find it."
"Steps right or left first, then forward or back," says Raven. "What do you notice if both numbers are negative?"
"Quadrant III," Rocket says. "Left and back. Behind the table, by the window."
Nova hovers above the sheet, her light tracing the axes. "Say the point. Then walk it," she says. "No peeking."
Rocket is already counting steps. "Negative two, negative three. Got it!" Nova hums. "Walk, do not run."
- Positive and negative numbers describe opposite directions from 0: above and below zero, won and lost, forward and back.
- Opposites sit the same distance from 0 on opposite sides. The opposite of -3 is 3, and 0 is its own opposite.
- On the number line, right is greater: -3 > -7. Every negative number is less than 0.
- Absolute value is distance from 0: |-7| = 7. Order and distance are different questions.
- A coordinate plane crosses two number lines at (0, 0). Points with the same x or y are |a| + |b| units apart when 0 sits between them.
◇ TREASURE MAP WITH A GROWN-UP
Mark a spot in the room as (0, 0). Agree on which way is positive x and positive y.
One person hides a counter and gives its coordinates in steps, like (3, -2). The other walks to find it.
Swap roles. Try a point in each quadrant, and one on an axis.
Pick two counters that share a coordinate and count the steps between them. Check with absolute values.
Draw the room on graph paper with every hidden point plotted and labeled.
One person hides a counter and gives its coordinates in steps, like (3, -2). The other walks to find it.
Swap roles. Try a point in each quadrant, and one on an axis.
Pick two counters that share a coordinate and count the steps between them. Check with absolute values.
Draw the room on graph paper with every hidden point plotted and labeled.
For a grown-up
This week your student used negative numbers, ordered them on a number line and plotted points in four quadrants.
Ask them to explain why -3 > -7 and why |-7| is still greater than |-3|. Both answers should come from the number line.
Counters stay away from children under three and pets. Walking the map is enough; no running indoors.
Ask them to explain why -3 > -7 and why |-7| is still greater than |-3|. Both answers should come from the number line.
Counters stay away from children under three and pets. Walking the map is enough; no running indoors.
Safety first
Walk, do not run, when finding a point. Move chairs and bags out of the path first.
Small counters stay away from children under three and pets.
Small counters stay away from children under three and pets.
DATA DAY CHECK
- Read the question.
- Tap your answer.
Point T is at (-2, -3). Which quadrant is it in?Counter A is at (3, -2) and Counter B is at (-1, -2). How many units apart are they?
What is the opposite of -6?
-1 ? -4
Draw your treasure map with the axes, (0, 0) at the table, and every hidden counter labeled with its point.
Great mapping, crew. Next week: hops on the number line, and adding and subtracting signed numbers.