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Ratios and Data 6-8 / Week 06 / Thursday
4/6
Week 06 · Below Zero

Thursday

The Field Day map
// Negative numbers, opposites, absolute value and the four-quadrant map
⏱ about 20 min

Thursday: The Field Day Map

Raven tapes two long strips of paper into a cross on the kitchen floor. "The Field Day map. The Numbers Desk is the center, (0, 0)."

"Right and up are positive," Rocket says. "Left and down are negative. Like two number lines."

"Ring Toss is 3 right and 2 up," Raven reads from her log. "That is (3, 2). What do you notice about the Hop Course?"

"Four left, two up. (-4, 2)." Rocket plants a counter. "Same height, other side."

Nova hovers above the cross. "Those two are 7 units apart," she says. "Count from one to the center, then out again."

"Four and three," Rocket says. "The absolute values, added."

Nova hums. "Now place the Scoop Station, and tell me which quadrant it lands in."

Four quadrants

A coordinate plane is two number lines crossed at 0. The horizontal one is the x-axis, the vertical one is the y-axis.

A point is named (x, y): across first, then up or down. (3, 2) is 3 right and 2 up. (-4, 2) is 4 left and 2 up.

The axes split the plane into four quadrants, numbered I, II, III and IV going counterclockwise from the upper right.

Quadrantx signy signExample
Ipositivepositive(3, 2)
IInegativepositive(-4, 2)
IIInegativenegative(-3, -3)
IVpositivenegative(3, -3)

The crew's map

StationxyPoint
Ring Toss32(3, 2)
Hop Course-42(-4, 2)
Scoop Station-3-3(-3, -3)
Finish Line3-3(3, -3)
Sign Tent14(1, 4)
A four-quadrant plane with the five Field Day stations marked by their initials.

Ring Toss (3, 2) and Hop Course (-4, 2) share a y-coordinate, so they sit on one horizontal line.

Their distance is |3| + |-4| = 7 units, because 0 is between them.

Mirror images: flipping the sign of x reflects a point across the y-axis. (3, 2) and (-3, 2) are reflections.

Flipping the sign of y reflects across the x-axis. (3, 2) and (3, -2) are reflections too.

WHICH QUADRANT?
  • Read the question.
  • Tap your answer.
A coordinate plane with four quadrants and point R at (3, 2)Point R is at (3, 2). Which quadrant is it in?
A coordinate plane with four quadrants and point H at (-4, 2)Point H is at (-4, 2). Which quadrant is it in?
A coordinate plane with four quadrants and point S at (-3, -3)Point S is at (-3, -3). Which quadrant is it in?
A coordinate plane with four quadrants and point F at (3, -3)Point F is at (3, -3). Which quadrant is it in?
MIRROR IMAGES
  • Read the question.
  • Tap your answer.
Ring Toss is at (3, 2). Its mirror image across the y-axis is at which point?
Ring Toss is at (3, 2). Its mirror image across the x-axis is at which point?
Hop Course is at (-4, 2). Its mirror image across the x-axis is at which point?
Scoop Station is at (-3, -3). Its mirror image across the y-axis is at which point?
HOW FAR APART?
  • Read the question.
  • Tap your answer.
Ring Toss is at (3, 2) and Hop Course is at (-4, 2). How many units apart are they?
Ring Toss is at (3, 2) and Finish Line is at (3, -3). How many units apart are they?
Hop Course is at (-4, 2) and Scoop Station is at (-4, -3). How many units apart are they?
How many units apart are the Hop Course (-4, 2) and the Ring Toss (3, 2)?
Which quadrant holds the Scoop Station at (-3, -3)? Type the Roman numeral.
Try it
Tape two strips into a cross on the floor. Mark 0 at the center and count steps along each arm.
Place an object at (2, -1) and another at (-2, -1). Count the units between them.
Draw the four-quadrant map with all five stations plotted and labeled. Add one station of your own in Quadrant IV.

Map drawn. Tomorrow you find signed numbers in everyday life and review the whole week.

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