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Ratios and Data 6-8 / Week 07 / Friday
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Week 07 · Adding and Subtracting Signed Numbers

Friday

Signed numbers everywhere
// Hops on the number line
⏱ about 20 min

Friday: Signed Numbers Everywhere

Rocket slides into his chair at the Numbers Desk. "I counted signed numbers all day. Nine of them."

"Such as?" Raven asks, pencil ready.

"The elevator at the library has floor -1 for the parking level," Rocket says. "The freezer is set to -18."

"My game score went -5, then +12. The dock ladder has rungs below the water, so those are negative too."

Raven writes them down. "What do you notice about every one of them?"

"Each one needs a zero," Rocket says. "Ground floor, freezing, zero points, the water line."

Nova brightens. "Zero is the agreement," she says. "Everything else is a hop from there."

"Then let us review the hops," Raven says, "before Field Day scoring starts for real."

Where the zero is

Every signed number needs an agreed zero. Above it is positive, below it is negative.

An elevator calls the ground floor 0, so a parking level is -1. A freezer setting of -18 means 18 degrees below zero.

A game score starts at 0. Losing 5 points is -5, and then winning 12 points is -5 + 12 = 7.

A dock ladder: rungs above the water are positive, rungs below are negative. Climbing is adding a positive number.

Nothing about these numbers is new. They are the hops you walked in the hallway.

Adding and subtracting, all together

  • Adding a positive number hops right. Adding a negative number hops left.
  • A number and its opposite add to 0. They are a zero pair.
  • Subtracting a number is adding its opposite: p - q = p + (-q).
  • The distance between two numbers is the absolute value of their difference.
  • Change is the new value minus the old value. A negative change means it went down.
EVERYDAY HOPS
  • Read the question.
  • Tap your answer.
A game score goes to -5, then wins 12 points. What is the score now?
An elevator is at floor -1 and goes down 2 floors. What floor is it on now?
A freezer at -18 warms by 6 degrees while the door is open. What does it read?
Rocket stands on the dock ladder rung at -3 and climbs 5 rungs. Which rung is he on?
THREE STEPS IN A ROW
  • Read the question.
  • Tap your answer.
4 + (-9) + 3 = ?
-6 - (-2) + 5 = ?
-1 + (-1) + (-1) = ?
DISTANCE OR CHANGE?
  • Read the question.
  • Tap your answer.
A freezer reads -18 and the kitchen reads 6. How many degrees apart are they?
A game score drops from 7 to -5 in one round. What was the change?
An elevator goes from floor -1 to floor 3. How many floors did it climb?
PUT THE HOPS IN ORDER TO SOLVE 7 - (-2) - 5
  • ?Rewrite: 7 + 2 + (-5)
  • ?Start at 7 and hop right 2 to land on 9
  • ?Hop left 5 from 9 to land on 4
  • ?Check: the answer 4 is positive, and the hops agree
WHY THIS EXERCISEThe same four moves solve any string of additions and subtractions.
StatementTrue or false?
Adding a negative number hops to the right.?
A number and its opposite add to 0.?
-7 - (-7) = 0?
2 - 9 = 7?
The distance between -4 and 4 is 8.?
WHY THIS EXERCISEThis is the week in five lines. If all five are clear, you are ready to multiply next week.
Try it
Over dinner, find three signed numbers around your home. A thermostat, a game score, a basement level.
For each one, say where the zero is and what a hop up or down would mean.
Draw a dock ladder as a vertical number line with the water at 0. Show a climb from -3 up 5 rungs.

Terrific week. You can add and subtract any signed numbers now. Tomorrow is Data Day with a hop game for the whole family.

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