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

Data Day

Data Day: the hop game
// Hops on the number line
⏱ about 20 min

Data Day: The Hop Game

Saturday morning, the whole crew sits around the Numbers Desk with a stack of paper slips.

Each slip has a signed number on it, from -6 to 6. Rocket shuffles them face down.

"Everyone starts at 0," Raven says. "Draw a slip, add it to your total, and say the new total out loud."

Rocket draws -4. "-4." Then 3. "-1." Then -5. "-6!" He groans.

Raven draws 2, then 2, then -3. "1."

Nova keeps the running tally on the whiteboard. "What do you notice about Rocket's three slips?" she asks.

"They add to -6," Rocket says. "I need a +6 to get back to zero. A zero pair."

"First to reach 10 or -10 wins," Raven says. "Either direction counts. Draw!"

  1. Adding a positive number hops right on the number line. Adding a negative number hops left.
  2. A number and its opposite add to 0. They are a zero pair, or additive inverses.
  3. Subtracting a number is the same as adding its opposite: p - q = p + (-q).
  4. The distance between two numbers is the absolute value of their difference, never negative.
  5. A change is the new value minus the old value. The crew's thermometer log and par scores are signed sums.
◇ FAMILY HOP GAME
Cut twenty paper slips. Write the numbers -6 to -1 and 1 to 6 on them, two of some, until you have twenty.
Everyone starts at 0. Take turns drawing a slip and adding it to your total. Say the new total out loud.
Keep a tally table: player, slip drawn, new total. Check each other's hops on a paper number line.
First to reach 10 or -10, in either direction, wins the round. Play three rounds.
Harder round: draw a slip and subtract it instead. Remember, subtracting is adding the opposite.
For a grown-up
The hop game is the week in one activity: adding signed numbers, zero pairs and the subtraction rule.
Keep the small paper slips away from children under three. Play at the table so slips do not scatter.
If a total is disputed, hop it out on a paper number line together rather than telling the answer.
Safety first
Play at the table, never while walking around. Pick up every slip when you finish.
Keep the slips and any counters away from little ones and pets.
HOP GAME CHECKS
  • Read the question.
  • Tap your answer.
Rocket drew -4, then 3, then -5. What was his total?
Raven drew 2, 2 and -3. What was her total?
Rocket is at -6 and draws a 6. What is his total now?
In the harder round, Raven is at 1 and draws a 4 to subtract. What is her total?
Hop game checkTrue or false?
A player at -7 who draws 7 is back at 0.?
-7 + 7 = 0?
Subtracting -3 moves your total 3 to the left.?
-9 - (-3) = -6?
WHY THIS EXERCISEFast, sure hops make the hop game fun, and they make Field Day scoring quick too.
Draw a number line from -10 to 10 and mark every total you reached in one round of the hop game.
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