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Ratios and Data 6-8 / Week 08 / Data Day
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Week 08 · Multiplying and Dividing Signed Numbers

Data Day

Data Day: the toss tournament
// Repeated hops and the sign rules
⏱ about 20 min

Data Day: The Toss Tournament

Saturday morning the crew clears the hallway for a family paper ball tournament.

"Same rules as the lab," Raven announces. "A hit is +3, a miss is -2, five throws a round, four rounds each."

Rocket throws first. His rounds are 5, -5, 0 and 10. "A perfect round!" he shouts at the last one.

"What do you notice about your total across four rounds?" Raven asks.

"5 + (-5) + 0 + 10," Rocket says. "The first two are a zero pair. Total 10."

Nova hovers over the score table, her light steady. "And 10 ÷ 4 tells you your average round," she says.

Rocket divides. "2.5 points a round. Hmm. My perfect round carried me."

"Everyone throws," Raven says. "Then we compare averages."

  1. Multiplying by a whole number is repeated hopping: 3 × (-2) is three hops of -2, which is -6.
  2. Same signs give a positive product or quotient. Different signs give a negative one.
  3. The pattern of products shows why (-1) × (-1) = 1, and so does the distributive property.
  4. Dividing undoes multiplying: -6 ÷ 3 = -2. You can never divide by 0.
  5. Every fraction is a division. Its decimal ends, like 0.375, or repeats, like 0.333...
◇ FAMILY TOSS TOURNAMENT
Set up the bowl and the tape line from the lab. A hit is +3, a miss is -2, five throws a round.
Each player throws four rounds. Score every round as hits × 3 + misses × (-2).
Add the four round scores to get each player's total. Then divide the total by 4 for the average round.
Compare: who had the highest total? Who had the most zero pairs between rounds?
Bonus round: change a miss to -4 and rescore one round each. Which player's score changed most?
For a grown-up
The tournament uses every rule from the week: signed products, sums of signed numbers and dividing a total into equal parts.
Pick a cleared spot with nothing breakable. Soft paper balls only, thrown at the bowl, never at anyone.
If a total is disputed, write the round as a number sentence together rather than giving the answer.
Safety first
Throw only soft crumpled paper, only at the bowl. Keep little ones out of the throwing lane.
Pick up every paper ball afterward so no one slips.
TOURNAMENT CHECKS
  • Read the question.
  • Tap your answer.
Rocket's rounds were 5, -5, 0 and 10. What is his total?
Rocket's total of 10 came over 4 rounds. What was his average round?
A round with 2 hits and 3 misses. Hits are +3, misses are -2. What is the score?
A player's total was -8 over 4 rounds. What was the average round?
Tournament checkTrue or false?
A round of 0 hits and 5 misses scores -10.?
5 × (-2) = -10?
A negative total divided by 4 rounds gives a positive average.?
-8 ÷ 4 = -2?
WHY THIS EXERCISEScoring a tournament fast and correctly is exactly what Field Day will ask of you.
Draw a bar for each player's total, above or below a zero line. Mark each player's average with a dot.
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