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Magic Number worksheet

Grade 6 · CCSS 6.EE.A.2.c

Solve each problem and show your work. Round answers to 2 decimal places where needed.

1.
Problem 1.
- Games in the season: 185
- Your team's wins: 110
- Your team's losses: 65
- Closest rival's wins: 105
- Closest rival's losses: 52
- Your team wins a tie with this rival (holds the tiebreaker): No
Find: Magic number
Answer
2.
Problem 2.
- Games in the season: 175
- Your team's wins: 105
- Your team's losses: 60
- Closest rival's wins: 85
- Closest rival's losses: 45
- Your team wins a tie with this rival (holds the tiebreaker): No
Find: Magic number
Answer
3.
Problem 3.
- Games in the season: 150
- Your team's wins: 80
- Your team's losses: 68
- Closest rival's wins: 80
- Closest rival's losses: 60
- Your team wins a tie with this rival (holds the tiebreaker): No
Find: Magic number
Answer
4.
Problem 4.
- Games in the season: 180
- Your team's wins: 78
- Your team's losses: 75
- Closest rival's wins: 85
- Closest rival's losses: 50
- Your team wins a tie with this rival (holds the tiebreaker): No
Find: Magic number
Answer
5.
Problem 5.
- Games in the season: 160
- Your team's wins: 80
- Your team's losses: 55
- Closest rival's wins: 90
- Closest rival's losses: 65
- Your team wins a tie with this rival (holds the tiebreaker): No
Find: Magic number
Answer
6.
Problem 6.
- Games in the season: 130
- Your team's wins: 70
- Your team's losses: 55
- Closest rival's wins: 80
- Closest rival's losses: 50
- Your team wins a tie with this rival (holds the tiebreaker): No
Find: Magic number
Answer
7.
Problem 7.
- Games in the season: 200
- Your team's wins: 90
- Your team's losses: 66
- Closest rival's wins: 80
- Closest rival's losses: 60
- Your team wins a tie with this rival (holds the tiebreaker): No
Find: Magic number
Answer
8.
Problem 8.
- Games in the season: 200
- Your team's wins: 65
- Your team's losses: 65
- Closest rival's wins: 90
- Closest rival's losses: 85
- Your team wins a tie with this rival (holds the tiebreaker): No
Find: Magic number
Answer
9.
Problem 9.
- Games in the season: 180
- Your team's wins: 120
- Your team's losses: 55
- Closest rival's wins: 86
- Closest rival's losses: 74
- Your team wins a tie with this rival (holds the tiebreaker): No
Find: Magic number
Answer
10.
Problem 10.
- Games in the season: 160
- Your team's wins: 96
- Your team's losses: 53
- Closest rival's wins: 85
- Closest rival's losses: 48
- Your team wins a tie with this rival (holds the tiebreaker): No
Find: Magic number
Answer

Answer key: Magic Number worksheet

1. Magic number: 24
1. Start from the games in the season plus one, so a tie isn't enough. Take away your wins and the rival's losses
  $M$ $= G + 1 - W - L (rival)$
2. Put in the season length and the two teams' records
  $185 + 1 - 110 - 52$ $= 24$
3. Add up the games both teams have left. That's the most the magic number can still fall
  $(185 - 175) + (185 - 157)$ $= 38$
4. Find how many games ahead you are: add the win gap and the loss gap, then halve it
  $\frac{(110 - 105) + (52 - 65)}{2}$ $= −4$
2. Magic number: 26
1. Start from the games in the season plus one, so a tie isn't enough. Take away your wins and the rival's losses
  $M$ $= G + 1 - W - L (rival)$
2. Put in the season length and the two teams' records
  $175 + 1 - 105 - 45$ $= 26$
3. Add up the games both teams have left. That's the most the magic number can still fall
  $(175 - 165) + (175 - 130)$ $= 55$
4. Find how many games ahead you are: add the win gap and the loss gap, then halve it
  $\frac{(105 - 85) + (45 - 60)}{2}$ $= 2.5$
3. Magic number: 11
1. Start from the games in the season plus one, so a tie isn't enough. Take away your wins and the rival's losses
  $M$ $= G + 1 - W - L (rival)$
2. Put in the season length and the two teams' records
  $150 + 1 - 80 - 60$ $= 11$
3. Add up the games both teams have left. That's the most the magic number can still fall
  $(150 - 148) + (150 - 140)$ $= 12$
4. Find how many games ahead you are: add the win gap and the loss gap, then halve it
  $\frac{(80 - 80) + (60 - 68)}{2}$ $= −4$
4. Magic number: 53
1. Start from the games in the season plus one, so a tie isn't enough. Take away your wins and the rival's losses
  $M$ $= G + 1 - W - L (rival)$
2. Put in the season length and the two teams' records
  $180 + 1 - 78 - 50$ $= 53$
3. Add up the games both teams have left. That's the most the magic number can still fall
  $(180 - 153) + (180 - 135)$ $= 72$
4. Find how many games ahead you are: add the win gap and the loss gap, then halve it
  $\frac{(78 - 85) + (50 - 75)}{2}$ $= −16$
5. Magic number: 16
1. Start from the games in the season plus one, so a tie isn't enough. Take away your wins and the rival's losses
  $M$ $= G + 1 - W - L (rival)$
2. Put in the season length and the two teams' records
  $160 + 1 - 80 - 65$ $= 16$
3. Add up the games both teams have left. That's the most the magic number can still fall
  $(160 - 135) + (160 - 155)$ $= 30$
4. Find how many games ahead you are: add the win gap and the loss gap, then halve it
  $\frac{(80 - 90) + (65 - 55)}{2}$ $= 0$
6. Magic number: 11
1. Start from the games in the season plus one, so a tie isn't enough. Take away your wins and the rival's losses
  $M$ $= G + 1 - W - L (rival)$
2. Put in the season length and the two teams' records
  $130 + 1 - 70 - 50$ $= 11$
3. Add up the games both teams have left. That's the most the magic number can still fall
  $(130 - 125) + (130 - 130)$ $= 5$
4. Find how many games ahead you are: add the win gap and the loss gap, then halve it
  $\frac{(70 - 80) + (50 - 55)}{2}$ $= −7.5$
7. Magic number: 51
1. Start from the games in the season plus one, so a tie isn't enough. Take away your wins and the rival's losses
  $M$ $= G + 1 - W - L (rival)$
2. Put in the season length and the two teams' records
  $200 + 1 - 90 - 60$ $= 51$
3. Add up the games both teams have left. That's the most the magic number can still fall
  $(200 - 156) + (200 - 140)$ $= 104$
4. Find how many games ahead you are: add the win gap and the loss gap, then halve it
  $\frac{(90 - 80) + (60 - 66)}{2}$ $= 2$
8. Magic number: 51
1. Start from the games in the season plus one, so a tie isn't enough. Take away your wins and the rival's losses
  $M$ $= G + 1 - W - L (rival)$
2. Put in the season length and the two teams' records
  $200 + 1 - 65 - 85$ $= 51$
3. Add up the games both teams have left. That's the most the magic number can still fall
  $(200 - 130) + (200 - 175)$ $= 95$
4. Find how many games ahead you are: add the win gap and the loss gap, then halve it
  $\frac{(65 - 90) + (85 - 65)}{2}$ $= −2.5$
9. Magic number: 0
1. Start from the games in the season plus one, so a tie isn't enough. Take away your wins and the rival's losses
  $M$ $= G + 1 - W - L (rival)$
2. Put in the season length and the two teams' records
  $180 + 1 - 120 - 74$ $= −13$
3. Zero or less means the spot is already clinched
  $M$ $= 0$
4. Add up the games both teams have left. That's the most the magic number can still fall
  $(180 - 175) + (180 - 160)$ $= 25$
5. Find how many games ahead you are: add the win gap and the loss gap, then halve it
  $\frac{(120 - 86) + (74 - 55)}{2}$ $= 26.5$
10. Magic number: 17
1. Start from the games in the season plus one, so a tie isn't enough. Take away your wins and the rival's losses
  $M$ $= G + 1 - W - L (rival)$
2. Put in the season length and the two teams' records
  $160 + 1 - 96 - 48$ $= 17$
3. Add up the games both teams have left. That's the most the magic number can still fall
  $(160 - 149) + (160 - 133)$ $= 38$
4. Find how many games ahead you are: add the win gap and the loss gap, then halve it
  $\frac{(96 - 85) + (48 - 53)}{2}$ $= 3$