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Games Behind worksheet

Grade 6 · CCSS 6.EE.A.2.c, 6.RP.A.2

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

1.
Problem 1.
- Teams in the standings: 5 teams
- Your team: wins: 80
- Your team: losses: 74
- Team 2: wins: 105
- Team 2: losses: 50
- Team 3: wins: 72
- Team 3: losses: 55
- Team 4: wins: 65
- Team 4: losses: 80
- Team 5: wins: 85
- Team 5: losses: 80
Find: Your team's games behind the leader
Answer
2.
Problem 2.
- Teams in the standings: 3 teams
- Your team: wins: 85
- Your team: losses: 55
- Team 2: wins: 105
- Team 2: losses: 75
- Team 3: wins: 110
- Team 3: losses: 62
Find: Your team's games behind the leader
Answer
3.
Problem 3.
- Teams in the standings: 6 teams
- Your team: wins: 105
- Your team: losses: 75
- Team 2: wins: 64
- Team 2: losses: 65
- Team 3: wins: 90
- Team 3: losses: 70
- Team 4: wins: 68
- Team 4: losses: 50
- Team 5: wins: 65
- Team 5: losses: 90
- Team 6: wins: 92
- Team 6: losses: 85
Find: Your team's games behind the leader
Answer
4.
Problem 4.
- Teams in the standings: 5 teams
- Your team: wins: 75
- Your team: losses: 79
- Team 2: wins: 76
- Team 2: losses: 80
- Team 3: wins: 80
- Team 3: losses: 55
- Team 4: wins: 70
- Team 4: losses: 74
- Team 5: wins: 60
- Team 5: losses: 95
Find: Your team's games behind the leader
Answer
5.
Problem 5.
- Teams in the standings: 3 teams
- Your team: wins: 104
- Your team: losses: 70
- Team 2: wins: 90
- Team 2: losses: 62
- Team 3: wins: 100
- Team 3: losses: 62
Find: Your team's games behind the leader
Answer
6.
Problem 6.
- Teams in the standings: 5 teams
- Your team: wins: 75
- Your team: losses: 60
- Team 2: wins: 80
- Team 2: losses: 60
- Team 3: wins: 90
- Team 3: losses: 74
- Team 4: wins: 60
- Team 4: losses: 74
- Team 5: wins: 55
- Team 5: losses: 65
Find: Your team's games behind the leader
Answer
7.
Problem 7.
- Teams in the standings: 4 teams
- Your team: wins: 110
- Your team: losses: 75
- Team 2: wins: 100
- Team 2: losses: 56
- Team 3: wins: 70
- Team 3: losses: 90
- Team 4: wins: 65
- Team 4: losses: 94
Find: Your team's games behind the leader
Answer
8.
Problem 8.
- Teams in the standings: 2 teams
- Your team: wins: 90
- Your team: losses: 90
- Team 2: wins: 90
- Team 2: losses: 72
Find: Your team's games behind the leader
Answer
9.
Problem 9.
- Teams in the standings: 4 teams
- Your team: wins: 65
- Your team: losses: 54
- Team 2: wins: 108
- Team 2: losses: 65
- Team 3: wins: 90
- Team 3: losses: 75
- Team 4: wins: 90
- Team 4: losses: 70
Find: Your team's games behind the leader
Answer
10.
Problem 10.
- Teams in the standings: 3 teams
- Your team: wins: 105
- Your team: losses: 70
- Team 2: wins: 70
- Team 2: losses: 61
- Team 3: wins: 55
- Team 3: losses: 72
Find: Your team's games behind the leader
Answer

Answer key: Games Behind worksheet

1. Your team's games behind the leader: 24.5
1. Rank the teams by winning percentage (wins divided by games played), the way standings do
  $Team 2 105–50 (.677), Team 3 72–55 (.567), Your team 80–74 (.519), Team 5 85–80 (.515), Team 4 65–80 (.448)$
2. Games behind (GB) adds the leader's extra wins (W) to your extra losses (L), then halves it
  $GB$ $= \frac{(W leader - W) + (L - L leader)}{2}$
3. Put in your team's record and the leader's (Team 2)
  $\frac{(105 - 80) + (74 - 50)}{2}$ $= 24.5$
4. Do the same with Team 3, the team directly above you, to see how close the next spot is
  $\frac{(72 - 80) + (74 - 55)}{2}$ $= 5.5$
2. Your team's games behind the leader: 9
1. Rank the teams by winning percentage (wins divided by games played), the way standings do
  $Team 3 110–62 (.640), Your team 85–55 (.607), Team 2 105–75 (.583)$
2. Games behind (GB) adds the leader's extra wins (W) to your extra losses (L), then halves it
  $GB$ $= \frac{(W leader - W) + (L - L leader)}{2}$
3. Put in your team's record and the leader's (Team 3)
  $\frac{(110 - 85) + (55 - 62)}{2}$ $= 9$
4. Do the same with Team 3, the team directly above you, to see how close the next spot is
  $\frac{(110 - 85) + (55 - 62)}{2}$ $= 9$
3. Your team's games behind the leader: 0
1. Rank the teams by winning percentage (wins divided by games played), the way standings do
  $Your team 105–75 (.583), Team 4 68–50 (.576), Team 3 90–70 (.563), Team 6 92–85 (.520), Team 2 64–65 (.496), Team 5 65–90 (.419)$
2. Games behind (GB) adds the leader's extra wins (W) to your extra losses (L), then halves it
  $GB$ $= \frac{(W leader - W) + (L - L leader)}{2}$
3. Your team leads, so its games behind is zero
  $\frac{(105 - 105) + (75 - 75)}{2}$ $= 0$
4. Your team's games behind the leader: 14.5
1. Rank the teams by winning percentage (wins divided by games played), the way standings do
  $Team 3 80–55 (.593), Team 2 76–80 (.487), Your team 75–79 (.487), Team 4 70–74 (.486), Team 5 60–95 (.387)$
2. Games behind (GB) adds the leader's extra wins (W) to your extra losses (L), then halves it
  $GB$ $= \frac{(W leader - W) + (L - L leader)}{2}$
3. Put in your team's record and the leader's (Team 3)
  $\frac{(80 - 75) + (79 - 55)}{2}$ $= 14.5$
4. Do the same with Team 2, the team directly above you, to see how close the next spot is
  $\frac{(76 - 75) + (79 - 80)}{2}$ $= 0$
5. Your team's games behind the leader: 2
1. Rank the teams by winning percentage (wins divided by games played), the way standings do
  $Team 3 100–62 (.617), Your team 104–70 (.598), Team 2 90–62 (.592)$
2. Games behind (GB) adds the leader's extra wins (W) to your extra losses (L), then halves it
  $GB$ $= \frac{(W leader - W) + (L - L leader)}{2}$
3. Put in your team's record and the leader's (Team 3)
  $\frac{(100 - 104) + (70 - 62)}{2}$ $= 2$
4. Do the same with Team 3, the team directly above you, to see how close the next spot is
  $\frac{(100 - 104) + (70 - 62)}{2}$ $= 2$
6. Your team's games behind the leader: 2.5
1. Rank the teams by winning percentage (wins divided by games played), the way standings do
  $Team 2 80–60 (.571), Your team 75–60 (.556), Team 3 90–74 (.549), Team 5 55–65 (.458), Team 4 60–74 (.448)$
2. Games behind (GB) adds the leader's extra wins (W) to your extra losses (L), then halves it
  $GB$ $= \frac{(W leader - W) + (L - L leader)}{2}$
3. Put in your team's record and the leader's (Team 2)
  $\frac{(80 - 75) + (60 - 60)}{2}$ $= 2.5$
4. Do the same with Team 2, the team directly above you, to see how close the next spot is
  $\frac{(80 - 75) + (60 - 60)}{2}$ $= 2.5$
7. Your team's games behind the leader: 4.5
1. Rank the teams by winning percentage (wins divided by games played), the way standings do
  $Team 2 100–56 (.641), Your team 110–75 (.595), Team 3 70–90 (.438), Team 4 65–94 (.409)$
2. Games behind (GB) adds the leader's extra wins (W) to your extra losses (L), then halves it
  $GB$ $= \frac{(W leader - W) + (L - L leader)}{2}$
3. Put in your team's record and the leader's (Team 2)
  $\frac{(100 - 110) + (75 - 56)}{2}$ $= 4.5$
4. Do the same with Team 2, the team directly above you, to see how close the next spot is
  $\frac{(100 - 110) + (75 - 56)}{2}$ $= 4.5$
8. Your team's games behind the leader: 9
1. Rank the teams by winning percentage (wins divided by games played), the way standings do
  $Team 2 90–72 (.556), Your team 90–90 (.500)$
2. Games behind (GB) adds the leader's extra wins (W) to your extra losses (L), then halves it
  $GB$ $= \frac{(W leader - W) + (L - L leader)}{2}$
3. Put in your team's record and the leader's (Team 2)
  $\frac{(90 - 90) + (90 - 72)}{2}$ $= 9$
4. Do the same with Team 2, the team directly above you, to see how close the next spot is
  $\frac{(90 - 90) + (90 - 72)}{2}$ $= 9$
9. Your team's games behind the leader: 16
1. Rank the teams by winning percentage (wins divided by games played), the way standings do
  $Team 2 108–65 (.624), Team 4 90–70 (.563), Your team 65–54 (.546), Team 3 90–75 (.545)$
2. Games behind (GB) adds the leader's extra wins (W) to your extra losses (L), then halves it
  $GB$ $= \frac{(W leader - W) + (L - L leader)}{2}$
3. Put in your team's record and the leader's (Team 2)
  $\frac{(108 - 65) + (54 - 65)}{2}$ $= 16$
4. Do the same with Team 4, the team directly above you, to see how close the next spot is
  $\frac{(90 - 65) + (54 - 70)}{2}$ $= 4.5$
10. Your team's games behind the leader: 0
1. Rank the teams by winning percentage (wins divided by games played), the way standings do
  $Your team 105–70 (.600), Team 2 70–61 (.534), Team 3 55–72 (.433)$
2. Games behind (GB) adds the leader's extra wins (W) to your extra losses (L), then halves it
  $GB$ $= \frac{(W leader - W) + (L - L leader)}{2}$
3. Your team leads, so its games behind is zero
  $\frac{(105 - 105) + (70 - 70)}{2}$ $= 0$