Education World ® - Lesson Planning Skills Page: Bowling Math Work ... - Free Printable

Problem Overview:

The task involves calculating the total scores for three players in each of two bowling games based on their frame-by-frame scores. The goal is to determine the winner of each game by summing up the scores for each player.

Key Rules for Bowling Scoring:

1. Strike (X): A strike means all 10 pins are knocked down in one roll. The score for a strike is 10 plus the number of pins knocked down in the next two rolls.
2. Spare (/): A spare means all 10 pins are knocked down in two rolls. The score for a spare is 10 plus the number of pins knocked down in the next roll.
3. Open Frame: If fewer than 10 pins are knocked down in two rolls, the score is simply the total number of pins knocked down in those two rolls.
4. Tenth Frame Bonus Rolls: In the tenth frame, if a strike or spare is rolled, bonus rolls are allowed to complete the scoring.

Solution Approach:

We will calculate the scores for each player in both games step by step, following the rules above.

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Bowling Math Work Sheet #1

#### Player: Jeff
Frame-by-frame scores:
- Frame 1: 2, 4 → 6
- Frame 2: X (Strike) → 10 + next two rolls (3, 7) = 10 + 3 + 7 = 20
- Frame 3: 3, / (Spare) → 10 + next roll (4) = 10 + 4 = 14
- Frame 4: 0, 7 → 7
- Frame 5: 2, 0 → 2
- Frame 6: 4, 8 → 12
- Frame 7: 1, 0 → 1
- Frame 8: 0, 9 → 9
- Frame 9: /, 7 (Spare) → 10 + next roll (1) = 10 + 1 = 11
- Frame 10: 1 → 1

Total Score for Jeff:
\[ 6 + 20 + 14 + 7 + 2 + 12 + 1 + 9 + 11 + 1 = 83 \]

#### Player: Lisa
Frame-by-frame scores:
- Frame 1: X (Strike) → 10 + next two rolls (1, 7) = 10 + 1 + 7 = 18
- Frame 2: 6, 3 → 9
- Frame 3: X (Strike) → 10 + next two rolls (2, 4) = 10 + 2 + 4 = 16
- Frame 4: 3, 4 → 7
- Frame 5: 5, 2 → 7
- Frame 6: 0, 0 → 0
- Frame 7: 9, 2 → 11
- Frame 8: 7 → 7

Total Score for Lisa:
\[ 18 + 9 + 16 + 7 + 7 + 0 + 11 + 7 = 75 \]

#### Player: Ellen
Frame-by-frame scores:
- Frame 1: 2, 3, / (Spare) → 10 + next roll (7) = 10 + 7 = 17
- Frame 2: 4, 2, 8 (Strike) → 10 + next two rolls (0, 8) = 10 + 0 + 8 = 18
- Frame 3: 1, 2 → 3
- Frame 4: 5, 1 → 6
- Frame 5: 8, 4, 4 (Strike) → 10 + next two rolls (4, 0) = 10 + 4 + 0 = 14
- Frame 6: 9, / (Spare) → 10 + next roll (7) = 10 + 7 = 17

Total Score for Ellen:
\[ 17 + 18 + 3 + 6 + 14 + 17 = 75 \]

#### Winner of Game 1:
Jeff has the highest score with 83 points. Lisa and Ellen both have 75 points.

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Bowling Math Work Sheet #2

#### Player: Kyle
Frame-by-frame scores:
- Frame 1: X (Strike) → 10 + next two rolls (0, 1) = 10 + 0 + 1 = 11
- Frame 2: 3, 1 → 4
- Frame 3: 8, 2 → 10
- Frame 4: 5, 2 → 7
- Frame 5: 5, 3 → 8
- Frame 6: 2, 2 → 4
- Frame 7: 4, 8 → 12
- Frame 8: 1, 2 → 3

Total Score for Kyle:
\[ 11 + 4 + 10 + 7 + 8 + 4 + 12 + 3 = 69 \]

#### Player: Tanya
Frame-by-frame scores:
- Frame 1: X (Strike) → 10 + next two rolls (9, 6) = 10 + 9 + 6 = 25
- Frame 2: 1, 5, 4 (Spare) → 10 + next roll (3) = 10 + 3 = 13
- Frame 3: 1, 6 → 7
- Frame 4: 2, 3 → 5
- Frame 5: 5, 4, 5 (Strike) → 10 + next two rolls (3, 3) = 10 + 3 + 3 = 16

Total Score for Tanya:
\[ 25 + 13 + 7 + 5 + 16 = 66 \]

#### Player: Josh
Frame-by-frame scores:
- Frame 1: 2, 5 → 7
- Frame 2: 6, 0 → 6
- Frame 3: 4, 5 → 9
- Frame 4: 0, 7 → 7
- Frame 5: 9, 0, X (Strike) → 10 + next two rolls (1, 1) = 10 + 1 + 1 = 12
- Frame 6: 5, 3 → 8
- Frame 7: 2, 4 → 6

Total Score for Josh:
\[ 7 + 6 + 9 + 7 + 12 + 8 + 6 = 55 \]

#### Winner of Game 2:
Kyle has the highest score with 69 points. Tanya has 66 points, and Josh has 55 points.

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Final Answers:

- Winner of Game 1: Jeff (83 points)
- Winner of Game 2: Kyle (69 points)

\[
\boxed{\text{Jeff, Kyle}}
\]