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Chess Club: Pairings, Clocks, and Ratings worksheet preview

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Chess Club: Pairings, Clocks, and Ratings

Solve chess club systems by inspection and algebra, estimate intersections on graphs, and distinguish approximate from exact solutions.

Grade 8MathInteractive · Printable

Aligned to8.EE.C.8.b

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What’s included

  • Single worksheet
  • Auto-graded online
  • 1 Common Core standard
  • Printable answer key
  • 14 questions
  • Classroom-ready

Details

Format
Interactive · Printable
Grade
Grade 8
Subject
Math
Question types
Fill in the blank, Multiple choice, Short answer

About this worksheet

What students practice

  • Students solve systems of two linear equations using substitution and elimination.
  • Students identify simple systems with one, no, or infinitely many solutions by inspection.
  • Students estimate intersections from graphs and distinguish approximate from exact solutions.

How to use

Use after introducing substitution and elimination. Have students show algebra on separate paper and sketch the added lines directly on the grids.

Curriculum

Common Core standard covered

8.EE.C.8.b

Solve systems of two linear equations with algebra, estimate solutions by graphing, and solve simple cases by inspection.

Preview

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Name Date

Chess Club: Pairings, Clocks, and Ratings

Solve tournament systems by inspection, algebra, and graphing.

Read the Rating Rules

Use inspection for Questions 1–3. Choose a useful substitution for Question 4. Rating changes may be positive, negative, or zero.

1.
Two players have equal signed rating changes, x and y. Their changes add to zero.
x = y
x + y = 0

x =   points; y =   points

2.
Two tournament records describe the same players' ratings, x and y.
x − y = 9
2x − 2y = 12
What can you tell by inspection?
  • A. The system has exactly one solution with x − y = 6.
  • B. The system has exactly one solution with x − y = 9.
  • C. The system has no solution because the required differences disagree.
  • D. The system has infinitely many solutions with x − y = 9.
3.
The chess club tests two rules for practice credits, x and y. Treat the variables as real numbers.
x + 2y = 10
0.5x + y = 5
Which statement describes the system?
  • A. It has infinitely many solutions because the equations are equivalent.
  • B. It has no solution because the constants are different.
  • C. It has only the solution (10, 0) because y must be zero.
  • D. It has only the solution (0, 5) because x must be zero.

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