Case Study

One envelope and three counters on the left equal eight counters on the right, showing x+3=8x + 3 = 8. What does each part mean in algebra: the envelope, one counter, and the center line?

Case context: An envelope holds an unknown number of counters. A counter is one item. A center line splits the left and right sides. Here the model shows x+3=8x + 3 = 8.

Question: One envelope and three counters on the left equal eight counters on the right, showing x+3=8x + 3 = 8. What does each part mean in algebra: the envelope, one counter, and the center line?

Sample answer: The envelope is the unknown, the variable xx. One counter is a known number, a constant. The center line is the equal sign, ==.

Key points:

  • The envelope represents the variable, an unknown number such as xx.
  • One counter represents a constant, a known number.
  • The center line represents the equal sign ==.

Rubric: Full credit: correctly names all three parts (envelope = variable/unknown, counter = constant/known number, center line = equal sign). Partial credit: names one or two parts correctly.

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Updated 2026-07-20

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