Math Arguments

Problems, Questions, and Puzzles to spark discussion and argument in the maths classroom.

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Item 409

Average Shmaverage

Assume a classroom where every grade has equal weight. Here are two sets of grades:

Student A (ave=80.0): 100, 100, 100, �0, �100
Student B (ave=80.2): �81, �80, 80, �80, �80

Questions:

  1. Who has better mastery?�

  2. Who will be better prepared for the next course?

  3. Which would you rather be?

Another set of grades, in sequence:

Student A: 25, 25, 50, 100, 100
Student B: 100, 100, 50, 25, 25

Same questions:
  1. Who has better mastery?�

  2. Who will be better prepared for the next course?

  3. Which would you rather be?


What other mathematical aspects of this caught your attention? What do you wonder about the situation?

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Notice, Wonder
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Examples from Step 1: Try Something.
More Information:
Noticing and wondering is a tool to help students:
- Understand the story, the quantities, and the relationships in the problem.
- Understand what the problem is asking and what the answer will look like. Have some ideas to begin to solve the problem.
More Here at NCTM


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