Astoundingly Average Number Game

This applet turns average into a pattern-building puzzle. Students drag number cards into shapes and test whether the center number is the average of the surrounding numbers.

How to Use It

• Choose a task from the drop-down menu, then read the instruction box carefully.
• Drag cards into the circles first, then decide what number should go in the center.
• Click Check to test the arrangement.
• Click Show Thinking to watch one guided solution, or to see a slow explanation of why a task has no solution.
• Use Reset to clear the board and try a different strategy.

Pedagogical Focus

• Tasks 1 to 3 are good for helping students connect sum, average, and missing number.
• Tasks 5 and 6 extend the idea to multiple shapes, encouraging students to organize information and plan systematically.
• Tasks 4 and 7 are especially rich because the goal is to prove that no solution exists, not just to keep guessing.

Suggested Lesson Flow

1. Predict a possible center value before dragging any cards.
2. Try one full solution without help.
3. Use Show Thinking only after an attempt, and compare the applet's reasoning with the student's reasoning.
4. Ask students to explain why a solution works, not just where the cards go.
5. For Tasks 4 and 7, ask for a proof of impossibility in words or symbols.

Teacher Prompts

• What has to be true about the sum of the outer numbers before the average can be an integer?
• Is there only one solution, or many solutions? How do you know?
• When a task has no solution, what is the fastest way to prove it?