About this Simulation

This interactive number game helps learners build a strong understanding of average by arranging number cards into shapes. The center number must be the average of the surrounding numbers, so students need to think about both sum and structure, not only trial and error.

Description

• Choose a task from the drop-down list.
• Drag cards into the outer circles first, then decide what number belongs in the center.
• Click Check to test whether the arrangement satisfies the average rule.
• Click Show Thinking to watch a guided step-by-step solution, or to see a slow explanation of why some tasks have no solution.
• Use Reset to clear the board and try a different approach.

Hints

• Task 1: Choose three outer numbers whose total is divisible by 3.
• Task 2: Solve one shape first, then use the remaining numbers to solve the second shape.
• Task 3: Add the three given outer numbers, then divide by 3 to find the missing center.
• Task 4: Let the four consecutive numbers be n, n+1, n+2, n+3. Look at the total carefully.
• Task 5: Try to split the numbers 1 to 8 into two groups with outer totals that produce whole-number centers.
• Task 6: For each pentagon, choose five outer numbers whose total is divisible by 5.
• Task 7: Add all the numbers from 1 to 12 and ask whether the total fits what three valid average patterns would require.

Pedagogical Notes

• Tasks 1 to 3 are good for introducing average as a relationship between sum and number of values.
• Tasks 5 and 6 encourage systematic search, grouping, and checking.
• Tasks 4 and 7 are rich proof tasks because the important outcome is to justify why no solution exists.