Preserve the total
Move counters between friends without adding or removing any.
Fair-Share Average
Redistribute counters among three friends while preserving their total to reveal the arithmetic mean.
Grades 3–5 · Math
Your goal
Redistribute all 15 counters so three friends each have the same number. Move one counter at a time.
Reduced motion is on. The controls still update the scene.
Ari has 2, Bo has 8, and Cleo has 5. Total 15. The fair share is 15 divided by 3, or 5 each.
Each counter is one whole item. The total is conserved on every transfer. The arithmetic mean is the total divided by the number of friends, even before everyone has an equal pile. These goals use totals that divide evenly into three whole shares.
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Learn with Fair-Share Average
Fair-Share Average gives elementary students a hands on interpretation of the arithmetic mean. Three friends begin with unequal piles of counters. Children choose a source and destination, then move one counter at a time until all three piles match. The total remains visible and unchanged throughout, while the feedback divides that total by the number of friends. Different goals use different whole number fair shares. Students can explain why redistribution changes individual counts without changing the mean, and why an average describes a fair share even before the piles are equal.
What to look for
Find the fair share
Divide the total number of counters by three friends.
Transfer toward balance
Move a counter from a pile above the fair share to one below it.
For teachers and curious learners
Explain the arithmetic mean as an equal share of a conserved total. Ask students to predict what will happen, change one setting, and explain what they observe. Learn gives a starting point. Practice and Challenge offer new goals with the same scene.
Each counter is one whole item. The total is conserved on every transfer. The arithmetic mean is the total divided by the number of friends, even before everyone has an equal pile. These goals use totals that divide evenly into three whole shares.