Share the blocks. Find the balance.

SparkClass

See the mean as an equal share—and as the point where deviations balance.

CCSS 6.SP.A.3 · 6.SP.B.5c
Live Fair Share
30 blocks · conserved
01Find the totalAdd every tower. No block is created or removed.
02Move the extraBlocks travel from towers above the mean to those below it.
03Stop at equalEach tower reaches total ÷ count, including an exact partial block if needed.
01

Five towers share 30 blocks. Move blocks from above the mean to below it; the total stays 30.

Count5
Total30
Mean · Total ÷ Count6

Teacher notes: two meanings, one mean

Start with a prediction: “If everyone receives the same number of blocks, how many will each tower have?” Then use the model to test the reasoning.

1

Conserve the total

In Fair Share, students should account for every block before and after moving. The total and count stay fixed while the heights change. Try Already fair to discuss why no blocks need to move.

2

Make fractional means visible

Use Fractional mean or add an outlier. A final tower may include part of a unit block. The mean line and partial heights use the exact value; any repeating decimal is labeled with ≈ and accompanied by a fraction.

3

Balance signed deviations

Switch to Balance Point. Read each arrow as value − mean, not as an undirected distance. Ask why the positive and negative deviations must cancel. Add 0 as an outlier and observe that the mean shifts even though the total does not.

CCSS alignment: 6.SP.A.3 — recognize that a measure of center summarizes a distribution with a single number. 6.SP.B.5c — use the mean as a measure of center and relate it to the data distribution. The deviation model builds the conceptual foundation for mean absolute deviation.