BOX COUNTING: INVESTIGATE A PATTERN
SME teaching draft, version 1, 2026-10-29. Not classroom-tested or externally reviewed.
Subject: mathematics and data. Suggested duration: two 45-minute sessions.
Materials: squared paper and pencil; optional spreadsheet or short script.
Goals: define a counting rule, make a labeled table and graph, explain how method affects a measurement.

LEARNER TASK
1. Divide a square into nine equal squares. Leave the center empty. Repeat within each remaining square. Draw the first two stages.
2. State your grid size, occupied-square rule and grid alignment. Count occupied squares at each stage.
3. Record stage, side length in cells, occupied squares and the rule. Keep corrections visible.
4. Make a labeled table and figure. Explain the pattern in your own words.
5. Compare with the worked example and explain one way the counting method could change a result.
6. Cite sources and assistance. State a limitation and your next check.

DELIVERABLE
One page: question, method, results table, figure, interpretation and limits.
Record supplied data as supplied, not as your own observations.

ADAPTATION
First investigation: two stages, counts and ratios; no logarithms needed.
High school: aligned box counts, log-log slope and comparison with shifted grids.
College / independent study: depth/offset comparison, scale selection and residuals or uncertainty.

SUGGESTED RUBRIC
Method / Evidence / Communication / Interpretation.
For each: 0 absent; 1 partly explained; 2 clear and supported. Maximum 8 points.
Adapt the rubric before assigning. A reproduction is not a claim of new mathematics.

SOURCE AND REUSE
Worked example: /examples/#fractal on this SME site.
Original assignment instructions and rubric: SME, CC BY 4.0.
https://creativecommons.org/licenses/by/4.0/
Credit SME, title, version and date; identify changes. Linked materials retain their own terms.
Student work requires its own publication permissions.