Sample, return and tally
Separate what a small sample showed from what is known about a hidden collection.
Adult planning suggestion: about4–6 · Observation & recall
- Players
- 2–4 per group
- Time
- 10–15 minutes
- Materials
- Six large folded slips: four R, two B; opaque envelope, pencil and tally sheet.
Prepare
An adult prepares four R and two B equal-size slips, folds them identically and shuffles inside an envelope. R and B also have distinct letters, so colour is optional. One child draws, one records and one checks return. Keep the original count hidden until the final reveal.
Play
Draw one slip without looking, open it, record R or B, refold and return it before mixing again. Complete six draws, then swap jobs for six more. Do not remove successful draws: that would change the collection. Each group uses a separate envelope; a class of thirty can work in ten groups of three.
Worked example
A possible first six results are R,R,B,R,R,R. This records five R sightings, not five different R slips. The same physical slip may be seen repeatedly. Ask the group to offer a tentative description before six further draws. A result with no B still does not prove B is absent.
Finish and check
After twelve draws, total both columns and check the total is twelve. Reveal and count the six actual slips. Compare observations with the real four-to-two collection without treating a mismatch as a mistake. There is no race or score for guessing the hidden counts.
Adaptation and limits
For young children, an adult records and reads the letters aloud. Use large paper rather than small objects; no blindfold is needed. Sampling is the task, not a test of a child’s intelligence. This shorter version removes the reference activity’s advanced numerical scoring.
Purpose, observation and provenance
Within this activity: Separate what a small sample showed from what is known about a hidden collection.
Ask whether zero B draws proves there are no B slips; accept uncertainty rather than reward a lucky guess.
Our rules, examples and printable diagrams are separately prepared. The earliest inventor of the broader mechanism is not established here.
NRICH — In the Bag — Sampling background, ages 11–14 in the source; our shorter paper activity and younger grouping are editorial adaptations, not validated by that page.
Age bands are planning suggestions. Goals describe observable actions, not measured long-term gains or institutional endorsement.
Free alternative: Copy the supplied grids, labels and cards onto reused paper. No specialist product is needed. Adults may prepare pieces or act as a scribe.
Printable materials
Preview at 100% scale, with browser headers and footers off. Cut with suitable help. Keep host keys separate. This is a manual tabletop kit, not an online opponent, automatic judge or solver.
Player materials · Sample, return and tally
Envelope label: R ×4 / B ×2 — hide this label from draw team.
Draw 1–12: result ___; returned □; tally R ___ B ___.
Player record · keep the host key separate
| Draw | Result | Returned? |
|---|---|---|
| ________ | ________ | ________ |
| ________ | ________ | ________ |
| ________ | ________ | ________ |
| ________ | ________ | ________ |
| ________ | ________ | ________ |
| ________ | ________ | ________ |
| ________ | ________ | ________ |
| ________ | ________ | ________ |
| ________ | ________ | ________ |
| ________ | ________ | ________ |
| ________ | ________ | ________ |
| ________ | ________ | ________ |
Host key · separate from players
Twelve records total twelve; the population remains R4/B2. Repeated sightings do not identify distinct slips.
Run the round
An adult prepares four R and two B equal-size slips, folds them identically and shuffles inside an envelope. R and B also have distinct letters, so colour is optional. One child draws, one records and one checks return. Keep the original count hidden until the final reveal.
Draw one slip without looking, open it, record R or B, refold and return it before mixing again. Complete six draws, then swap jobs for six more. Do not remove successful draws: that would change the collection. Each group uses a separate envelope; a class of thirty can work in ten groups of three.
A possible first six results are R,R,B,R,R,R. This records five R sightings, not five different R slips. The same physical slip may be seen repeatedly. Ask the group to offer a tentative description before six further draws. A result with no B still does not prove B is absent.
After twelve draws, total both columns and check the total is twelve. Reveal and count the six actual slips. Compare observations with the real four-to-two collection without treating a mismatch as a mistake. There is no race or score for guessing the hidden counts.
For young children, an adult records and reads the letters aloud. Use large paper rather than small objects; no blindfold is needed. Sampling is the task, not a test of a child’s intelligence. This shorter version removes the reference activity’s advanced numerical scoring.