Signed change ledger
Distinguish a signed change from the resulting value and verify cancellation.
Adult planning suggestion: about 6–9 · Logic & rule checking
- Players
- 1–4 cooperatively
- Time
- 15–25 minutes
- Materials
- Number line−6…6 and change cards+5,−4,+3,−2
Prepare
Use a paper number line from−6 to 6. Start at−2. The cards are changes, not new temperatures: +5 means five steps right and−4 means four steps left. No hot or cold objects are needed.
Play
Apply+5,−4,+3,−2 in that exact order. Write before, change and after separately. Every landing must remain on the printed number line; count unit intervals rather than counting both endpoints as steps.
Worked example
The results are−2+5=3,3−4=−1,−1+3=2,2−2=0. The four changes sum to+2, which cancels the initial−2. Reaching 0 only after the fourth card is the example’s finish condition.
Finish and check
On a second line start 0 and apply+3 then−3; the final value is 0. Reversing those two cards also finishes 0, but the intermediate point is−3 rather than 3. Compare intermediate positions as well as totals.
Adaptation and limits
Partners replay all arrows and sign labels, then stop. If arranging the four cards in a new order, use each exactly once and require every intermediate value within−6…6. A route that leaves the printed line is outside this activity even if its final total would be 0.
Purpose, observation and provenance
Within this activity: Distinguish a signed change from the resulting value and verify cancellation.
Observe whether arrows count unit intervals and whether the log keeps change and resulting value in different columns.
Our rules, examples and printable diagrams are separately prepared. The earliest inventor of the broader mechanism is not established here.
OpenStax: Add Integers — Reference supports number-line addition; the bounded card route is our own.
Secondary practice: Cooperation and explaining a check.
For a class of 30, use ten groups of three. Prepare one player-material set per group and keep the host key with the adult. Rotate operator, recorder and checker after each worked example; a reader or scribe may help without choosing answers. Avoid public ranking or diagnostic labels.
Age bands are planning suggestions. Background references may address older learners and do not validate suitability for this age band. 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.
Rules to keep beside the materials
- Use a paper number line from−6 to 6. Start at−2. The cards are changes, not new temperatures: +5 means five steps right and−4 means four steps left. No hot or cold objects are needed.
- Apply+5,−4,+3,−2 in that exact order. Write before, change and after separately. Every landing must remain on the printed number line; count unit intervals rather than counting both endpoints as steps.
- The results are−2+5=3,3−4=−1,−1+3=2,2−2=0. The four changes sum to+2, which cancels the initial−2. Reaching 0 only after the fourth card is the example’s finish condition.
- On a second line start 0 and apply+3 then−3; the final value is 0. Reversing those two cards also finishes 0, but the intermediate point is−3 rather than 3. Compare intermediate positions as well as totals.
- Partners replay all arrows and sign labels, then stop. If arranging the four cards in a new order, use each exactly once and require every intermediate value within−6…6. A route that leaves the printed line is outside this activity even if its final total would be 0.
Signed change ledger — play materials
| Before | Change | After |
|---|---|---|
| ________ | ________ | ________ |
| ________ | ________ | ________ |
| ________ | ________ | ________ |
| ________ | ________ | ________ |
| ________ | ________ | ________ |
| ________ | ________ | ________ |
Host check — keep private until finished
Landings 3,−1,2,0; total change+2.
These are model answers or legal examples, not records of an experiment or learner outcomes.