Place-value exchange bank
Preserve quantity while exchanging ten ones for a ten and reading a two-place numeral.
Adult planning suggestion: about 6–9 · Logic & rule checking · Cooperation & communication
- Players
- Cooperative pairs
- Time
- 10–15 minutes
- Materials and quantities
- Fifteen large one-unit cards, three ten-unit cards, a tens/ones mat, ordinary die and twelve-turn log.
Thirty pupils: fifteen pairs, with roller and banker swapping after each audited turn.
Prepare
Put fifteen one-unit cards and three ten-unit cards in the bank. Begin with no cards on the pair’s tens/ones mat. The pair cooperates toward exactly thirty in at most twelve turns. Cards may be the same physical size: the printed unit value, not paper area or weight, determines quantity. A one-unit card belongs in the ones column and a ten-unit card in tens.
Play
Each turn roll an ordinary die and propose adding that many ones. If the new total would exceed thirty, add nothing and record a skipped turn. Otherwise move that many one-unit cards from bank to mat. Whenever ten ones are on the mat, return ten to the bank and take one ten-unit card. Regroup until fewer than ten ones remain. Then read tens×10 plus ones and swap roller/banker roles.
Worked example
At one ten and seven ones, a roll of five temporarily makes one ten and twelve ones. Exchange ten ones for another ten: the mat becomes two tens and two ones, still twenty-two. Counting the visible cards as four would be wrong because the card values differ. At twenty-eight a roll of four is skipped; it does not bounce backward or secretly use only two of the four.
Finish and check
Stop immediately at three tens and zero ones, or after twelve turns and read the audited current number. Reaching the goal is a shared outcome, not a contest between the two pupils. A regrouping must preserve value and return exactly ten one-unit cards. The supplied quantities are sufficient: before an allowed addition there are at most nine ones, so adding at most six needs no more than fifteen one-unit cards.
Adaptation and practical limits
Thirty pupils: fifteen cooperative pairs. Adult planning suggestion is around 6–9 with number-word support. The mathematics source explains place-value exchanges, not evidence that this game improves arithmetic. Use large handwritten cards; no toy money or purchase is required. An adult can supply a face value 1–6 instead of a die, clearly labelling that as a chosen rather than random sequence. Keep passing and observation available.
Aim: Preserve quantity while exchanging ten ones for a ten and reading a two-place numeral.
Practice within this activity: Maintain value through an exchange and read each positional unit correctly.
Adult observation: Ask what stayed equal before and after regrouping, not only whether thirty was reached.
Mechanism and adaptation: Our version uses base-ten regrouping and quotient/remainder representation. Examples and sheets are separately written; the earliest inventor is not established here.
Reference checked 25 October 2026: NCETM · Subject Knowledge Audit, Addition/Subtraction — Teacher subject-knowledge discussion of exchanging a ten and ten ones. Our cooperative thirty-unit game and capacity check are separate; no copied worksheet.
Goals describe observable activity choices, not measured long-term gains or institutional endorsement.
Free alternatives: Use paper or clean reused cardboard and a pencil. Copy the supplied diagrams and tables by hand; no specialist kit or purchase is needed.
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 base-ten bank cards
One shared quantity. Exchange10 ones for1 ten; paper size does not determine value.
Player place mat and twelve-turn log
| TENS | ONES |
|---|---|
| ________________ | ________________ |
| Turn | Roll | Add / skip | Tens | Ones | Total |
|---|---|---|---|---|---|
| ________ | ________ | ________ | ________ | ________ | ________ |
| ________ | ________ | ________ | ________ | ________ | ________ |
| ________ | ________ | ________ | ________ | ________ | ________ |
| ________ | ________ | ________ | ________ | ________ | ________ |
| ________ | ________ | ________ | ________ | ________ | ________ |
| ________ | ________ | ________ | ________ | ________ | ________ |
| ________ | ________ | ________ | ________ | ________ | ________ |
| ________ | ________ | ________ | ________ | ________ | ________ |
| ________ | ________ | ________ | ________ | ________ | ________ |
| ________ | ________ | ________ | ________ | ________ | ________ |
| ________ | ________ | ________ | ________ | ________ | ________ |
| ________ | ________ | ________ | ________ | ________ | ________ |
Host / teacher checked example · separate
Thirty pupils: fifteen pairs, with roller and banker swapping after each audited turn.
Fifteen large one-unit cards, three ten-unit cards, a tens/ones mat, ordinary die and twelve-turn log.
Keep this answer page separate. Read the full web rules and preview materials before leading; allow pauses, passing and supported writing.
| State | Tens | Ones | Value |
|---|---|---|---|
| Before | 1 | 7 | 17 |
| Add5 | 1 | 12 | 22 |
| Regroup | 2 | 2 | 22 |
28+4 is skipped. Stop at30 or after12 turns. Up to9 ones before addition plus at most6 =15 cards; bank supply suffices. Three tens is the goal, not three units.