Postfix value stack
Evaluate postfix expressions while preserving the order of the two operands.
Adult planning suggestion: about 9–12 · Logic & rule checking
- Players
- 3 per group
- Time
- 20–30 minutes
- Materials
- Printed record sheet, pencil and paper markers
Prepare
Give each trio a bottom-to-top stack strip, number tokens and the expression 4 2 − 3 ×. The operator reads the next token, the recorder logs the stack and the checker confirms the action before anything is erased.
Follow the rule
Read strictly left to right. A number is pushed on top. For +,− or×, pop the top value as the right operand, then the next as the left. Compute left operator right and push the result. Never reverse subtraction to avoid a negative answer.
Check each step
Fewer than two values at an operator means invalid input: record the position and stop that attempt. At the end exactly one value is required. Leftover values are not silently added.
Worked example
For 4 2 − 3 ×, stacks are[4],[4,2],[2],[2,3],[6]. Independent tasks:8 3 − 2 × and 2 5 −. Diagnose 2 + and 2 3 without inventing missing tokens.
Finish and adapt
Rotate roles after each expression. Finish with all four attempts classified and a complete trace for the two valid ones. Adults may read token names or supply multiplication facts; correct tracing is the observed action, not a claim about improved intelligence.
Purpose, observation and provenance
Within this activity: Evaluate postfix expressions while preserving the order of the two operands.
Notice whether the learner names the right operand first when popping and stops on underflow.
Our rules, examples and printable diagrams are separately prepared. The earliest inventor of the broader mechanism is not established here.
Runestone: postfix evaluation — Technical background, not an evaluated primary-school lesson. This paper exercise and examples are our adaptation; age and support are adult planning suggestions.
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.
Postfix value stack · Player sheet
Before you begin
- Give each trio a bottom-to-top stack strip, number tokens and the expression 4 2 − 3 ×. The operator reads the next token, the recorder logs the stack and the checker confirms the action before anything is erased.
- Read strictly left to right. A number is pushed on top. For +,− or×, pop the top value as the right operand, then the next as the left. Compute left operator right and push the result. Never reverse subtraction to avoid a negative answer.
- Fewer than two values at an operator means invalid input: record the position and stop that attempt. At the end exactly one value is required. Leftover values are not silently added.
| Attempt | Expression |
|---|---|
| A | 8 3 − 2 × |
| B | 2 5 − |
| C | 2 + |
| D | 2 3 |
| Token | Stack bottom→top | Check |
|---|---|---|
| ________ | ________ | ________ |
| ________ | ________ | ________ |
| ________ | ________ | ________ |
| ________ | ________ | ________ |
| ________ | ________ | ________ |
| ________ | ________ | ________ |
Postfix value stack · Host key — keep separate
8 3 − 2 ×=10;2 5 −=−3.2 + underflows at +;2 3 ends with two values.
What to observe
Notice whether the learner names the right operand first when popping and stops on underflow.
Use the three-person roles described in the rules; offer reading or writing support without selecting answers.
Read the rules as well as this example. Other valid solutions may exist for the puzzle boards. This key is not a claim of uniqueness or measured learning gains.
| Constraint / action | Evidence / correction |
|---|---|
| ________ | ________ |
| ________ | ________ |
| ________ | ________ |
| ________ | ________ |