Series and parallel resistance
Distinguish series addition from parallel reciprocal addition in a paper network.
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
Use resistor cards 2Ω,3Ω,6Ω and the printed node ledger. No powered circuit or mains electricity is involved. Label the network before calculating; a zigzag’s shape on paper does not establish which nodes it joins.
Follow the rule
In the first task connect 3Ω and 6Ω directly between the same two nodes X,Y. They are parallel, so 1/R=1/3+1/6=1/2 and R=2Ω. Add a 2Ω card in series before this branch pair, giving total 4Ω.
Check each step
In a separate task put all three cards on one uninterrupted route. They are series and total 11Ω. Do not add 3+6 for the parallel pair merely because the two cards are adjacent in the drawing.
Worked example
Use roles node mapper, calculator and auditor. For an optional ideal 12V source on the 4Ω whole network, total current is 3A. The series 2Ω drop is 6V; both branches have 6V, carrying 2A and 1A respectively.
Finish and adapt
Finish with both equivalent resistances and the optional current audit 2+1=3A. This ideal model assumes resistors have fixed values and wires negligible resistance. It is not permission to build a live circuit or a real measurement of parts.
Purpose, observation and provenance
Within this activity: Distinguish series addition from parallel reciprocal addition in a paper network.
Observe whether nodes, not visual proximity, determine series or parallel and branch currents balance.
Our rules, examples and printable diagrams are separately prepared. The earliest inventor of the broader mechanism is not established here.
OpenStax: resistors in series and parallel — 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.
Series and parallel resistance · Player sheet
Before you begin
- Use resistor cards 2Ω,3Ω,6Ω and the printed node ledger. No powered circuit or mains electricity is involved. Label the network before calculating; a zigzag’s shape on paper does not establish which nodes it joins.
- In the first task connect 3Ω and 6Ω directly between the same two nodes X,Y. They are parallel, so 1/R=1/3+1/6=1/2 and R=2Ω. Add a 2Ω card in series before this branch pair, giving total 4Ω.
- In a separate task put all three cards on one uninterrupted route. They are series and total 11Ω. Do not add 3+6 for the parallel pair merely because the two cards are adjacent in the drawing.
| Network | Equivalent Ω |
|---|---|
| 3 and6 share X,Y;2 before branch | |
| 2,3,6 on one route |
| Element | Voltage V | Current A |
|---|---|---|
| ________ | ________ | ________ |
| ________ | ________ | ________ |
| ________ | ________ | ________ |
| ________ | ________ | ________ |
Series and parallel resistance · Host key — keep separate
Parallel 3||6=2Ω; with series 2 gives 4Ω. All-series=11Ω. At 12V, total 3A and branches 2A,1A.
What to observe
Observe whether nodes, not visual proximity, determine series or parallel and branch currents balance.
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 |
|---|---|
| ________ | ________ |
| ________ | ________ |
| ________ | ________ |
| ________ | ________ |