Year 8 · 75 minutes · Neural networks
What can one artificial neuron actually compute?
This artificial neuron multiplies each input by a weight, adds a bias and applies a sigmoid. It computes a number; it is not a miniature person. The weights determine how inputs influence the output. A single linear boundary can represent an AND-like decision but cannot separate XOR’s diagonal classes. A high activation is not automatically a calibrated probability.
Write z = w1x1 + w2x2 + b and sigmoid(z) = 1/(1+exp(−z)). Prepare AND and XOR truth tables. Explain that learners adjust parameters directly; automatic training is a later investigation.
Substitute values into a weighted sum. Useful earlier investigations: y1-branch Use pairs for investigation, with operator/reviewer swaps after each comparison. Keep individual predictions, journals and a short oral defence so group work does not hide understanding.
Australian Curriculum Version 9 · Digital Technologies: AC9TDI8P06, AC9TDI8P08. Selected aspects only. This activity contributes evidence; it does not cover the full descriptor or achievement standard. A programming descriptor is not claimed for merely moving controls. ACARA AI curriculum connection · V9 Technologies These are planning connections, not ACARA endorsement or exhaustive descriptor alignment.
Calculate a weighted sum with inputs 1 and 0, then inspect the activated output.
Ask: “Which contribution disappears when its input is zero?”
Listen for: “That input’s weight times zero.”
Predict the output direction when w1 increases with x1=1 and all else fixed.
Ask: “Would that same change matter when x1=0?”
Listen for: “No, its contribution would remain zero.”
Adjust weights and bias while linked edge contributions, sum and output update. Test all four input pairs, not just the currently visible one.
Ask: “Why did changing the bias affect every case?”
Listen for: “It is added regardless of the inputs.”
Switch the target table to XOR and try to separate its diagonal positives with one boundary.
Ask: “Can one straight boundary put both opposite corners on one side?”
Listen for: “Not without including a negative corner.”
Return to AND, find parameters that classify all four cases, then document why this architecture is insufficient for XOR.
Ask: “What change is needed beyond more tuning?”
Listen for: “A different representation or a hidden layer.”
Submit weights, four sums and the architecture limitation.
Ask: “Does a 0.95 activation prove 95% accuracy?”
Listen for: “No; calibration requires evidence across cases.”
A neural unit thinks like a person.
Increase one weight with its input fixed at 1, then at 0. Predict both output changes before testing.
XOR cannot be separated by a single linear boundary, regardless of tuning these weights.
Build an AND-like gate, verify four cases and propose a two-stage representation for XOR on paper.
Ask learners to calculate an unseen weighted sum and explain the XOR geometry. Do not require a formal proof, but reject a claim that more random tuning will necessarily solve it.
Begin with step activation and integer sums, then introduce sigmoid. Provide a formula sheet.
Construct two hidden units for XOR and trace their outputs into a final unit.
A four-case neuron specification with a demonstrated architecture limit.
Inputs are synthetic binary signals. No brain-like or human-understanding claims should be inferred from the diagram.
Use real MPS/CUDA matrix operations to evaluate thousands of weight pairs against AND and XOR truth tables. Change bias and compare the best and mean number correct over the weight grid.
| Criterion | Beginning | Secure | Extending |
|---|---|---|---|
| Mechanism | Describes a thinking node | Calculates contributions and activation | Predicts zero-input and bias effects |
| Architecture critique | Tests only one input | Verifies all four AND cases | Explains XOR’s representational limitation |
Australian Curriculum Version 9 · Digital Technologies
References: AC9TDI8P06, AC9TDI8P08. Read the current source (checked 2026-09-07).
Evidence to assess: A four-case neuron specification with a demonstrated architecture limit.
Selected aspects only. This activity contributes evidence; it does not cover the full descriptor or achievement standard. A programming descriptor is not claimed for merely moving controls. Moderate the supplied illustrative responses against your school unit and current achievement standard.
These are planning estimates to test with your class. A short session develops one supported claim; it does not compress the whole senior project.
| Stage | 45 minute focus | 60 minute investigation |
|---|---|---|
| Readiness and prediction | 0–5 | 0–5 |
| Trace the supplied example | 5–13 | 5–15 |
| Author and run cases | 13–25 | 15–35 |
| Counterexample and redesign | 25–35 | 35–45 |
| Explain and discuss | 35–42 | 45–55 |
| Export and handover | 42–45 | 55–60 |
For a longer project, use three 50-minute sessions. Session 1 (0–50): readiness, model, hypothesis and initial cases. Export a project and record the next test. Session 2 (50–100): reopen, check settings, author counterexamples and revise the design. Export the changed project and identify unresolved evidence. Session 3 (100–150): independent peer test, final artefact, individual explanation and moderation. If using two 60-minute sessions, stop at minute 60 after saving the first comparison; use 60–120 for redesign, independent test and defence.
Entry check: Substitute values into a weighted sum. Ask the learner to demonstrate it before choosing the level of support.
Preparation: allow about 15 minutes to run the starter, print the cards and check a project can be reopened. This estimate has not yet been measured in a classroom pilot.
Read the entry question aloud, model one row, and label the units. Offer the case table as a large-print sheet. Keep mathematical derivations optional until the learner can explain the comparison.
For one device, use a projector: one pair predicts, one operates, and the class records on paper. Swap roles after the first comparison. For individual access, support keyboard controls and a written table equivalent to each visual. Learners may explain orally or with an annotated diagram. Never require personal data, a recorded voice, or a photograph.
Mixed readiness: if the entry check is difficult, use the linked prerequisite and the first two case cards; retain the same central question. If secure, ask the learner to design an unseen test and state which explanation it could disprove.
One unit thresholds a weighted sum. The two-unit network computes OR and NAND, then ANDs their outputs.
Starting parameters: Use two hidden units = False, Weight A = 1, Weight B = 1, Bias = -0.5
4 cases calculated from your supplied inputs. Compare the evidence with your prediction.
| a | b | expected | predicted | correct | hidden OR | hidden NAND |
|---|---|---|---|---|---|---|
| 0 | 0 | 0 | 0 | True | 0 | 1 |
| 0 | 1 | 1 | 1 | True | 1 | 1 |
| 1 | 0 | 1 | 1 | True | 1 | 1 |
| 1 | 1 | 0 | 1 | False | 1 | 0 |
These are authored examples, not work collected from children. Assess reasoning using the lesson rubric, not whether the first prediction was correct.
Beginning: “It worked because the result looks right.” This identifies no exact case, control or measurement. Ask the learner to point to one row and say what happened.
Developing: “In the first case I recorded a: 0; b: 0; expected: 0; predicted: 0; correct: True; hidden OR: 0; hidden NAND: 1.” This cites evidence, but does not yet explain how the result follows from the rule. Ask the learner to trace the relevant step.
Secure: “For the first supplied case, a: 0; b: 0; expected: 0; predicted: 0; correct: True; hidden OR: 0; hidden NAND: 1. I can trace it using this mechanism: One unit thresholds a weighted sum. The two-unit network computes OR and NAND, then ANDs their outputs. My result supports a claim about these supplied cases. It does not establish that the same result holds outside them.” Look for an accurate trace, the actual settings and a bounded claim; accept equivalent oral or visual evidence.
Extending: The learner constructs and reruns a new case, reports whether the first explanation survives, and defends a revised design. Use this concrete challenge: Compare a single threshold with a two-hidden-unit network on all four XOR inputs. Require the original and changed evidence and this boundary: The hand-designed XOR network demonstrates representation capacity, not a training result.
Moderation: first assess independently against each lesson criterion. Compare the exact trace or artefact that led to your judgement. Resolve differences using evidence, not polished language. Keep each learner's individual explanation even when the artefact was produced in a group.