Year 3 · 55 minutes · Representation
What does a picture lose when we turn it into numbers?
A digital picture can be represented as a grid of numbers. This lab uses 0 for an empty pixel and 1 for a filled pixel. A smaller representation keeps only the sum of each row. That saves information space but loses where pixels sit inside a row. Two different pictures can therefore have identical row summaries. A useful feature must preserve the differences relevant to our task.
Print two 5 by 5 grids. Prepare an L shape and its horizontal reflection. Calculate row sums in advance to show why they collide. Check keyboard access to every pixel cell.
Count filled squares in a small grid. Useful earlier investigations: f-sort Use pairs with predictor/operator roles. Swap after the first comparison. Each learner draws or writes their own explanation using one exact case.
Australian Curriculum Version 9 · Digital Technologies: AC9TDI4K03. 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.
Draw an L and translate each cell into 0 or 1.
Ask: “Could the machine reconstruct the picture from all 25 values?”
Listen for: “Yes, if it knows the cell order.”
Predict whether reflecting the L changes its row totals before using the mirror control.
Ask: “Which information do row totals keep?”
Listen for: “How many marks, but not their columns.”
Edit cells and inspect the matrix, row bars and column totals. Keep row totals fixed while moving a pixel sideways.
Ask: “What changed in the picture but stayed in the summary?”
Listen for: “The pixel position changed; the row total did not.”
Use the reflected image edge case. Confirm all row totals match even though orientation differs.
Ask: “Can a row-only classifier tell left from right here?”
Listen for: “No, its inputs are identical.”
Choose column totals or a left-half count. Test both original images plus a third image and state any remaining collision.
Ask: “Does your extra feature preserve what this task needs?”
Listen for: “It separates these two orientations.”
Collect two grids, their totals and a feature proposal.
Ask: “Did we prove the feature works for every image?”
Listen for: “No; we tested three and can still find collisions.”
A computer receives a whole object.
Predict whether a horizontal mirror changes the row-sum representation.
An L and its reflection have equal row sums but different orientations. Identical representations force a row-only model to treat them alike.
Add a column-based feature and test whether it separates the pair; then search for another collision.
Ask learners to produce a collision themselves. If they only repeat the supplied example, change the starting image and require a new pair.
Start with a 3 by 3 paper grid and move physical counters within a row. Use the larger browser grid with a partner.
Can two images share both row and column totals? Construct a 2 by 2 diagonal swap as a counterexample.
A representation collision exhibit with an improved feature and its limits.
Use abstract marks only; no student images, handwriting samples or photographed work are required.
Enumerate or sample many binary images and group them by row-sum signatures; measure collision rates when column features are added.
| Criterion | Beginning | Secure | Extending |
|---|---|---|---|
| Encoding | Draws without linking cells to numbers | Accurately encodes and sums rows | Explains the information discarded |
| Feature design | Adds arbitrary numbers | Adds a feature that separates the pair | Finds and documents a remaining collision |
Australian Curriculum Version 9 · Digital Technologies
References: AC9TDI4K03. Read the current source (checked 2026-09-07).
Evidence to assess: A representation collision exhibit with an improved feature and its limits.
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: Count filled squares in a small grid. 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.
Count filled squares and compare row counts. Different pictures can share one or both summaries.
Starting parameters: The supplied cases define the inputs.
3 cases calculated from your supplied inputs. Compare the evidence with your prediction.
| picture | filled | row counts |
|---|---|---|
| diagonal | 4 | 1, 1, 1, 1 |
| top row | 4 | 4, 0, 0, 0 |
| corners | 4 | 2, 0, 0, 2 |
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 picture: diagonal; filled: 4; row counts: 1, 1, 1, 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, picture: diagonal; filled: 4; row counts: 1, 1, 1, 1. I can trace it using this mechanism: Count filled squares and compare row counts. Different pictures can share one or both summaries. 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: Create two different pictures that share a count; then design a better description. Require the original and changed evidence and this boundary: A compact representation discards information; even row counts do not uniquely encode every image.
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.