Year 6 · 35 minutes · Explicit teaching model
Move around a calendar, record the ordinary sum and then wrap back to January. The circle is a model you can fully inspect.
Student paper journal · Interactive notebook · Editable Python
Try the starting controls, save two runs and reopen a downloaded project. Print the student journal before class. If Python cannot load, use the supplied example below for a prediction and evidence critique; rerunning changed inputs requires the live or native notebook. Do not present paper discussion as a new model experiment. Draw, point or explain aloud. A partner or adult may record your words.
Start with 5–8 minutes of prediction, use about half the lesson for paired comparisons, then reserve at least 10 minutes for a counterexample and an individual explanation. Act out months in a circle before using the notebook. The research identifies internal base-10 addition before cyclic remapping; avoid saying Llama literally thinks in our drawn circle.
Settings: {'month': 10, 'step': 4}
Nov + 4 months = Mar. First add the numbers (10 + 4 = 14), then take the remainder after dividing by 12 (2).
| step | unwrapped_number | month | x | y |
|---|---|---|---|---|
| 0 | 10 | Nov | 0.5000000000000001 | -0.8660254037844386 |
| 1 | 11 | Dec | 0.8660254037844384 | -0.5000000000000004 |
| 2 | 12 | Jan | 1.0 | -2.4492935982947064e-16 |
| 3 | 13 | Feb | 0.8660254037844386 | 0.5 |
| 4 | 14 | Mar | 0.5000000000000006 | 0.8660254037844384 |
The table shows up to eight rows. Inspect the notebook for all values, controls and denominators.
Method and scope: Month number = (starting number + steps) mod 12. This drawn circle is an explicit teaching representation, not an activation measurement from Llama.
Assess four criteria, each 0–2: testable prediction; comparison identifying what stayed fixed; accurate use of exact evidence; counterexample and limited conclusion. 0 means absent or contradicted by the record, 1 means partly supported, and 2 means clear and supported. A surprising result earns no penalty.
Beginning response: ‘The picture looks right.’ Ask for a particular case. Developing response: names one number without its setting. Ask what comparison supports it. Secure response: states the setting and measured change and separates the notebook's result from the source paper's claim. Extending response: authors or reserves a new case, tests an alternative explanation, and revises the claim if needed. These are marking examples, not pupil data.
Extension: Replace 12 months with 7 weekdays in the downloaded code.
System and data: Llama 3.1 8B arithmetic and cyclic tasks
Method: Tracks layer/token representations, identifies a shared addition mechanism and checks it with causal interventions.
Task: Add month numbers, then wrap around the calendar. Use the linked notebook to make two observations. Draw or describe one result and one thing this activity cannot tell us about the source system.
Boundary: The paper does not claim that Llama simply adds directly around a circle. Our calendar is a teaching model.
System and data: Synthetic manifolds, DINOv3 and SDXL
Method: Trains block-sparse featurizers, compares reconstruction and subspace coverage, and tests edits; multidimensional features are evaluated against direction-based baselines.
Task: A changing shape may need more than one clue. Use the linked notebook to make two observations. Draw or describe one result and one thing this activity cannot tell us about the source system.
Boundary: The experiments concern vision and diffusion models; the classroom geometry is an analogy for representation, not an LLM replication.
System and data: Llama 3.1 8B weekday behaviour and activations
Method: Fits related behavioural and activation geometry, then compares movement along fitted manifolds with linear edits.
Task: Compare travelling along a circle with cutting through its middle. Use the linked notebook to make two observations. Draw or describe one result and one thing this activity cannot tell us about the source system.
Boundary: Only selected fitted manifolds and tasks were tested; not every concept is circular.
System and data: Research collection across several model domains
Method: Organises related studies of representation geometry; the collection is not an independent experiment beyond its linked papers.
Task: Choose a geometry question and follow its original investigation. Use the linked notebook to make two observations. Draw or describe one result and one thing this activity cannot tell us about the source system.
Boundary: This is an index, not an additional independent experiment.
System and data: Evo 2 representations of cross-species DNA
Method: Constructs data to distinguish evolutionary relationship from simple sequence similarity and compares distances along learned geometry.
Task: A map can group related things, but we must test it with new examples. Use the linked notebook to make two observations. Draw or describe one result and one thing this activity cannot tell us about the source system.
Boundary: Biological geometry does not establish an equivalent map inside text LLMs.
System and data: Cross-domain neural-geometry perspective
Method: Connects structured data to learned representations and an unsupervised geometry-discovery pipeline; individual causal claims require their own experiments.
Task: Look for a useful shape, then ask what the picture leaves out. Use the linked notebook to make two observations. Draw or describe one result and one thing this activity cannot tell us about the source system.
Boundary: A cross-domain research perspective does not prove every useful concept has an easily readable geometry.
Independent Brightlab adaptations; no Goodfire endorsement or full reproduction claim. Source methods reviewed 7 September 2026. Curriculum connections are selected planning links; confirm your school syllabus.