015 min
Clap the beginning
Clap tap–rest–tap–rest and invite the next beat. Do not announce that there is only one answer.
Ask: “What rule are you using?”
Listen for: “Tap and rest keep repeating.”
Brightlab
brightlab.Made for curious mindsbrightlab.Made for curious mindsBrightlab
Year 1 · Patterns
Two patterns look the same at first. What comes next?
Go to the investigation ↓
Investigate with Kiki the kookaburraA two-rule pattern strip with a marked distinguishing test.
Two patterns look the same at first. What comes next?
A short pattern gives clues, but it may fit more than one rule. Red, blue, red, blue might repeat forever, or a rule might change after four beats. We test by finding a place where the rules make different predictions. A good explanation says which rule it uses and what evidence could show it is wrong.
Before this lesson: Continue a repeating two-symbol pattern. Useful earlier investigations: The sorting stream.
A short pattern gives clues, but it may fit more than one rule. Red, blue, red, blue might repeat forever, or a rule might change after four beats. We test by finding a place where the rules make different predictions. A good explanation says which rule it uses and what evidence could show it is wrong.
Continue a repeating two-symbol pattern. Useful earlier investigations: The sorting stream.
Prepare red and blue counters, a strip numbered 1–12 and two rule envelopes: repeat AB; repeat AB for four beats then AA. Keep the second rule hidden until the counterexample.
ACARA V9 AI curriculum connection ↗ · Technologies ↗
A complete teaching sequence · 40 minutes
Clap tap–rest–tap–rest and invite the next beat. Do not announce that there is only one answer.
Ask: “What rule are you using?”
Listen for: “Tap and rest keep repeating.”
Display two possible rules. Children mark beat 5 for each before extending the ribbon.
Ask: “Will these rules always agree?”
Listen for: “They agree at the start, but maybe not later.”
Edit the repeating unit and reveal the ribbon one beat at a time. Keep the seed sequence fixed while comparing both rules.
Ask: “Which is the first beat that could tell the rules apart?”
Listen for: “The beat where one says rest and the other says tap.”
Activate the rule that changes after the shared prefix. Trace why the earlier observations did not exclude it.
Ask: “Was our first rule silly, or did we need more evidence?”
Listen for: “It fitted what we had, but we needed another beat.”
Partners write two rules with the same first four beats. Exchange a proposed test position and justify it.
Ask: “Would looking at beat 2 help?”
Listen for: “No, both rules say the same there.”
Collect both rules, test position and observation.
Ask: “What would change your mind about the rule?”
Listen for: “Seeing a beat my rule does not predict.”
A few examples prove the only rule.
A rule can repeat AB for four beats and then switch. It matches the beginning perfectly but disagrees later.
Create two matching beginnings and choose the earliest observation that distinguishes their rules.
Check the selected test is a disagreement, not merely a later beat. Ask learners to run each rule with counters if they cannot explain the difference.
| Criterion | Beginning | Secure | Extending |
|---|---|---|---|
| Rule description | Copies visible beats | Names a repeat unit | Describes the repeat and switch condition |
| Test design | Chooses an agreeing beat | Finds a disagreeing beat | Explains why earlier observations cannot decide |
Use audible beats and tactile counters; compare only six positions. Adult records rule descriptions.
Invent a third rule consistent with all observed beats. Discuss why we prefer some explanations while remaining open to revision.
Patterns use synthetic colours and beats. Offer a silent version and avoid loud clapping for sound-sensitive students.
Shared device? Turn remembering off. A project file lets you continue on another device.
Your browser is the laboratory
Two patterns look the same at first. What comes next?
Rule A repeats AB forever. Rule B repeats AB for four beats, then produces A every time. Both begin ABAB. Predict beat 6 under each rule.
The experiment opens after your prediction.
There is no penalty for being surprised.
Apple Silicon · PyTorch MPS
Evaluate repeating four-bit programs against switched continuations over twelve beats; count the first distinguishing beat. The larger workload repeats the finite rule set and cannot prove infinite behaviour.
Teacher-operated extension: students predict and interpret the visual report together.
The bundle contains lesson-specific working code, a configuration file, a reactive notebook, a deterministic CPU check and hardware setup instructions. Acceleration is reported only after a tensor operation and result read-back succeed.
Download Mac Studio investigation ↓unzip y1-pattern-mac-pathway.zip -d y1-pattern-mac cd y1-pattern-mac bash setup-mac.sh source .venv/bin/activate python experiment.py --device mps --output results marimo edit notebook.py
CPU and available-device execution status is recorded in the downloaded README and validation report. DGX Spark execution requires that hardware; static validation alone does not establish GPU compatibility or performance. The browser lesson remains fully available without this extension.
NVIDIA DGX Spark · PyTorch CUDA
Evaluate repeating four-bit programs against switched continuations over twelve beats; count the first distinguishing beat. The larger workload repeats the finite rule set and cannot prove infinite behaviour.
Teacher-operated extension: students predict and interpret the visual report together.
The bundle contains lesson-specific working code, a configuration file, a reactive notebook, a deterministic CPU check and hardware setup instructions. Acceleration is reported only after a tensor operation and result read-back succeed.
Download DGX Spark investigation ↓unzip y1-pattern-dgx-pathway.zip -d y1-pattern-dgx cd y1-pattern-dgx bash run-dgx.sh # Open the localhost notebook URL printed by the container.
CPU and available-device execution status is recorded in the downloaded README and validation report. DGX Spark execution requires that hardware; static validation alone does not establish GPU compatibility or performance. The browser lesson remains fully available without this extension.
A two-rule pattern strip with a marked distinguishing test.
Download the editable handout →