Number
Mathematics
Estimate, show the method, then ask a tool to check the path — never the soul of the work.
AI may review a method you already wrote. It may not be the first hand that touches the problem.
5–10
Little Thinkers
Ready · 6 lessons
11–14
Young Minds
Ready · 7 lessons
15–18
Emerging Adults
Ready · 7 lessons
Adult
Lifelong Learners
Ready · 7 lessons
Start here
Guess, Then Count
Estimate Before the Oracle · Little Thinkers · 18 min
Use objects on the table
Units
Estimate Before the Oracle
ReadyA number in the head before a tool in the hand. Little arc: guess, path, catch a wild number, two ways, about, then the machine.
6 sittings (little); flagship all bands · little · young · emerging · adult
Show the Path
ReadyProof as a sentence other people can walk.
6 sittings · young · emerging · adult
Open a sitting
Little Thinkers5–10
- 1. Guess, Then CountReadyUse objects on the table
- 2. The Path on PaperReadySitting 1 was guess, then count
- 3. Catch a Wild NumberReadyYou will say a wrong number on purpose, confidently
- 4. Count It Two WaysReadySame objects
- 5. About, Not ExactReadyUse a jar of beans, a bookshelf, or cars in a lot from the window — something they cannot finish…
- 6. Catch the MachineReadyThis is the capstone of the little math arc, not a calculator lesson
Young Minds11–14
- 1. What Is a Proof?ReadyA proof is a path
- 1. Estimate Before the OracleReadyPick a real quantity: phone battery, trip time, a word-problem from their book
- 2. The Missing StepReadyA proof is a path
- 3. The Model Checks, You WalkReadyThis sitting establishes the order: walk first, check second
- 4. The Blank Board TestReadyThis is the reproducibility test
- 5. A Proof Is for Other PeopleReadyA proof is a social act
- 6. Show the PathReadyThis is the capstone
Emerging Adults15–18
- 1. The Path Is the MathematicsReadyThis sitting teaches the student that the path is the mathematics, not the answer
- 1. Show the PathReadyThis is the math version of ghostwriter ethics
- 2. Hunting the GapReadyThis sitting teaches the student to audit the model's solutions the way an editor audits a draft
- 3. The Model Is a Hostile ReviewerReadyThis sitting teaches the student to use the model as a hostile reviewer
- 4. Reproducibility Is the StandardReadyThis sitting makes the blank board test the standard
- 5. Proof as a Social ActReadyThis sitting teaches the student that proof is social
- 6. The Full PathReadyThis is the emerging capstone
Lifelong LearnersAdult
- 1. Model the PathReadyThe adult models the path
- 1. Numbers in the HouseReadyTip, travel time, a news statistic
- 2. Show Your Work, Even at HomeReadyThis sitting is about the adult showing work at home
- 3. The Reviewer at HomeReadyThe adult models the reviewer relationship
- 4. The Blank Board at the TableReadyThe adult models the blank board test
- 5. Show the Path for OthersReadyThe adult models the social act of proof
- 6. The Path at the TableReadyThis is the adult capstone