Library

Learn through designed investigations.

Start with a complete Museion course, then use individual lessons for focused practice. Every response is checked by lesson rules, never by a model.

Museion Originals

Follow a designed reasoning path.

Museion-authored sequences across math, physics, biology, and computer science — every lesson diagnoses specific misconceptions, and the checker's truth stays private.

Create from your sources

Algebradeveloping · Ages 12–15 · early secondary

Algebra as Balance

Understand why equation moves work before memorizing how.

3 lessons · 50 min

Computer Scienceextension · Ages 14+ · basic arrays

Search by Halving

Build binary search from its invariant, not from copied code.

3 lessons · 55 min

Arithmeticdeveloping · Ages 12+ · fraction foundations

Probability as Evidence

Name the reference group before trusting a probability claim.

3 lessons · 55 min

Algebradeveloping · Ages 13+ · early secondary

Functions as Change

Read a rule as a relationship, then ask where its model stops.

4 lessons · 55 min

Research Methodsdeveloping · Ages 12–16 · early secondary

Claims to Evidence

Turn a broad claim into a comparison that could prove it wrong.

3 lessons · 55 min

Research Methodsdeveloping · Ages 12–16 · fraction foundations

Samples to Conclusions

Ask who could enter the sample before trusting its estimate.

3 lessons · 55 min

Physicsdeveloping · Ages 14+ · secondary physics

Forces and Motion

Predict what changes motion, then compute exactly how much.

3 lessons · 55 min

Biologydeveloping · Ages 13+ · secondary biology

Natural Selection as Evidence

Selection acts on variation that already exists — not on effort.

3 lessons · 55 min

Computer Scienceextension · Ages 14+ · intro programming

Recursion: Trust the Smaller Case

A base case, and every call moving toward it.

4 lessons · 55 min

Arithmeticdeveloping · Ages 11–14 · upper primary to secondary

Proportional Reasoning

Keep the ratio fixed — scale without losing the rate.

3 lessons · 50 min

Prerequisite graph

The authored knowledge map

This map covers only the lessons below. It does not imply standards alignment or silently treat external curricula as Museion content.

Find a lesson or concept

Search titles, descriptions, subjects, and registered concepts.

Subject

Showing 37 of 37 lessons

Algebra4 verified steps

Solving Linear Equations

Learn to solve one-variable linear equations by keeping both sides balanced, one verified step at a time.

balance-principleinverse-operations

Hint-free practice after the lesson

Arithmetic4 verified steps

Order of Operations

Why 3 + 4 × 2 is not 14 — learn the precedence rules that make every calculator agree.

operation-precedenceparentheses-first

Hint-free practice after the lesson

Arithmetic4 verified steps

Working with Negative Numbers

Build a number-line intuition for adding, subtracting and multiplying below zero.

adding-negativessubtracting-negatives

Hint-free practice after the lesson

Arithmetic3 verified steps

Adding Fractions with Unlike Denominators

Discover why fractions need a common denominator before they can be added, and how to find one.

common-denominatorequivalent-fractions

Hint-free practice after the lesson

Computer Science4 verified steps

Binary Numbers

How computers count with only two digits — read and write base-2 numbers from scratch.

binary-place-valuebinary-to-decimal

Hint-free practice after the lesson

Algebra5 verified steps

Equality as an Invariant

Read equality as a relationship between two values and decide which moves keep that relationship true.

algebra-balance-expression-vs-equationalgebra-balance-equality-relation

Hint-free practice after the lesson

Algebra5 verified steps

Inverse Operations and Isolation

Undo one operation on both sides, distinguish coefficients from constants, and isolate an unknown with justification.

algebra-balance-additive-inversesalgebra-balance-multiplicative-inverses

Hint-free practice after the lesson

Algebra5 verified steps

Two-Step Equations and Transfer

Plan reversible moves, compare valid paths, verify solutions by substitution, and model a new situation.

algebra-balance-reversible-planalgebra-balance-substitution-check

Hint-free practice after the lesson

Computer Science5 verified steps

Prepare a Search Space

For learners ages 14+ who can read arrays: decide when halving is valid, predict the useful side, and set inclusive boundaries.

search-halving-sorted-preconditionsearch-halving-side-prediction

Hint-free practice after the lesson

Computer Science5 verified steps

Keep the Target in the Interval

For learners ages 14+ who understand sorted arrays and zero-based indices: trace inclusive binary search without losing a possible target.

search-halving-candidate-invariantsearch-halving-deterministic-midpoint

Hint-free practice after the lesson

Computer Science4 verified steps

Reason About Repeated Halving

For learners ages 14+ who can trace binary search: count candidate reductions, compare growth carefully, and transfer the invariant to a new sorted search.

search-halving-candidate-countsearch-halving-logarithmic-growth

Hint-free practice after the lesson

Arithmetic3 verified steps

Probability as Evidence: Name the Possible Outcomes

Build a probability claim from a stated sample space, then check what the denominator is counting.

sample-spaceequally-likely-outcomes

Hint-free practice after the lesson

Arithmetic3 verified steps

Probability as Evidence: Condition on What You Know

Use a stated subgroup as the denominator when evidence tells you where to look.

conditional-probabilityevidence-subgroup

Hint-free practice after the lesson

Arithmetic3 verified steps

Probability as Evidence: Keep the Base Rate Visible

Use a full count table to distinguish a starting rate, a test result, and the evidence-conditioned conclusion.

base-rateevidence-update

Hint-free practice after the lesson

Algebra3 verified steps

Functions as Change: One Input, One Output

Read a function as a dependable rule that maps an allowed input to one output.

function-ruleinput-output

Hint-free practice after the lesson

Algebra3 verified steps

Functions as Change: Read the Rate

Find how much an output changes for each unit of input, then separate that rate from a starting value.

rate-of-changeconstant-rate

Hint-free practice after the lesson

Algebra3 verified steps

Functions as Change: Build and Bound a Linear Model

Connect a linear rule to its rate and initial value, then state what a model does and does not justify.

linear-modelrate-and-intercept

Hint-free practice after the lesson

Algebra3 verified steps

The Transformation Lab: Move the Curve

Shape a parabola with the parameters a, h and k until it matches a target — and learn why the horizontal shift works backwards.

vertex-formhorizontal-shift

Hint-free practice after the lesson

Research Methods3 verified steps

Claims to Evidence: Make a Claim Observable

Turn a broad claim into an observable outcome, a stated group, and a repeatable way to record evidence.

operational-definitionpopulation

Hint-free practice after the lesson

Research Methods3 verified steps

Claims to Evidence: Separate What Was Seen from What Is Inferred

Distinguish recorded observations from interpretations, then choose conclusions whose wording stays within the evidence collected.

observationinference

Hint-free practice after the lesson

Research Methods3 verified steps

Claims to Evidence: Design a Comparison That Could Challenge a Claim

Specify a comparison and an outcome that could count against a claim instead of collecting only confirming stories.

comparisonfalsifiability

Hint-free practice after the lesson

Research Methods3 verified steps

Samples to Conclusions: Check the Frame Before the Count

Name the group a conclusion concerns, inspect who can enter the sample, and recognize clear coverage gaps.

target-populationsampling-frame

Hint-free practice after the lesson

Research Methods3 verified steps

Samples to Conclusions: Expect Variation in a Sample

Compute simple sample proportions, compare repeated samples, and treat variation as information rather than proof that one count is wrong.

sample-proportionsampling-variability

Hint-free practice after the lesson

Research Methods3 verified steps

Samples to Conclusions: Report an Estimate Without Overclaiming

Turn a sample count into an estimate, state the sample’s scope, and avoid claims that the observed data cannot support.

Hint-free practice after the lesson

Physics5 verified steps

Net Force and Newton's First Law

Combine forces acting on an object and use Newton's first law to decide when motion changes and when it doesn't.

net-force-combiningfirst-law-motion-persists

Hint-free practice after the lesson

Physics6 verified steps

Newton's Second Law: a = F/m

Compute acceleration, force, or mass with F = ma, reason about how doubling force or mass changes acceleration, and separate mass from weight.

force-vs-accelerationsecond-law-computing

Hint-free practice after the lesson

Physics6 verified steps

Net Force, Friction, and Newton's Third Law

Apply net force and F = ma to a sled opposed by friction, then reason about Newton's third law action-reaction pairs acting on different objects.

net-force-with-frictionsecond-law-application

Hint-free practice after the lesson

Biology3 verified steps

Variation and Heritability

Natural selection acts on heritable variation that already exists in a population — individuals do not adapt during their own lifetime and pass that change on.

heritable-variationacquired-traits

Hint-free practice after the lesson

Biology3 verified steps

Differential Survival and Reproduction

Compute how a population's trait mix shifts across one generation of selection, and separate fitness — survival and reproduction that matches the environment — from raw physical strength.

fitness-and-environmenttrait-frequency

Hint-free practice after the lesson

Biology3 verified steps

Transfer: Antibiotic Resistance

Apply differential survival to a fresh case — antibiotic resistance in bacteria — and design an observation that could actually falsify a claim about how the resistance arose.

pre-existing-resistanceselection-not-learning

Hint-free practice after the lesson

Computer Science4 verified steps

Base Case and Progress

For learners ages 14+ starting recursion: a correct recursive definition needs a base case, and every recursive call must move the input toward it.

recursion-requires-base-caserecursion-requires-progress

Hint-free practice after the lesson

Computer Science4 verified steps

Tracing the Call Stack

For learners ages 14+ who understand base case and progress: hand-trace a recursive function's return value, see when work happens on the way down versus the way back up, and count stack depth precisely.

recursion-unwind-orderrecursion-trace-result

Hint-free practice after the lesson

Computer Science4 verified steps

Near Transfer: A New Recursive Definition

For learners ages 14+ who can trace base case, progress, and unwind order: apply that same reasoning to a brand-new recursive definition, power(b, e), and to a fresh doubling context.

recursion-base-case-identificationrecursion-predicted-value

Hint-free practice after the lesson

Computer Science3 verified steps

The Recursion Lab: Build It, Watch It Run

Complete two recursive functions slot by slot, watch the call stack respond, and see exactly why a bad recursive argument never stops.

complete-a-recursionwatch-the-stack

Hint-free practice after the lesson

Arithmetic3 verified steps

Proportional Reasoning: Unit Rate as the Invariant

Find the unit rate that stays fixed inside a relationship, and use it to tell a proportional relationship from one that only looks like it.

recognizing-proportionalityunit-rate

Hint-free practice after the lesson

Arithmetic3 verified steps

Proportional Reasoning: Scaling Quantities

Scale a recipe, mixture, or map up or down while keeping its ratio intact, and match the right quantities to each other when solving for a missing value.

recipe-scalingmissing-value

Hint-free practice after the lesson

Arithmetic3 verified steps

Proportional Reasoning: Proportional or Not?

Decide whether a fresh real-world relationship — currency, speed, or density — is actually proportional before computing with it, and watch for a hidden fixed fee.

decide-proportionalunit-rate-transfer

Hint-free practice after the lesson