Math Relationship Trainer

Adaptive math practice for building relationship intuition. Arithmetic facts are still available, but the main conceptual modes train connections like parts-of-a-whole, percent-as-multiplier, a% of b = b% of a, (cos(theta), sin(theta)), and b^x = y <=> log_b(y) = x.

CLI

go run . -minutes 10

The CLI times each answer, records misses, and prints the current weak facts when the session ends.

Interactive shell:

go run . shell

The shell shows the available modes, lesson options for staged modes, arithmetic range when needed, and session length before starting practice. It returns to the menu after each session so you can switch modes without restarting.

Fraction/decimal mode:

go run . -mode fractions -minutes 10

Percentage mode:

go run . -mode percentages -minutes 10

Percentage relationship mode:

go run . -mode percent-relations -minutes 10

Unit circle mode:

go run . -mode unit-circle -minutes 10
go run . -mode unit-circle -lesson quadrants -minutes 10

Exponent/log mode:

go run . -mode exponents-logs -minutes 10
go run . -mode root-exponent-log -minutes 10

Algebra identities mode:

go run . -mode algebra-identities -minutes 10
go run . -mode algebra-identities -lesson expand -minutes 10
go run . -mode algebra-identities -lesson factor -minutes 10
go run . -mode algebra-identities -lesson recognize -minutes 10

Triangle relationships mode:

go run . -mode triangles -minutes 10
go run . -mode triangles -lesson angle-sum -minutes 10
go run . -mode triangles -lesson pythagorean -minutes 10
go run . -mode triangles -lesson special-right -minutes 10
go run . -mode triangles -lesson sohcahtoa -minutes 10

All relationship modes together:

go run . -mode relationships -minutes 10

Web

go run . web -addr 127.0.0.1:8080

Open http://127.0.0.1:8080.

Fraction/decimal mode:

go run . web -mode fractions -addr 127.0.0.1:8080

Percentage mode:

go run . web -mode percentages -addr 127.0.0.1:8080

Percentage relationship mode:

go run . web -mode percent-relations -addr 127.0.0.1:8080

Unit circle mode:

go run . web -mode unit-circle -addr 127.0.0.1:8080
go run . web -mode unit-circle -lesson quadrants -addr 127.0.0.1:8080

Exponent/log mode:

go run . web -mode exponents-logs -addr 127.0.0.1:8080
go run . web -mode root-exponent-log -addr 127.0.0.1:8080

Algebra identities mode:

go run . web -mode algebra-identities -addr 127.0.0.1:8080
go run . web -mode algebra-identities -lesson expand -addr 127.0.0.1:8080

Triangle relationships mode:

go run . web -mode triangles -addr 127.0.0.1:8080
go run . web -mode triangles -lesson pythagorean -addr 127.0.0.1:8080

All relationship modes together:

go run . web -mode relationships -addr 127.0.0.1:8080

Progress

Progress is stored in ~/.math-study-progress.json by default. Pass -progress ./progress.json to keep a local file instead.

Facts that are missed or slow are weighted more heavily. Facts answered correctly several times without misses or slow responses are treated as mastered and appear less often.

Relationship mode combines the conceptual decks without arithmetic fact practice: fractions, percentages, percent swaps, unit circle, exponents/logs, algebra identities, and triangles.

Fraction mode trains parts-of-a-whole relationships, numerator/denominator roles, fraction-as-division, fraction/decimal equivalence, complements to one, and reciprocals. For fraction-to-decimal prompts, .125 and 0.125 are both accepted. Equivalent quantities like 2/8, .25, and 0.25 can satisfy exact relationship prompts for 1/4.

Percentage mode trains percent-as-multiplier and percent-means-per-100 relationships, plus fraction/decimal/percent equivalence. Equivalent forms like 25%, 25, .25, 0.25, and 1/4 are accepted for the same value where the prompt is asking for an equivalent percentage value.

Percentage relationship mode trains the swap a% of b = b% of a, so prompts like 20% of 35 expect 35% of 20 or the numeric value 7.

Unit circle mode is a staged curriculum, not one giant deck. The default lesson is concepts; do not start with mixed.

Recommended unit-circle order:

go run . -mode unit-circle -lesson concepts
go run . -mode unit-circle -lesson quadrants
go run . -mode unit-circle -lesson reference-angles
go run . -mode unit-circle -lesson reference-values
go run . -mode unit-circle -lesson assemble
go run . -mode unit-circle -lesson tangent
go run . -mode unit-circle -lesson reciprocals
go run . -mode unit-circle -lesson mixed

Lessons:

• concepts: point order (cos, sin), sine is y, cosine is x, and tangent is y/x.
• quadrants: quadrant identification and signs of sin/cos/tan; no exact trig values.
• reference-angles: angle to reference angle and angle to quadrant; no trig values.
• reference-values: first-quadrant values for 30, 45, and 60 degrees only.
• assemble: combine reference angle plus quadrant sign for sin/cos only.
• tangent: tangent ratio, tangent signs, tangent values, and undefined cases.
• reciprocals: sec/csc/cot values and reciprocal relationship prompts.
• mixed: full review after the pieces are individually comfortable.

Each relationship drill carries an explanation and tags such as sin-is-y, cos-is-x, tan-is-y-over-x, quadrant-signs, and reference-angles. Exact radical answers like sqrt(3)/2 are expected instead of decimal approximations.

Exponent/log mode trains exact relationships like 2^5 = 32 <=> log_2(32) = 5, including negative exponents, missing bases, missing exponents, missing values, inverse forms like log_2(2^5) and 2^(log_2(32)), and concept prompts like "a logarithm asks for the exponent." For positive exponents it also trains root/exponent/log triads like 2^5=32 <=> log_2(32)=5 <=> root_5(32)=2, with each source-target direction tracked as its own fact. Aliases include root-exponent-log and roots-exponents-logs.

Triangles mode trains relationships that support later trig and unit-circle intuition. The default lesson is concepts, which focuses on right-angle, hypotenuse, opposite, and adjacent relationships. Triangle facts are not mixed into unit-circle lessons.

Recommended triangles order:

go run . -mode triangles -lesson concepts
go run . -mode triangles -lesson angle-sum
go run . -mode triangles -lesson pythagorean
go run . -mode triangles -lesson special-right
go run . -mode triangles -lesson sohcahtoa
go run . -mode triangles -lesson mixed

Lessons:

• concepts: right angle, hypotenuse, opposite side, and adjacent side meanings.
• angle-sum: triangle angle sums and missing-angle prompts.
• pythagorean: a^2+b^2=c^2, missing hypotenuse, and missing leg prompts.
• special-right: 45-45-90 and 30-60-90 ratios, side identification, and simple missing sides.
• sohcahtoa: sine, cosine, and tangent as right-triangle side ratios.
• mixed: full review after the pieces are individually comfortable.

Algebra identities mode is also staged. The default lesson is concepts, which trains the meaning of identity, expand, factor, and equivalent expression before asking for transformations.

Recommended algebra-identities order:

go run . -mode algebra-identities -lesson concepts
go run . -mode algebra-identities -lesson expand
go run . -mode algebra-identities -lesson factor
go run . -mode algebra-identities -lesson recognize
go run . -mode algebra-identities -lesson mixed

Lessons:

• concepts: identity, expand, factor, and equivalent-expression vocabulary.
• expand: forward transformations like (a+b)^2 to a^2+2ab+b^2.
• factor: reverse transformations like a^2-b^2 to (a+b)(a-b).
• recognize: pattern-name prompts such as difference of squares or perfect-square trinomial.
• mixed: full review, including the staged lessons plus broader patterns like cubes and binomial products.