Canonical combined lesson MATH30B-L090 · week 18 day 5 · CURRICULUM_BASELINE

MATH30B-L090 - Buffer: authorized strand exit tickets - no silent switch

• Delivery id: MATH30B (combined classroom; not a fourth credential)
• Official courses: Mathematics 30-1 (MAT3791), 30-2 (MAT3792), 30-3 (MAT3793)
• Lesson ID: MATH30B-L090
• Calendar: Week 18 Day 5 of 18 weeks × 5 days (lesson 90 of 90)
• Object type: canonical combined-classroom lesson
• Braid class: B
• Labels: ALL STRANDS launch → 30-1 REQUIRED / 30-2 REQUIRED / 30-3 REQUIRED workshops → CROSS-STRAND EXPOSURE ≠ mastery
• Source: Alberta Mathematics 10-12 Program of Studies, https://open.alberta.ca/publications/mathematics-grades-10-12
• Official outcome IDs today: MATH30-1-TRIGONOM-06-012, MATH30-1-TRIGONOM-10-016, MATH30-1-TRIGONOM-06-006, MATH30-1-TRIGONOM-04-024, MATH30-2-LOGICALR-03-011, MATH30-2-LOGICALR-03-005, MATH30-2-MATHEMAT-01-017, MATH30-3-X-02-006, MATH30-3-X-03-007, MATH30-3-X-01-002

Labels (post on the board)

1. ALL STRANDS - shared launch only.
2. 30-1 REQUIRED - MAT3791 tray; mastery evidence for 30-1 SOs listed below.
3. 30-2 REQUIRED - MAT3792 tray; mastery evidence for 30-2 SOs listed below.
4. 30-3 REQUIRED - MAT3793 tray; mastery evidence for 30-3 SOs listed below.
5. CROSS-STRAND EXPOSURE ≠ mastery - hearing another tray is logged as EXPOSURE, never as an SO tick, never as a silent enrolment change.

ALL STRANDS launch (~10-14 min)

Final calendar day 90. Confirm PASI codes. Exposure log is not a credential.

Clock ~75 min unless the school uses 60; cut the workshop block first, never the strand exit ticket. Class C parallel workshops are the default when one strand is on exclusive work.

Official outcomes (REQUIRED on home strand)

Strand	Official ID	Role today
30-1	MATH30-1-TRIGONOM-06-012	REQUIRED - Demonstrate an understanding of inverses of relations
30-1	MATH30-1-TRIGONOM-10-016	REQUIRED - Solve problems that involve exponential and logarithmic equations
30-1	MATH30-1-TRIGONOM-06-006	REQUIRED - Prove trigonometric identities, using: • reciprocal identities • quotient identities • Pythagorean identities • sum or difference identities (restricted to sine, cosine and tangent
30-1	MATH30-1-TRIGONOM-04-024	REQUIRED - Expand powers of a binomial in a variety of ways, including using the binomial theorem (restricted to exponents that are natural numbers)
30-2	MATH30-2-LOGICALR-03-011	REQUIRED - Solve problems that involve rational equations (limited to numerators and denominators that are monomials and binomials)
30-2	MATH30-2-LOGICALR-03-005	REQUIRED - Solve problems that involve the probability of two events
30-2	MATH30-2-MATHEMAT-01-017	REQUIRED - Research and give a presentation on a current event or an area of interest that involves mathematics
30-3	MATH30-3-X-02-006	REQUIRED - Solve problems that involve the acquisition of a vehicle by: • buying • leasing • leasing to buy
30-3	MATH30-3-X-03-007	REQUIRED - Critique the viability of small business options by considering: • expenses • sales • profit or loss
30-3	MATH30-3-X-01-002	REQUIRED - Solve problems by using the sine law and cosine law, excluding the ambiguous case

30-1 workshop - 30-1 REQUIRED

Clock: ~22-28 min after launch (cut workshop before cutting the strand exit ticket). Learners on this tray stay on 30-1.

MATH30-1-TRIGONOM-06-012

Official text: Demonstrate an understanding of inverses of relations

Worked example (unique to this hour, this strand, this SO): Find the inverse of f(x)=8x−3. Restrict if needed so the inverse is a function. Show (f∘f⁻¹)(x)=x on that domain. Numeric undo: f(4) then invert.

Level	Prompt (inside the home strand)
FOUNDATION	Numeric undo.
CORE	Swap coordinates on a table.
PROFICIENT	Algebraic inverse with domain.
ADVANCED	Prove composition identity.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. Inverse visual: points swapped; y=x mirror.

MATH30-1-TRIGONOM-10-016

Official text: Solve problems that involve exponential and logarithmic equations

Worked example (unique to this hour, this strand, this SO): Solve 8^x = 4 exactly (x=log_8 4) then a decimal check. Solve log_8(x−3)+log_8 x = log_8 4 with domain x>3 (and x>0). Reject extraneous roots.

Level	Prompt (inside the home strand)
FOUNDATION	Solve 2^x=8.
CORE	Exact then tech check.
PROFICIENT	Log equation with domain.
ADVANCED	Extraneous root rejected.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. Equation-graph link: intersection of y=b^x and y=k.

MATH30-1-TRIGONOM-06-006

Official text: Prove trigonometric identities, using: • reciprocal identities • quotient identities • Pythagorean identities • sum or difference identities (restricted to sine, cosine and tangent) • double-angle identities (restricted to sine, cosine and tangent)

Worked example (unique to this hour, this strand, this SO): Prove (1 − cos²θ)/sin θ = sin θ for sin θ ≠ 0 using Pythagorean and reciprocal identities. Second item (sum): expand sin(π/3 + θ) using the sum identity (sin, cos, tan only). Third (double-angle): rewrite sin(2θ) if sin θ = 3/8 in QI.

Level	Prompt (inside the home strand)
FOUNDATION	Verify 1+tan²θ=sec²θ at 45°.
CORE	Prove a reciprocal/quotient identity.
PROFICIENT	Sum or double-angle proof with restrictions.
ADVANCED	Reject an illegal step in a near-proof.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. Identity map: reciprocal / quotient / Pythagorean / sum-diff / double-angle.

MATH30-1-TRIGONOM-04-024

Official text: Expand powers of a binomial in a variety of ways, including using the binomial theorem (restricted to exponents that are natural numbers)

Worked example (unique to this hour, this strand, this SO): Expand (x+8)^5 using the binomial theorem (natural exponent). Give the general term and the term containing x^3.

Level	Prompt (inside the home strand)
FOUNDATION	(x+1)² by Pascal.
CORE	Full expansion natural n.
PROFICIENT	General term.
ADVANCED	Coefficient of a named power.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. Pascal row / binomial expansion aligned to coefficients.

Independent practice: a new instance of today’s SO(s) with different numbers than the worked example. Two sentences on reasonableness.

Wrong-answer repair (do not praise):

• 30-1 SO 012: Swapping a and b in y=ax+b incorrectly, or claiming every inverse is a function. Repair: name the first wrong line, replace it, and re-complete the CORE tray item. Do not praise the wrong line.
• 30-1 SO 016: Exponentiating only one side, or keeping an extraneous root from a log domain. Repair: name the first wrong line, replace it, and re-complete the CORE tray item. Do not praise the wrong line.
• 30-1 SO 006: Moving from one side to the other by adding the same expression without justification, or using sine law as an “identity.” Repair: name the first wrong line, replace it, and re-complete the CORE tray item. Do not praise the wrong line.
• 30-1 SO 024: Writing binomial coefficients as n+r or expanding with subtraction signs ignored. Repair: name the first wrong line, replace it, and re-complete the CORE tray item. Do not praise the wrong line.

30-2 workshop - 30-2 REQUIRED

Clock: ~22-28 min after launch (cut workshop before cutting the strand exit ticket). Learners on this tray stay on 30-2.

MATH30-2-LOGICALR-03-011

Official text: Solve problems that involve rational equations (limited to numerators and denominators that are monomials and binomials)

Worked example (unique to this hour, this strand, this SO): Solve 8/x + 3/(x+3) = 4/(x(x+3)) with x≠0, x≠−3. Check for extraneous roots. Context option: two work rates filling a tank.

Level	Prompt (inside the home strand)
FOUNDATION	Clear a single-term rational equation.
CORE	Binomial denominators + check.
PROFICIENT	Work-rate context.
ADVANCED	Explain an extraneous root.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. Rate table that becomes a rational equation; restrictions boxed.

MATH30-2-LOGICALR-03-005

Official text: Solve problems that involve the probability of two events

Worked example (unique to this hour, this strand, this SO): Two tests in sequence. P(detect)=0.7 each if independent: find P(both) and P(at least one). Then a dependent version: second-test P changes to 0.7 if the first was positive. Use a tree.

Level	Prompt (inside the home strand)
FOUNDATION	Independent P(A and B)=P(A)P(B).
CORE	Tree with two stages.
PROFICIENT	Dependent branch.
ADVANCED	Conditional language in context.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. Tree or two-way table for two events (independent then dependent).

MATH30-2-MATHEMAT-01-017

Official text: Research and give a presentation on a current event or an area of interest that involves mathematics

Worked example (unique to this hour, this strand, this SO): Research question (30-2 only): “How does a published article use mathematics in a current water or hygiene issue?” Required product: question, two sources, one model or calculation, and a limits sentence. Do not tick this SO for 30-1 or 30-3.

Level	Prompt (inside the home strand)
FOUNDATION	Write a research question.
CORE	Math in the story named.
PROFICIENT	Sources + model.
ADVANCED	Limits of the model.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. Project board: question, sources, model, limits - 30-2 only.

Independent practice: a new instance of today’s SO(s) with different numbers than the worked example. Two sentences on reasonableness.

Wrong-answer repair (do not praise):

• 30-2 SO 011: Clearing denominators then keeping a restricted x as a root. Repair: name the first wrong line, replace it, and re-complete the CORE tray item. Do not praise the wrong line.
• 30-2 SO 005: Multiplying for dependent events as if independent. Repair: name the first wrong line, replace it, and re-complete the CORE tray item. Do not praise the wrong line.
• 30-2 SO 017: A poster with no mathematics, or copying a news claim with no sources. Repair: name the first wrong line, replace it, and re-complete the CORE tray item. Do not praise the wrong line.

30-3 workshop - 30-3 REQUIRED

Clock: ~22-28 min after launch (cut workshop before cutting the strand exit ticket). Learners on this tray stay on 30-3.

MATH30-3-X-02-006

Official text: Solve problems that involve the acquisition of a vehicle by: • buying • leasing • leasing to buy

Worked example (unique to this hour, this strand, this SO): Vehicle price $18000. Buy: tax 5% + $280 fees. Lease: $280/month for 36 months + $1700 due at signing, residual $8500. Lease-to-buy: add a stated buyout. Compare total cost vs monthly cash flow. Table after retrieval.

Level	Prompt (inside the home strand)
FOUNDATION	Define buy / lease / lease-to-buy.
CORE	Total cost vs monthly.
PROFICIENT	Choose with a cash-flow condition.
ADVANCED	Interest/residual sensitivity.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. Vehicle comparison table VIS-M30B-VEH (buy / lease / lease-to-buy).

MATH30-3-X-03-007

Official text: Critique the viability of small business options by considering: • expenses • sales • profit or loss

Worked example (unique to this hour, this strand, this SO): Month expenses $2700, sales $3350, so profit/loss = sales − expenses. Second scenario: sales drop 16%. Critique viability (can this hygiene kiosk continue?).

Level	Prompt (inside the home strand)
FOUNDATION	Label expense vs revenue.
CORE	Compute profit or loss.
PROFICIENT	Critique viability.
ADVANCED	Two scenarios.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. Ledger: expenses, sales, profit or loss.

MATH30-3-X-01-002

Official text: Solve problems by using the sine law and cosine law, excluding the ambiguous case

Worked example (unique to this hour, this strand, this SO): Triangle: angle A=35°, angle B=42°, side a=12 m (AAS). Use sine law (no ambiguous case). Second item: sides 18, 15, included angle 50° - cosine law for the third side. Never assign 30-1 radian identities as this SO.

Level	Prompt (inside the home strand)
FOUNDATION	Identify AAS vs SAS from a sketch.
CORE	Sine law numerical (no ambiguous case).
PROFICIENT	Cosine law numerical.
ADVANCED	Choose the law from given parts.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. Oblique triangle with sides/angles labelled; sine or cosine law choice boxed.

Independent practice: a new instance of today’s SO(s) with different numbers than the worked example. Two sentences on reasonableness.

Wrong-answer repair (do not praise):

• 30-3 SO 006: Comparing monthly payment only, ignoring down payment, residual, or term length. Repair: name the first wrong line, replace it, and re-complete the CORE tray item. Do not praise the wrong line.
• 30-3 SO 007: Calling revenue “profit,” or ignoring a category of expense. Repair: name the first wrong line, replace it, and re-complete the CORE tray item. Do not praise the wrong line.
• 30-3 SO 002: Using sine law when SAS needs cosine law, or entering the ambiguous case (excluded). Repair: name the first wrong line, replace it, and re-complete the CORE tray item. Do not praise the wrong line.

CROSS-STRAND EXPOSURE ≠ mastery

• CROSS-STRAND EXPOSURE ≠ mastery. Log D items. Do not tick another strand’s SO.
• AI Tutor must not treat an exposure card as proficiency.
• 30-1 and 30-3 do strand tasks during 017 hour. Do not mark 017 complete for them.
• Sine/cosine law (30-3) and identities (30-1) may share a room clock; they are different POS objects.

Project or clean math

Project overlay today: none. Use a clean math prompt on the home-strand tray. Do not force Sustainable Community Water & Hygiene onto work that is not genuinely that mathematics.

AI Tutor

• Load the authorized home strand only: MAT3791 (Mathematics 30-1) or MAT3792 (Mathematics 30-2) or MAT3793 (Mathematics 30-3) from the authorized profile.
• Never silent-switch a struggling 30-1 learner into 30-2/30-3 banks (or the reverse) to “make it easier.”
• Serve today’s home-strand SOs. Exposure cards are read-only.
• Never dump diploma keys or released exam wording. Original items only.
• Wrong answers: name the error and repair; do not praise.

Human-tutor handoff

Call a human tutor when: the learner cannot complete CORE after two documented repairs; an identity proof (30-1 006) is stuck after the identity map; a 30-2 017 source is unsafe or empty; a 30-3 vehicle/business number is being faked to match a hoped-for answer; distress, disclosure, or a request to change official enrolment. Enrolment changes are an office/PASI process, not a tutor action.

Diagram / whiteboard

Approved starter math30-quadratic-shift. Strand workshops may add axes/tables. Never praise a translated parabola as a circle.

Strand exit ticket (~8-12 min)

Collect only the home-strand row. Exposure ≠ mastery. Lesson MATH30B-L090.

Home strand	Primary SO	Exit ticket (unique to this lesson)
30-1	MATH30-1-TRIGONOM-06-012	CORE exit: Find the inverse of f(x)=8x−3. Restrict if needed so the inverse is a function. Show (f∘f⁻¹)(x)=x on that domain. Numeric undo: f(4) then invert. FOUNDATION alternate: Numeric undo. Do not submit another strand’s ticket as 30-1 mastery.
30-2	MATH30-2-LOGICALR-03-011	CORE exit: Solve 8/x + 3/(x+3) = 4/(x(x+3)) with x≠0, x≠−3. Check for extraneous roots. Context option: two work rates filling a tank. FOUNDATION alternate: Clear a single-term rational equation. Do not submit another strand’s ticket as 30-2 mastery.
30-3	MATH30-3-X-02-006	CORE exit: Vehicle price $18000. Buy: tax 5% + $280 fees. Lease: $280/month for 36 months + $1700 due at signing, residual $8500. Lease-to-buy: add a stated buyout. Compare total cost vs monthly cash flow. Table after retrieval. FOUNDATION alternate: Define buy / lease / lease-to-buy. Do not submit another strand’s ticket as 30-3 mastery.

Provenance

Official IDs/text: _official_math_calm_outcomes.json. Pacing: MATH30_COMBINED_CLASSROOM_PACING.md. Crosswalk: MATH30_1_30_2_30_3_OUTCOME_CROSSWALK.csv. Generated by oeom/core/training/rapid3/write_math30b_lessons.py.