Canonical combined lesson MATH30B-L061 · week 13 day 1 · CURRICULUM_BASELINE

MATH30B-L061 - Pascal and binomial coefficients; 017 question; sine/cosine gap

• Delivery id: MATH30B (combined classroom; not a fourth credential)
• Official courses: Mathematics 30-1 (MAT3791), 30-2 (MAT3792), 30-3 (MAT3793)
• Lesson ID: MATH30B-L061
• Calendar: Week 13 Day 1 of 18 weeks × 5 days (lesson 61 of 90)
• Object type: canonical combined-classroom lesson
• Braid class: C
• 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-04-024, MATH30-2-MATHEMAT-01-017, 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)

30-2 research question on a current event involving mathematics. 30-1 expands a binomial. 30-3 gap-fills triangle law.

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-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-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-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-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+7)^6 using the binomial theorem (natural exponent). Give the general term and the term containing x^4.

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 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-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 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-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=36°, angle B=45°, side a=13 m (AAS). Use sine law (no ambiguous case). Second item: sides 17, 16, included angle 51° - 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 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.

Project or clean math

Project (Sustainable Community Water & Hygiene) - genuine math only: 30-2: SO 017 research/presentation on a current event that uses mathematics (water/hygiene allowed if the math is real). Never tick 017 for 30-1/30-3. 30-3: site layout, vehicle if the enterprise needs one, ledger, linear fill-rate, or measurement of volume/chlorine - matching today’s SO.

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-L061.

Home strand	Primary SO	Exit ticket (unique to this lesson)
30-1	MATH30-1-TRIGONOM-04-024	CORE exit: Expand (x+7)^6 using the binomial theorem (natural exponent). Give the general term and the term containing x^4. FOUNDATION alternate: (x+1)² by Pascal. Do not submit another strand’s ticket as 30-1 mastery.
30-2	MATH30-2-MATHEMAT-01-017	CORE exit: 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 … FOUNDATION alternate: Write a research question. Do not submit another strand’s ticket as 30-2 mastery.
30-3	MATH30-3-X-01-002	CORE exit: Triangle: angle A=36°, angle B=45°, side a=13 m (AAS). Use sine law (no ambiguous case). Second item: sides 17, 16, included angle 51° - cosine law for the third side. Never assign 30-1 radian identities as this SO. FOUNDATION alternate: Identify AAS vs SAS from a sketch. 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.