Canonical combined lesson MATH30B-L074 · week 15 day 4 · CURRICULUM_BASELINE

MATH30B-L074 - Original mixed: trig block; probability block; stats block

• Delivery id: MATH30B (combined classroom; not a fourth credential)
• Official courses: Mathematics 30-1 (MAT3791), 30-2 (MAT3792), 30-3 (MAT3793)
• Lesson ID: MATH30B-L074
• Calendar: Week 15 Day 4 of 18 weeks × 5 days (lesson 74 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-01-001, MATH30-1-TRIGONOM-02-002, MATH30-1-TRIGONOM-03-003, MATH30-1-TRIGONOM-04-004, MATH30-1-TRIGONOM-05-005, MATH30-1-TRIGONOM-06-006, MATH30-2-LOGICALR-01-003, MATH30-2-LOGICALR-02-004, MATH30-2-LOGICALR-03-005, MATH30-3-ALGEBRA-01-009, MATH30-3-ALGEBRA-02-010, MATH30-3-ALGEBRA-01-011

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)

Original WR-style stems. Never paste released diploma wording.

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-01-001	REQUIRED - Demonstrate an understanding of angles in standard position, expressed in degrees and radians
30-1	MATH30-1-TRIGONOM-02-002	REQUIRED - Develop and apply the equation of the unit circle
30-1	MATH30-1-TRIGONOM-03-003	REQUIRED - Solve problems, using the six trigonometric ratios for angles expressed in radians and degrees
30-1	MATH30-1-TRIGONOM-04-004	REQUIRED - Graph and analyze the trigonometric functions sine, cosine and tangent to solve problems
30-1	MATH30-1-TRIGONOM-05-005	REQUIRED - Solve, algebraically and graphically, first and second degree trigonometric equations with the domain expressed in degrees and radians
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
30-2	MATH30-2-LOGICALR-01-003	REQUIRED - Interpret and assess the validity of odds and probability statements
30-2	MATH30-2-LOGICALR-02-004	REQUIRED - Solve problems that involve the probability of mutually exclusive and non-mutually exclusive events
30-2	MATH30-2-LOGICALR-03-005	REQUIRED - Solve problems that involve the probability of two events
30-3	MATH30-3-ALGEBRA-01-009	REQUIRED - Solve problems that involve measures of central tendency, including: • mean • median • mode • weighted mean • trimmed mean
30-3	MATH30-3-ALGEBRA-02-010	REQUIRED - Analyze and describe percentiles
30-3	MATH30-3-ALGEBRA-01-011	REQUIRED - Analyze and interpret problems that involve probability

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-01-001

Official text: Demonstrate an understanding of angles in standard position, expressed in degrees and radians

Worked example (unique to this hour, this strand, this SO): Place 30° and the coterminal angle 390° in standard position. Convert 30° to radians: 30π/180 = simplify. Also convert 6π/7 to degrees. State the quadrant of both.

Level	Prompt (inside the home strand)
FOUNDATION	Convert 90° to radians.
CORE	Convert 30° both ways and name quadrant.
PROFICIENT	Two coterminal angles, one positive one negative.
ADVANCED	Arc length on a circle of radius a with θ in radians.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. VIS-M30B-TRIG unit circle in standard position (degrees and radians labelled).

MATH30-1-TRIGONOM-02-002

Official text: Develop and apply the equation of the unit circle

Worked example (unique to this hour, this strand, this SO): A terminal ray intersects the unit circle at a point with x-coordinate −6/6 in QII. Use x²+y²=1 to find y (positive). Verify the point satisfies the unit-circle equation.

Level	Prompt (inside the home strand)
FOUNDATION	Does (1,0) lie on x²+y²=1?
CORE	Find y given x on the unit circle in a named quadrant.
PROFICIENT	Show a point off the circle fails the equation.
ADVANCED	Connect cos²θ+sin²θ=1 to x²+y²=1.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. VIS-M30B-TRIG unit circle with x²+y²=1 and a point (cos θ, sin θ).

MATH30-1-TRIGONOM-03-003

Official text: Solve problems, using the six trigonometric ratios for angles expressed in radians and degrees

Worked example (unique to this hour, this strand, this SO): θ = 6π/7. Find exact sin, cos, tan if on a special ray; otherwise use the point from SO 002. Also evaluate csc, sec, cot, stating undefined cases. Repeat for 30°.

Level	Prompt (inside the home strand)
FOUNDATION	sin 30° and cos 90°.
CORE	Six ratios for a special angle in radians.
PROFICIENT	Undefined tan or cot on the unit circle.
ADVANCED	Exact ratios for a non-quadrantal angle using a point.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. Right triangle beside the unit circle; six ratios labelled.

MATH30-1-TRIGONOM-04-004

Official text: Graph and analyze the trigonometric functions sine, cosine and tangent to solve problems

Worked example (unique to this hour, this strand, this SO): Sketch y=6 sin(b(x − π/3)) + 3 for one full period. State amplitude, period, phase shift, and midline. Contrast y=tan x asymptotes - do not treat tan like a bounded sine.

Level	Prompt (inside the home strand)
FOUNDATION	Amplitude of y=2 sin x.
CORE	Full parameter list for a sine graph.
PROFICIENT	Tan asymptotes vs sine intercepts.
ADVANCED	Write an equation from a given trig graph.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. Parent y=sin x, y=cos x, y=tan x on −2π to 2π (or −360° to 360°).

MATH30-1-TRIGONOM-05-005

Official text: Solve, algebraically and graphically, first and second degree trigonometric equations with the domain expressed in degrees and radians

Worked example (unique to this hour, this strand, this SO): Solve 2 cos θ = 1 for θ ∈ [0, 2π] and in degrees on [0°, 360°]. Then solve 6 sin²θ − 3 = 0 on the same domains. Show unit-circle rays, not calculator dumps only.

Level	Prompt (inside the home strand)
FOUNDATION	Solve sin θ=0 on [0,2π].
CORE	First-degree equation in degrees and radians.
PROFICIENT	Second-degree in sin or cos with domain.
ADVANCED	Justify extraneous from a squared equation.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. Unit circle with solution rays for the equation; related graph.

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/7 + θ) using the sum identity (sin, cos, tan only). Third (double-angle): rewrite sin(2θ) if sin θ = 3/6 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.

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 001: Treating 180° as π/180 radians, or placing a negative angle clockwise from the wrong side of the initial arm. Repair: name the first wrong line, replace it, and re-complete the CORE tray item. Do not praise the wrong line.
• 30-1 SO 002: Using x²+y²=r² with r≠1 for the unit circle, or taking both signs for y without a quadrant. Repair: name the first wrong line, replace it, and re-complete the CORE tray item. Do not praise the wrong line.
• 30-1 SO 003: Writing tan θ = adjacent/opposite, or giving cos 90°=1. Repair: name the first wrong line, replace it, and re-complete the CORE tray item. Do not praise the wrong line.
• 30-1 SO 004: Calling period of sin(bx) equal to b, or drawing tan as a bounded wave. Repair: name the first wrong line, replace it, and re-complete the CORE tray item. Do not praise the wrong line.
• 30-1 SO 005: Losing solutions when dividing by a trig function, or giving only the principal calculator value. 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.

30-2 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-01-003

Official text: Interpret and assess the validity of odds and probability statements

Worked example (unique to this hour, this strand, this SO): A claim: “odds of a false positive are 1:7 so the probability is 1/7.” Convert odds a:b to P=a/(a+b). Assess validity of the original sentence.

Level	Prompt (inside the home strand)
FOUNDATION	Odds 1:1 as a fair coin in words.
CORE	Convert odds to P.
PROFICIENT	Assess a media claim.
ADVANCED	Odds against vs odds in favour.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. Odds-versus-probability two-column table.

MATH30-2-LOGICALR-02-004

Official text: Solve problems that involve the probability of mutually exclusive and non-mutually exclusive events

Worked example (unique to this hour, this strand, this SO): P(A)=6/10, P(B)=7/10, P(A∩B)=1/10. Decide mutually exclusive or not. Compute P(A∪B). Contrast a pair of events that cannot occur together.

Level	Prompt (inside the home strand)
FOUNDATION	Exclusive pair example.
CORE	P(A or B) exclusive.
PROFICIENT	Non-exclusive with overlap.
ADVANCED	Justify overlap from a story.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. Venn overlay for exclusive vs overlapping events.

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 0.9 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).

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 003: Equating odds a:b with probability a/b. Repair: name the first wrong line, replace it, and re-complete the CORE tray item. Do not praise the wrong line.
• 30-2 SO 004: Using P(A)+P(B) when events overlap. 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.

30-3 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-ALGEBRA-01-009

Official text: Solve problems that involve measures of central tendency, including: • mean • median • mode • weighted mean • trimmed mean

Worked example (unique to this hour, this strand, this SO): Chlorine residual data (mg/L): 1.5, 1.2, 1.4, 0.9, 1.3, 2.8, 1.1. Mean, median, mode. Weighted mean if two labs weight 6:7. 15% trimmed mean after ordering.

Level	Prompt (inside the home strand)
FOUNDATION	Mean of a small list.
CORE	Mean, median, mode together.
PROFICIENT	Weighted mean.
ADVANCED	Trimmed mean after ordering.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. Dot plot with mean/median/mode markers.

MATH30-3-ALGEBRA-02-010

Official text: Analyze and describe percentiles

Worked example (unique to this hour, this strand, this SO): Ordered times (min) to fill a jerry-can: eight values around 42. Find the percentile rank of 49 min and interpret (“percent of observations ≤ this value” in the school’s stated definition).

Level	Prompt (inside the home strand)
FOUNDATION	Percentile as “at or below” in words.
CORE	Percentile from an ordered list.
PROFICIENT	Interpret a percentile rank.
ADVANCED	Contrast percentile vs percent score.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. Ordered list or ogive for percentile.

MATH30-3-ALGEBRA-01-011

Official text: Analyze and interpret problems that involve probability

Worked example (unique to this hour, this strand, this SO): A poster: “There is a 90% chance the water is safe.” Critique: 90% of what? Sample size? Given P(fail)=6/100, interpret in words. Do not compute nPr as evidence for this SO.

Level	Prompt (inside the home strand)
FOUNDATION	Likely/unlikely from a given P.
CORE	Interpret a given P in the story.
PROFICIENT	Critique a claim.
ADVANCED	Sample-space talk without nPr.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. Probability-statement cards (interpret, do not run nPr).

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 009: Reporting the mean when an outlier makes the median the better centre, without comment. Repair: name the first wrong line, replace it, and re-complete the CORE tray item. Do not praise the wrong line.
• 30-3 SO 010: Treating “80th percentile” as “80% correct on a test.” Repair: name the first wrong line, replace it, and re-complete the CORE tray item. Do not praise the wrong line.
• 30-3 SO 011: Computing nPr or a 30-1 counting proof as if it were 011. 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.

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-L074.

Home strand	Primary SO	Exit ticket (unique to this lesson)
30-1	MATH30-1-TRIGONOM-01-001	CORE exit: Place 30° and the coterminal angle 390° in standard position. Convert 30° to radians: 30π/180 = simplify. Also convert 6π/7 to degrees. State the quadrant of both. FOUNDATION alternate: Convert 90° to radians. Do not submit another strand’s ticket as 30-1 mastery.
30-2	MATH30-2-LOGICALR-01-003	CORE exit: A claim: “odds of a false positive are 1:7 so the probability is 1/7.” Convert odds a:b to P=a/(a+b). Assess validity of the original sentence. FOUNDATION alternate: Odds 1:1 as a fair coin in words. Do not submit another strand’s ticket as 30-2 mastery.
30-3	MATH30-3-ALGEBRA-01-009	CORE exit: Chlorine residual data (mg/L): 1.5, 1.2, 1.4, 0.9, 1.3, 2.8, 1.1. Mean, median, mode. Weighted mean if two labs weight 6:7. 15% trimmed mean after ordering. FOUNDATION alternate: Mean of a small list. 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.