Canonical combined lesson MATH30B-L047 · week 10 day 2 · CURRICULUM_BASELINE

MATH30B-L047 - Trig review: ratios and graphs; exclusive events; percentiles review

• Delivery id: MATH30B (combined classroom; not a fourth credential)
• Official courses: Mathematics 30-1 (MAT3791), 30-2 (MAT3792), 30-3 (MAT3793)
• Lesson ID: MATH30B-L047
• Calendar: Week 10 Day 2 of 18 weeks × 5 days (lesson 47 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-03-003, MATH30-1-TRIGONOM-04-004, MATH30-2-LOGICALR-02-004, MATH30-3-ALGEBRA-02-010

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)

Venn overlay for exclusive vs non-exclusive after retrieval.

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-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
30-2	MATH30-2-LOGICALR-02-004	REQUIRED - Solve problems that involve the probability of mutually exclusive and non-mutually exclusive events
30-3	MATH30-3-ALGEBRA-02-010	REQUIRED - Analyze and describe percentiles

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-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 = 7π/5. 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 55°.

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=7 sin(b(x − π/4)) + 6 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°).

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 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.

30-2 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-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)=7/10, P(B)=5/10, 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.

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 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.

30-3 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-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 51. Find the percentile rank of 47 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.

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 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.

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-L047.

Home strand	Primary SO	Exit ticket (unique to this lesson)
30-1	MATH30-1-TRIGONOM-03-003	CORE exit: θ = 7π/5. 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 55°. FOUNDATION alternate: sin 30° and cos 90°. Do not submit another strand’s ticket as 30-1 mastery.
30-2	MATH30-2-LOGICALR-02-004	CORE exit: P(A)=7/10, P(B)=5/10, P(A∩B)=1/10. Decide mutually exclusive or not. Compute P(A∪B). Contrast a pair of events that cannot occur together. FOUNDATION alternate: Exclusive pair example. Do not submit another strand’s ticket as 30-2 mastery.
30-3	MATH30-3-ALGEBRA-02-010	CORE exit: Ordered times (min) to fill a jerry-can: eight values around 51. Find the percentile rank of 47 min and interpret (“percent of observations ≤ this value” in the school’s stated definition). FOUNDATION alternate: Percentile as “at or below” in words. 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.