Canonical combined lesson MATH30B-L036 · week 8 day 1 · CURRICULUM_BASELINE

MATH30B-L036 - Sin/cos/tan graphs; sinusoidal continue; percentile language

• Delivery id: MATH30B (combined classroom; not a fourth credential)
• Official courses: Mathematics 30-1 (MAT3791), 30-2 (MAT3792), 30-3 (MAT3793)
• Lesson ID: MATH30B-L036
• Calendar: Week 8 Day 1 of 18 weeks × 5 days (lesson 36 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-04-004, MATH30-2-RELATION-08-016, 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)

Show parent trig graphs after retrieval. Percentile is not a 30-1 trig intercept.

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-04-004	REQUIRED - Graph and analyze the trigonometric functions sine, cosine and tangent to solve problems
30-2	MATH30-2-RELATION-08-016	REQUIRED - Represent data, using sinusoidal functions, to solve problems
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-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=3 sin(b(x − π/1)) + 1 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 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-RELATION-08-016

Official text: Represent data, using sinusoidal functions, to solve problems

Worked example (unique to this hour, this strand, this SO): Tank level (m): midline 2, amplitude 1.3, period 12 months, max in month 1. Write a sinusoidal model and predict month 8. This is data modelling, not 30-1 identity proof.

Level	Prompt (inside the home strand)
FOUNDATION	Read amplitude from a graph.
CORE	Write midline/period/amp from data.
PROFICIENT	Predict a future month.
ADVANCED	Discuss a poor sine fit.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. Sine data graph: amplitude, period, midline labelled from data.

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 016: Proving a trig identity instead of fitting amplitude/period/midline. 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 40. Find the percentile rank of 46 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-L036.

Home strand	Primary SO	Exit ticket (unique to this lesson)
30-1	MATH30-1-TRIGONOM-04-004	CORE exit: Sketch y=3 sin(b(x − π/1)) + 1 for one full period. State amplitude, period, phase shift, and midline. Contrast y=tan x asymptotes - do not treat tan like a bounded sine. FOUNDATION alternate: Amplitude of y=2 sin x. Do not submit another strand’s ticket as 30-1 mastery.
30-2	MATH30-2-RELATION-08-016	CORE exit: Tank level (m): midline 2, amplitude 1.3, period 12 months, max in month 1. Write a sinusoidal model and predict month 8. This is data modelling, not 30-1 identity proof. FOUNDATION alternate: Read amplitude from a graph. 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 40. Find the percentile rank of 46 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.