Canonical combined lesson MATH30B-L032 · week 7 day 2 · CURRICULUM_BASELINE

MATH30B-L032 - Arc length and standard position; midline; mean vs median

• Delivery id: MATH30B (combined classroom; not a fourth credential)
• Official courses: Mathematics 30-1 (MAT3791), 30-2 (MAT3792), 30-3 (MAT3793)
• Lesson ID: MATH30B-L032
• Calendar: Week 7 Day 2 of 18 weeks × 5 days (lesson 32 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, MATH30-2-RELATION-08-016, MATH30-3-ALGEBRA-01-009

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)

Do not serve 30-3 sine-law items as 30-1 radian practice.

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
30-2	MATH30-2-RELATION-08-016	REQUIRED - Represent data, using sinusoidal functions, to solve problems
30-3	MATH30-3-ALGEBRA-01-009	REQUIRED - Solve problems that involve measures of central tendency, including: • mean • median • mode • weighted mean • trimmed mean

30-1 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 20° and the coterminal angle 380° in standard position. Convert 20° to radians: 20π/180 = simplify. Also convert 6π/5 to degrees. State the quadrant of both.

Level	Prompt (inside the home strand)
FOUNDATION	Convert 90° to radians.
CORE	Convert 20° 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).

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.

30-2 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 4, amplitude 1.4, period 12 months, max in month 3. 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-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): 1.3, 1.2, 1.4, 0.9, 1.3, 2.8, 1.1. Mean, median, mode. Weighted mean if two labs weight 6:5. 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.

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.

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-L032.

Home strand	Primary SO	Exit ticket (unique to this lesson)
30-1	MATH30-1-TRIGONOM-01-001	CORE exit: Place 20° and the coterminal angle 380° in standard position. Convert 20° to radians: 20π/180 = simplify. Also convert 6π/5 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-RELATION-08-016	CORE exit: Tank level (m): midline 4, amplitude 1.4, period 12 months, max in month 3. 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-01-009	CORE exit: Chlorine residual data (mg/L): 1.3, 1.2, 1.4, 0.9, 1.3, 2.8, 1.1. Mean, median, mode. Weighted mean if two labs weight 6:5. 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.