Canonical combined lesson MATH30B-L018 · week 4 day 3 · CURRICULUM_BASELINE

MATH30B-L018 - Exp/log equations exact-first; data fit; cosine law SSS

• Delivery id: MATH30B (combined classroom; not a fourth credential)
• Official courses: Mathematics 30-1 (MAT3791), 30-2 (MAT3792), 30-3 (MAT3793)
• Lesson ID: MATH30B-L018
• Calendar: Week 4 Day 3 of 18 weeks × 5 days (lesson 18 of 90)
• Object type: canonical combined-classroom lesson
• Braid class: B
• 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-10-016, MATH30-2-RELATION-05-013, 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)

30-1 exact then technology. 30-2 context solve. 30-3 cosine law (no ambiguous case).

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-10-016	REQUIRED - Solve problems that involve exponential and logarithmic equations
30-2	MATH30-2-RELATION-05-013	REQUIRED - Solve problems that involve exponential equations
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-10-016

Official text: Solve problems that involve exponential and logarithmic equations

Worked example (unique to this hour, this strand, this SO): Solve 6^x = 4 exactly (x=log_6 4) then a decimal check. Solve log_6(x−3)+log_6 x = log_6 4 with domain x>3 (and x>0). Reject extraneous roots.

Level	Prompt (inside the home strand)
FOUNDATION	Solve 2^x=8.
CORE	Exact then tech check.
PROFICIENT	Log equation with domain.
ADVANCED	Extraneous root rejected.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. Equation-graph link: intersection of y=b^x and y=k.

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 016: Exponentiating only one side, or keeping an extraneous root from a log domain. 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-05-013

Official text: Solve problems that involve exponential equations

Worked example (unique to this hour, this strand, this SO): Solve 1.04^t = 3 using logs or tech after a table guess. State what the solution means for the water-enterprise users and one model limit.

Level	Prompt (inside the home strand)
FOUNDATION	Guess-check table for a^t=k.
CORE	Log or tech solve.
PROFICIENT	Model limits.
ADVANCED	Compare two growth models.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. Table-to-equation growth model.

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 013: Reporting a negative time without checking the model. 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=43°, angle B=42°, side a=15 m (AAS). Use sine law (no ambiguous case). Second item: sides 16, 18, included angle 53° - 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.

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-L018.

Home strand	Primary SO	Exit ticket (unique to this lesson)
30-1	MATH30-1-TRIGONOM-10-016	CORE exit: Solve 6^x = 4 exactly (x=log_6 4) then a decimal check. Solve log_6(x−3)+log_6 x = log_6 4 with domain x>3 (and x>0). Reject extraneous roots. FOUNDATION alternate: Solve 2^x=8. Do not submit another strand’s ticket as 30-1 mastery.
30-2	MATH30-2-RELATION-05-013	CORE exit: Solve 1.04^t = 3 using logs or tech after a table guess. State what the solution means for the water-enterprise users and one model limit. FOUNDATION alternate: Guess-check table for a^t=k. Do not submit another strand’s ticket as 30-2 mastery.
30-3	MATH30-3-X-01-002	CORE exit: Triangle: angle A=43°, angle B=42°, side a=15 m (AAS). Use sine law (no ambiguous case). Second item: sides 16, 18, included angle 53° - 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.