Canonical combined lesson MATH30B-L017 · week 4 day 2 · CURRICULUM_BASELINE

MATH30B-L017 - Log graph features; exponential equations; sine law continue

• Delivery id: MATH30B (combined classroom; not a fourth credential)
• Official courses: Mathematics 30-1 (MAT3791), 30-2 (MAT3792), 30-3 (MAT3793)
• Lesson ID: MATH30B-L017
• Calendar: Week 4 Day 2 of 18 weeks × 5 days (lesson 17 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-09-015, 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)

Asymptotes and intercepts for 30-1; tech-checked growth solve for 30-2; AAS/ASA sine law for 30-3.

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-09-015	REQUIRED - Graph and analyze exponential and logarithmic functions
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-09-015

Official text: Graph and analyze exponential and logarithmic functions

Worked example (unique to this hour, this strand, this SO): Graph y=5^x and y=log_5 x. State intercepts, asymptotes, and domain/range. Compare to y=5^{x−2}+5.

Level	Prompt (inside the home strand)
FOUNDATION	Intercept of y=2^x.
CORE	Asymptote and domain of log.
PROFICIENT	Describe a transformed explog graph.
ADVANCED	Compare two bases on one axes.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. Exp and log graphs with intercepts, asymptotes, and end behaviour.

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 015: Drawing y=log_b x with a y-intercept of 1, or an asymptote on the y-axis forgotten. 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 1.09^t = 5 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=42°, angle B=41°, side a=14 m (AAS). Use sine law (no ambiguous case). Second item: sides 15, 17, included angle 52° - 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-L017.

Home strand	Primary SO	Exit ticket (unique to this lesson)
30-1	MATH30-1-TRIGONOM-09-015	CORE exit: Graph y=5^x and y=log_5 x. State intercepts, asymptotes, and domain/range. Compare to y=5^{x−2}+5. FOUNDATION alternate: Intercept of y=2^x. Do not submit another strand’s ticket as 30-1 mastery.
30-2	MATH30-2-RELATION-05-013	CORE exit: Solve 1.09^t = 5 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=42°, angle B=41°, side a=14 m (AAS). Use sine law (no ambiguous case). Second item: sides 15, 17, included angle 52° - 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.