Canonical combined lesson MATH30B-L019 · week 4 day 4 · CURRICULUM_BASELINE

MATH30B-L019 - Mixed exp/log equations; represent exp/log data; cosine law SAS

• Delivery id: MATH30B (combined classroom; not a fourth credential)
• Official courses: Mathematics 30-1 (MAT3791), 30-2 (MAT3792), 30-3 (MAT3793)
• Lesson ID: MATH30B-L019
• Calendar: Week 4 Day 4 of 18 weeks × 5 days (lesson 19 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-06-014, 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)

Same water-user table can feed 30-2 modelling and a 30-1 equation, but success criteria stay on home SOs.

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-06-014	REQUIRED - Represent data, using exponential and logarithmic functions, to solve problems
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 7^x = 5 exactly (x=log_7 5) then a decimal check. Solve log_7(x−4)+log_7 x = log_7 5 with domain x>4 (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-06-014

Official text: Represent data, using exponential and logarithmic functions, to solve problems

Worked example (unique to this hour, this strand, this SO): Given points (0,17), (1,17), (2,18), choose exponential vs linear and write a model in words plus an equation. Residual: one point off by 7.

Level	Prompt (inside the home strand)
FOUNDATION	Table to graph.
CORE	Choose exp vs linear.
PROFICIENT	Fit language.
ADVANCED	Residual talk.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. Scatter + exponential/log model VIS-M30B-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 014: Forcing a linear model on clearly exponential data. 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=44°, angle B=43°, side a=16 m (AAS). Use sine law (no ambiguous case). Second item: sides 17, 19, included angle 54° - 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 (Sustainable Community Water & Hygiene) - genuine math only: 30-1: users, rates, or sampling paths - composition, logs, or FCP/nPr as today’s SO requires. 30-2: model users, kits, or committees with today’s relation/counting SO. 30-3: site layout, vehicle if the enterprise needs one, ledger, linear fill-rate, or measurement of volume/chlorine - matching today’s SO.

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-L019.

Home strand	Primary SO	Exit ticket (unique to this lesson)
30-1	MATH30-1-TRIGONOM-10-016	CORE exit: Solve 7^x = 5 exactly (x=log_7 5) then a decimal check. Solve log_7(x−4)+log_7 x = log_7 5 with domain x>4 (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-06-014	CORE exit: Given points (0,17), (1,17), (2,18), choose exponential vs linear and write a model in words plus an equation. Residual: one point off by 7. FOUNDATION alternate: Table to graph. Do not submit another strand’s ticket as 30-2 mastery.
30-3	MATH30-3-X-01-002	CORE exit: Triangle: angle A=44°, angle B=43°, side a=16 m (AAS). Use sine law (no ambiguous case). Second item: sides 17, 19, included angle 54° - 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.