Canonical combined lesson MATH30B-L028 · week 6 day 3 · CURRICULUM_BASELINE

MATH30B-L028 - Rational functions holes vs VA; polynomial data continue; lease-to-buy

• Delivery id: MATH30B (combined classroom; not a fourth credential)
• Official courses: Mathematics 30-1 (MAT3791), 30-2 (MAT3792), 30-3 (MAT3793)
• Lesson ID: MATH30B-L028
• Calendar: Week 6 Day 3 of 18 weeks × 5 days (lesson 28 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-14-020, MATH30-2-RELATION-07-015, MATH30-3-X-02-006

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 hole vs vertical asymptote is not 30-2 contextual rational equation.

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-14-020	REQUIRED - Graph and analyze rational functions (limited to numerators and denominators that are monomials, binomials or trinomials)
30-2	MATH30-2-RELATION-07-015	REQUIRED - Represent data, using polynomial functions (of degree ≤ 3), to solve problems
30-3	MATH30-3-X-02-006	REQUIRED - Solve problems that involve the acquisition of a vehicle by: • buying • leasing • leasing to buy

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-14-020

Official text: Graph and analyze rational functions (limited to numerators and denominators that are monomials, binomials or trinomials)

Worked example (unique to this hour, this strand, this SO): Analyse y=(x²−4)/(x−2). Factor; identify the hole at x=2 vs any vertical asymptote. State horizontal behaviour and sketch with the hole marked, not as a VA.

Level	Prompt (inside the home strand)
FOUNDATION	Vertical asymptote of 1/x.
CORE	Hole vs VA on a cancelled factor.
PROFICIENT	Horizontal behaviour.
ADVANCED	Full analysis of a proper/improper rational.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. Rational graph with holes vs vertical asymptotes 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 020: Labelling a hole as a vertical asymptote after cancelling. 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-07-015

Official text: Represent data, using polynomial functions (of degree ≤ 3), to solve problems

Worked example (unique to this hour, this strand, this SO): Weekly demand looks curved: (0,12), (1,14), (2,18), (3,24). Argue for a polynomial of degree ≤3 (here quadratic-like second differences). Do not invoke 30-1 factor theorem.

Level	Prompt (inside the home strand)
FOUNDATION	Plot deg ≤3 data.
CORE	Choose quadratic vs cubic in words.
PROFICIENT	Reasonableness.
ADVANCED	Do not factor-theorem the data.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. Scatter + polynomial (deg ≤ 3) with a reasonableness comment.

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 015: Invoking the factor theorem on a scatter plot. 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-02-006

Official text: Solve problems that involve the acquisition of a vehicle by: • buying • leasing • leasing to buy

Worked example (unique to this hour, this strand, this SO): Vehicle price $22000. Buy: tax 5% + $295 fees. Lease: $295/month for 48 months + $1080 due at signing, residual $5400. Lease-to-buy: add a stated buyout. Compare total cost vs monthly cash flow. Table after retrieval.

Level	Prompt (inside the home strand)
FOUNDATION	Define buy / lease / lease-to-buy.
CORE	Total cost vs monthly.
PROFICIENT	Choose with a cash-flow condition.
ADVANCED	Interest/residual sensitivity.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. Vehicle comparison table VIS-M30B-VEH (buy / lease / lease-to-buy).

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 006: Comparing monthly payment only, ignoring down payment, residual, or term length. 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-L028.

Home strand	Primary SO	Exit ticket (unique to this lesson)
30-1	MATH30-1-TRIGONOM-14-020	CORE exit: Analyse y=(x²−4)/(x−2). Factor; identify the hole at x=2 vs any vertical asymptote. State horizontal behaviour and sketch with the hole marked, not as a VA. FOUNDATION alternate: Vertical asymptote of 1/x. Do not submit another strand’s ticket as 30-1 mastery.
30-2	MATH30-2-RELATION-07-015	CORE exit: Weekly demand looks curved: (0,12), (1,14), (2,18), (3,24). Argue for a polynomial of degree ≤3 (here quadratic-like second differences). Do not invoke 30-1 factor theorem. FOUNDATION alternate: Plot deg ≤3 data. Do not submit another strand’s ticket as 30-2 mastery.
30-3	MATH30-3-X-02-006	CORE exit: Vehicle price $22000. Buy: tax 5% + $295 fees. Lease: $295/month for 48 months + $1080 due at signing, residual $5400. Lease-to-buy: add a stated buyout. Compare total cost vs monthly cash flow. Table after retrieval. FOUNDATION alternate: Define buy / lease / lease-to-buy. 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.