Canonical combined lesson MATH30B-L027 · week 6 day 2 · CURRICULUM_BASELINE

MATH30B-L027 - Radical transforms; rational equations continue; leasing

• Delivery id: MATH30B (combined classroom; not a fourth credential)
• Official courses: Mathematics 30-1 (MAT3791), 30-2 (MAT3792), 30-3 (MAT3793)
• Lesson ID: MATH30B-L027
• Calendar: Week 6 Day 2 of 18 weeks × 5 days (lesson 27 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-13-019, MATH30-2-LOGICALR-03-011, 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)

Show the radical graph after retrieval. Vehicle lease table after retrieval, before independent 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-13-019	REQUIRED - Graph and analyze radical functions (limited to functions involving one radical)
30-2	MATH30-2-LOGICALR-03-011	REQUIRED - Solve problems that involve rational equations (limited to numerators and denominators that are monomials and binomials)
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-13-019

Official text: Graph and analyze radical functions (limited to functions involving one radical)

Worked example (unique to this hour, this strand, this SO): Graph y=√(x−4)+8. Domain x≥4. Show the translation from y=√x. Evaluate y(8) exactly.

Level	Prompt (inside the home strand)
FOUNDATION	Domain of √(x−1).
CORE	Graph a translated radical.
PROFICIENT	Match equation to graph.
ADVANCED	One radical only - reject a second nested radical.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. Radical graph with domain ray and transform from √x.

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 019: Including x-values inside the radical that make the radicand negative. 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-LOGICALR-03-011

Official text: Solve problems that involve rational equations (limited to numerators and denominators that are monomials and binomials)

Worked example (unique to this hour, this strand, this SO): Solve 8/x + 5/(x+4) = 7/(x(x+4)) with x≠0, x≠−4. Check for extraneous roots. Context option: two work rates filling a tank.

Level	Prompt (inside the home strand)
FOUNDATION	Clear a single-term rational equation.
CORE	Binomial denominators + check.
PROFICIENT	Work-rate context.
ADVANCED	Explain an extraneous root.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. Rate table that becomes a rational equation; restrictions 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):

• 30-2 SO 011: Clearing denominators then keeping a restricted x as a root. 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 $21500. Buy: tax 5% + $280 fees. Lease: $280/month for 36 months + $1070 due at signing, residual $5350. 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-L027.

Home strand	Primary SO	Exit ticket (unique to this lesson)
30-1	MATH30-1-TRIGONOM-13-019	CORE exit: Graph y=√(x−4)+8. Domain x≥4. Show the translation from y=√x. Evaluate y(8) exactly. FOUNDATION alternate: Domain of √(x−1). Do not submit another strand’s ticket as 30-1 mastery.
30-2	MATH30-2-LOGICALR-03-011	CORE exit: Solve 8/x + 5/(x+4) = 7/(x(x+4)) with x≠0, x≠−4. Check for extraneous roots. Context option: two work rates filling a tank. FOUNDATION alternate: Clear a single-term rational equation. Do not submit another strand’s ticket as 30-2 mastery.
30-3	MATH30-3-X-02-006	CORE exit: Vehicle price $21500. Buy: tax 5% + $280 fees. Lease: $280/month for 36 months + $1070 due at signing, residual $5350. 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.