Canonical combined lesson MATH30B-L053 · week 11 day 3 · CURRICULUM_BASELINE

MATH30B-L053 - Permutations nPr; dependent events; profit or loss

• Delivery id: MATH30B (combined classroom; not a fourth credential)
• Official courses: Mathematics 30-1 (MAT3791), 30-2 (MAT3792), 30-3 (MAT3793)
• Lesson ID: MATH30B-L053
• Calendar: Week 11 Day 3 of 18 weeks × 5 days (lesson 53 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-02-022, MATH30-2-LOGICALR-03-005, MATH30-3-X-03-007

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)

Order matters for 30-1. 30-3 does not receive nPr as 007 evidence.

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-02-022	REQUIRED - Determine the number of permutations of n elements taken r at a time to solve problems
30-2	MATH30-2-LOGICALR-03-005	REQUIRED - Solve problems that involve the probability of two events
30-3	MATH30-3-X-03-007	REQUIRED - Critique the viability of small business options by considering: • expenses • sales • profit or loss

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-02-022

Official text: Determine the number of permutations of n elements taken r at a time to solve problems

Worked example (unique to this hour, this strand, this SO): Compute P(16,3) = n!/(n−r)!. Schedule 3 distinct speakers from 16 where order of speaking matters. Contrast a case with a repeated identical role (preview only if ADVANCED).

Level	Prompt (inside the home strand)
FOUNDATION	List permutations of 3 letters.
CORE	P(n,r) formula.
PROFICIENT	Restrictions (cannot be first).
ADVANCED	Identical items preview.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. Ordered-arrangement visual VIS-M30B-PERM.

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 022: Using nCr when order matters. 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-03-005

Official text: Solve problems that involve the probability of two events

Worked example (unique to this hour, this strand, this SO): Two tests in sequence. P(detect)=0.6 each if independent: find P(both) and P(at least one). Then a dependent version: second-test P changes to 0.9 if the first was positive. Use a tree.

Level	Prompt (inside the home strand)
FOUNDATION	Independent P(A and B)=P(A)P(B).
CORE	Tree with two stages.
PROFICIENT	Dependent branch.
ADVANCED	Conditional language in context.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. Tree or two-way table for two events (independent then dependent).

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 005: Multiplying for dependent events as if independent. 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-03-007

Official text: Critique the viability of small business options by considering: • expenses • sales • profit or loss

Worked example (unique to this hour, this strand, this SO): Month expenses $1960, sales $2425, so profit/loss = sales − expenses. Second scenario: sales drop 14%. Critique viability (can this hygiene kiosk continue?).

Level	Prompt (inside the home strand)
FOUNDATION	Label expense vs revenue.
CORE	Compute profit or loss.
PROFICIENT	Critique viability.
ADVANCED	Two scenarios.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. Ledger: expenses, sales, profit or loss.

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 007: Calling revenue “profit,” or ignoring a category of expense. 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-L053.

Home strand	Primary SO	Exit ticket (unique to this lesson)
30-1	MATH30-1-TRIGONOM-02-022	CORE exit: Compute P(16,3) = n!/(n−r)!. Schedule 3 distinct speakers from 16 where order of speaking matters. Contrast a case with a repeated identical role (preview only if ADVANCED). FOUNDATION alternate: List permutations of 3 letters. Do not submit another strand’s ticket as 30-1 mastery.
30-2	MATH30-2-LOGICALR-03-005	CORE exit: Two tests in sequence. P(detect)=0.6 each if independent: find P(both) and P(at least one). Then a dependent version: second-test P changes to 0.9 if the first was positive. Use a tree. FOUNDATION alternate: Independent P(A and B)=P(A)P(B). Do not submit another strand’s ticket as 30-2 mastery.
30-3	MATH30-3-X-03-007	CORE exit: Month expenses $1960, sales $2425, so profit/loss = sales − expenses. Second scenario: sales drop 14%. Critique viability (can this hygiene kiosk continue?). FOUNDATION alternate: Label expense vs revenue. 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.