Canonical combined lesson MATH30B-L059 · week 12 day 4 · CURRICULUM_BASELINE

MATH30B-L059 - Mixed combination problems; nCr vs nPr choice; linear applied

• Delivery id: MATH30B (combined classroom; not a fourth credential)
• Official courses: Mathematics 30-1 (MAT3791), 30-2 (MAT3792), 30-3 (MAT3793)
• Lesson ID: MATH30B-L059
• Calendar: Week 12 Day 4 of 18 weeks × 5 days (lesson 59 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-03-023, MATH30-2-LOGICALR-06-008, MATH30-3-ALGEBRA-01-008

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)

Interpolate a linear cost model (30-3) while 30-1 counts subsets.

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-03-023	REQUIRED - Determine the number of combinations of n different elements taken r at a time to solve problems
30-2	MATH30-2-LOGICALR-06-008	REQUIRED - Solve problems that involve combinations
30-3	MATH30-3-ALGEBRA-01-008	REQUIRED - Demonstrate an understanding of linear relations by: • recognizing patterns and trends • graphing • creating tables of values • writing equations • interpolating and extrapolating

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-03-023

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

Worked example (unique to this hour, this strand, this SO): Compute C(13,5). Choose 5 test kits from 13 where order does not matter. Show C(n,r)=P(n,r)/r! and why dividing by r! is required.

Level	Prompt (inside the home strand)
FOUNDATION	List combinations of 3 from 4.
CORE	C(n,r) formula.
PROFICIENT	Choose nCr vs nPr.
ADVANCED	Restriction on a committee.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. Unordered-subset visual (nCr) distinct from nPr.

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 023: Using nPr when order does not matter. 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-06-008

Official text: Solve problems that involve combinations

Worked example (unique to this hour, this strand, this SO): Choose 5 people from 13 for a water-test committee (order does not matter). Compute nCr. Write one sentence on why this is not nPr.

Level	Prompt (inside the home strand)
FOUNDATION	List committees of 2 from 4.
CORE	nCr in context.
PROFICIENT	Choose nCr vs nPr.
ADVANCED	Optional harder restriction.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. Committee diagram: order does not matter.

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 008: Using nPr for an unordered committee. 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-ALGEBRA-01-008

Official text: Demonstrate an understanding of linear relations by: • recognizing patterns and trends • graphing • creating tables of values • writing equations • interpolating and extrapolating • solving problems

Worked example (unique to this hour, this strand, this SO): Table: hours 0, 1, 2, 3 vs litres treated 0, 17, 34, 51. Graph, write litres = (rate)(hours), interpolate at 1.5 h, extrapolate to 5 h with a caution.

Level	Prompt (inside the home strand)
FOUNDATION	Complete a table.
CORE	Graph + equation.
PROFICIENT	Interpolate.
ADVANCED	Extrapolate with caution.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. VIS-M30B-LINEAR: table, graph, equation together.

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 008: Extrapolating far beyond the table with no caution. 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: 30-2: 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-L059.

Home strand	Primary SO	Exit ticket (unique to this lesson)
30-1	MATH30-1-TRIGONOM-03-023	CORE exit: Compute C(13,5). Choose 5 test kits from 13 where order does not matter. Show C(n,r)=P(n,r)/r! and why dividing by r! is required. FOUNDATION alternate: List combinations of 3 from 4. Do not submit another strand’s ticket as 30-1 mastery.
30-2	MATH30-2-LOGICALR-06-008	CORE exit: Choose 5 people from 13 for a water-test committee (order does not matter). Compute nCr. Write one sentence on why this is not nPr. FOUNDATION alternate: List committees of 2 from 4. Do not submit another strand’s ticket as 30-2 mastery.
30-3	MATH30-3-ALGEBRA-01-008	CORE exit: Table: hours 0, 1, 2, 3 vs litres treated 0, 17, 34, 51. Graph, write litres = (rate)(hours), interpolate at 1.5 h, extrapolate to 5 h with a caution. FOUNDATION alternate: Complete a table. 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.