Canonical combined lesson MATH30B-L080 · week 16 day 5 · CURRICULUM_BASELINE

MATH30B-L080 - Reteach: combinatorics; FCP/nPr/nCr/017; linear/puzzles

• Delivery id: MATH30B (combined classroom; not a fourth credential)
• Official courses: Mathematics 30-1 (MAT3791), 30-2 (MAT3792), 30-3 (MAT3793)
• Lesson ID: MATH30B-L080
• Calendar: Week 16 Day 5 of 18 weeks × 5 days (lesson 80 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-01-021, MATH30-1-TRIGONOM-02-022, MATH30-1-TRIGONOM-03-023, MATH30-1-TRIGONOM-04-024, MATH30-2-LOGICALR-04-006, MATH30-2-LOGICALR-05-007, MATH30-2-LOGICALR-06-008, MATH30-2-MATHEMAT-01-017, MATH30-3-X-01-005, 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)

No silent strand switch as a “easier reteach.”

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-01-021	REQUIRED - Apply the fundamental counting principle to solve problems
30-1	MATH30-1-TRIGONOM-02-022	REQUIRED - Determine the number of permutations of n elements taken r at a time to solve problems
30-1	MATH30-1-TRIGONOM-03-023	REQUIRED - Determine the number of combinations of n different elements taken r at a time to solve problems
30-1	MATH30-1-TRIGONOM-04-024	REQUIRED - Expand powers of a binomial in a variety of ways, including using the binomial theorem (restricted to exponents that are natural numbers)
30-2	MATH30-2-LOGICALR-04-006	REQUIRED - Solve problems that involve the fundamental counting principle
30-2	MATH30-2-LOGICALR-05-007	REQUIRED - Solve problems that involve permutations
30-2	MATH30-2-LOGICALR-06-008	REQUIRED - Solve problems that involve combinations
30-2	MATH30-2-MATHEMAT-01-017	REQUIRED - Research and give a presentation on a current event or an area of interest that involves mathematics
30-3	MATH30-3-X-01-005	REQUIRED - Analyze puzzles and games that involve logical reasoning, using problem-solving strategies
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-01-021

Official text: Apply the fundamental counting principle to solve problems

Worked example (unique to this hour, this strand, this SO): A lock uses 5 digits (0-9) then 3 letters (26). Count codes if repetition is allowed, then if digits cannot repeat. Add a restriction: first digit not 0.

Level	Prompt (inside the home strand)
FOUNDATION	Two-stage menu count.
CORE	Multi-stage FCP.
PROFICIENT	FCP with a restriction.
ADVANCED	Justify an overcount.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. Tree diagram VIS-M30B-FCP.

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(16,2) = n!/(n−r)!. Schedule 2 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.

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(16,2). Choose 2 test kits from 16 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.

MATH30-1-TRIGONOM-04-024

Official text: Expand powers of a binomial in a variety of ways, including using the binomial theorem (restricted to exponents that are natural numbers)

Worked example (unique to this hour, this strand, this SO): Expand (x+5)^5 using the binomial theorem (natural exponent). Give the general term and the term containing x^3.

Level	Prompt (inside the home strand)
FOUNDATION	(x+1)² by Pascal.
CORE	Full expansion natural n.
PROFICIENT	General term.
ADVANCED	Coefficient of a named power.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. Pascal row / binomial expansion aligned to coefficients.

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 021: Adding choices instead of multiplying stages. Repair: name the first wrong line, replace it, and re-complete the CORE tray item. Do not praise the wrong line.
• 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.
• 30-1 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.
• 30-1 SO 024: Writing binomial coefficients as n+r or expanding with subtraction signs ignored. 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-04-006

Official text: Solve problems that involve the fundamental counting principle

Worked example (unique to this hour, this strand, this SO): Outfit a sample kit: 5 bottle types × 3 labels × 6 cap colours. Count with FCP. Then forbid one labelled combination and recount.

Level	Prompt (inside the home strand)
FOUNDATION	Two-stage FCP.
CORE	Three-stage kit count.
PROFICIENT	Forbidden combo.
ADVANCED	Explain FCP vs listing.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. Tree diagrams VIS-M30B-FCP in a chance context.

MATH30-2-LOGICALR-05-007

Official text: Solve problems that involve permutations

Worked example (unique to this hour, this strand, this SO): Arrange 2 distinct volunteer shifts from 16 people (order matters). Compute nPr. List if n is small. One restriction: a named person cannot be first.

Level	Prompt (inside the home strand)
FOUNDATION	List orders of 3 people.
CORE	nPr in context.
PROFICIENT	Light restriction.
ADVANCED	Optional identical-order stretch.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. Ordered lists then nPr formula card.

MATH30-2-LOGICALR-06-008

Official text: Solve problems that involve combinations

Worked example (unique to this hour, this strand, this SO): Choose 2 people from 16 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.

MATH30-2-MATHEMAT-01-017

Official text: Research and give a presentation on a current event or an area of interest that involves mathematics

Worked example (unique to this hour, this strand, this SO): Research question (30-2 only): “How does a published article use mathematics in a current water or hygiene issue?” Required product: question, two sources, one model or calculation, and a limits sentence. Do not tick this SO for 30-1 or 30-3.

Level	Prompt (inside the home strand)
FOUNDATION	Write a research question.
CORE	Math in the story named.
PROFICIENT	Sources + model.
ADVANCED	Limits of the model.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. Project board: question, sources, model, limits - 30-2 only.

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 006: Listing a few outcomes and treating the list as complete. Repair: name the first wrong line, replace it, and re-complete the CORE tray item. Do not praise the wrong line.
• 30-2 SO 007: Using nCr for an ordered schedule. Repair: name the first wrong line, replace it, and re-complete the CORE tray item. Do not praise the wrong line.
• 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.
• 30-2 SO 017: A poster with no mathematics, or copying a news claim with no sources. 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-01-005

Official text: Analyze puzzles and games that involve logical reasoning, using problem-solving strategies

Worked example (unique to this hour, this strand, this SO): Logic grid: three pumps and three flow rates including 5 L/min. Use elimination. Name the strategy. This is 30-3 005, not 30-2 001 mastery for 30-3 learners (they own 005).

Level	Prompt (inside the home strand)
FOUNDATION	Attempt with hints.
CORE	Solve and name strategy.
PROFICIENT	Transfer.
ADVANCED	Create a variant.

Diagram: Timing: after retrieval, before independent practice. Do not open the diagram during the first retrieval prompt. Logic-puzzle card (30-3 wording, not 30-1 diploma).

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 005: Random guessing with no elimination trail. Repair: name the first wrong line, replace it, and re-complete the CORE tray item. Do not praise the wrong line.
• 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.
• 30-1 and 30-3 do strand tasks during 017 hour. Do not mark 017 complete for them.

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-L080.

Home strand	Primary SO	Exit ticket (unique to this lesson)
30-1	MATH30-1-TRIGONOM-01-021	CORE exit: A lock uses 5 digits (0-9) then 3 letters (26). Count codes if repetition is allowed, then if digits cannot repeat. Add a restriction: first digit not 0. FOUNDATION alternate: Two-stage menu count. Do not submit another strand’s ticket as 30-1 mastery.
30-2	MATH30-2-LOGICALR-04-006	CORE exit: Outfit a sample kit: 5 bottle types × 3 labels × 6 cap colours. Count with FCP. Then forbid one labelled combination and recount. FOUNDATION alternate: Two-stage FCP. Do not submit another strand’s ticket as 30-2 mastery.
30-3	MATH30-3-X-01-005	CORE exit: Logic grid: three pumps and three flow rates including 5 L/min. Use elimination. Name the strategy. This is 30-3 005, not 30-2 001 mastery for 30-3 learners (they own 005). FOUNDATION alternate: Attempt with hints. 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.